fusion

Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain John Lindi Lawrence Livermore National Laboratory, Livermore, California 94551 (Received 14 November 1994; accepted 14 June 1995) Inertial confinement fusion (ICF) is an approach to fusion that relies on the inertia of the fuel mass to provide confinement. To achieve conditions under which inertial confinement is sufficient for efficient thermonuclear burn, a capsule (generally a spherical shell) containing thermonuclear fuel is compressed in an implosion process to conditions of high density and temperature. ICF capsules rely on either electron conduction (direct drive) or x rays (indirect drive) for energy transport to drive an implosion. In direct drive, the laser beams [or charged particle beams) are aimed directly at a target. The laser energy is transferred to electrons by means of inverse bremsstrahlung or a variety of plasma collective processes. In indirect drive, the driver energy (from laser beams or ion beams) is first absorbed in a high-2 enclosure (a hohlraum), which surrounds the capsule. The material heated by the driver emits x rays, which drive the capsule implosion. For optimally designed targets, 70%-80% of the driver energy can be converted to x rays. The optimal hohlraum geometry depends on the driver. Because of relaxed requirements on laser beam uniformity, and reduced sensitivity to hydrodynamic instabilities, the U.S. ICF Program has concentrated most of its effort since 1976 on the x-ray or indirect-drive approach to ICE As a result of years of experiments and modeling, we are building an increasingly strong case for achieving ignition by indirect drive on the proposed National Ignition Facility (NIF). The ignition target requirements for hohlraum energetics, radiation symmetry, hydrodynamic instabilities and mix, laser plasma interaction, pulse shaping, and ignition requirements are all consistent with experiments. The NIF laser design, at 1.8 MJ and 500 TW, has the margin to cover uncertainties in the baseline ignition targets. In addition, data from the NIF will provide a solid database for ion-beam-driven hohlraums being considered for future energy applications. In this paper we analyze the requirements for indirect drive ICF and review the theoretical and experimental basis for these requirements. Although significant parts of the discussion apply to both direct and indirect drive, the principal focus is on indirect drive. 0 1995 American Institute of Physics. TABLE OF CONTENTS I. ICF OVERVIEW .......................... 3933 II. HISTORICAL DEVELOPMENT OF INDIRECT DRIVE IN THE U.S. ICF PROGRAM .............................. 3940 III. IGNITION PHYSICS. ..................... 3952 IV. PULSE SHAPING ......................... 3955 V. IMPLOSION DYNAMICS. ................. 3958 VI. HYDRODYNAMIC INSTABILITY ........... 3961 VII. CAPSULE GAIN .......................... 3969 VIII. Ix. X. XI. IXII. XIII. XIV. HOHLRAUM COUPLING EFFICIENCY. . . . . 3969 HOHLRAUM RADIATION UNIFORMITY.. . . 3979 COMBINED TESTS OF SYMMETRY AND HYDRODYNAMIC INSTABILITY. . . . . . . . . . 3992 HOHLRAUM PLASMA CONDITIONS. . . . . . . 3994 HOT ELECTRON PREHEAT. . . . . . . . . . . . . . . 4002 NATIONAL IGNITION FACILITY AND IGNITION TARGETS. . . . . . . . . . . . . . . . . . . . . 4004 INERTIAL FUSION ENERGY. . . . . . . . . . . . . . 4015 I. ICF OVERVIEW Inertial confinement fusion (ICF) is an approach to fu- sion that relies on the inertia of the fuel mass to provide confinement. l-3 To achieve conditions under which inertial confinement is sufficient for efficient thermonuclear burn, high-gain ICF targets have features similar to those shown in Fig. 1. A capsule generally is a spherica shell filled with low-density gas (s1.0 mg/cm3). The shell is composed of an outer re- gion, which forms the ablator, and an inner region of frozen or liquid deuterium-tritium (DT), which forms the main fuel. As shown in Fig. 2, the cross section4 for DT fusion reactions is approximately two orders of magnitude larger than that for the next largest reaction in the relevant tempera- ture range, up to about 40 keV. Hence, ignition and high-gain targets planned for the near term use DT fuel. Many of the near-term targets discussed later, which only use neutrons for diagnostic purposes, contain deuterium-deuterium (DD) fuel. Energy from a driver is delivered rapidly to the ablator, which heats up and expands. As the ablator expands outward, Phys. Plasmas 2 (ll), November 1995 1070-664X/95/2(1 1)/3933/92/$6.00 Q 1995 American Institute of Physics 3933 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Drive L Capsule ablator ensrgy 3 i r.;-.. K Main K VI’,, \ fuel layer Driver-target coupling 3 I, 51 Oi5 W/cm2 or 5300 eV To control: l Absorption/preheat . X-ray conversion l Transport/drive I ~~~~~~~~ 2 =Conv;;rce = 20-35 j ,c”I”;~,9yo L I L I 1 8 Stability: _L = in-filght L 25-35 =+ $ Z 4 x 1O”‘W/Cm* Or AR aspect ratfo 250eV surface cl000 ii ignition: l Ti = ltj kev l prHs - 0.3 gtcm * 4m,3-4x107cIn/s for Eddvar = 1-2 MJ FIG. 1. The target physics specifications on current ICF ignition targets include constraints on drive intensity, symmetry, stability, and ignition. the rest of the shell is forced inward to conserve momentum. The capsule behaves as a spherical, ablation-driven rocket. The efficiency with which the fusion fuel is imploded typi- cally lies in the range of 5%-15%. The work that can be done on the imploding fuel is the product of the pressure generated by the ablation process times the volume enclosed by the shell. Hence, for a given pressure, a larger, thinner shell that encloses more volume can be accelerated to a higher velocity than can a thicker shell of the same mass. The peak achievable implosion velocity determines the mini- mum energy (and mass) required for ignition of the fusion fuel in the shell. In its final configuration, the fuel is nearly isobaric at pressures up to -200 Gbars but consists of two effectively distinct regions-a central hot spot. containing -2%-5% of the fuel and a dense main fuel region comprising the remain- ing mass. Fusion initiates in this central region, and a ther- monuclear burn front propagates radially outward into the main fuel, producing high gain. The efficient assembly of the fuel into this configuration places stringent requirements on IO-= 100 IO’ 102 ld Tempetature (keV) FIG. 2. Thermonuclear reaction rates are strongly temperature dependent, and DT is by far the easiest fuel to ignite. 3934 Phys. Plasmas, Vol. 2, No. 11, November 1995 the details of the driver coupling, including the time history of the irradiance and the hydrodynamics of the implosion In the implosion process, several features are important. The in-flight aspect ratio (IFAR) is defined as the ratio of the shell radius R as it implodes to its thickness AR, which is less than the initial thickness because the shell is compressed as it implodes. Hydrodynamic instabilities,5 similar to the classical Rayleigh-Taylor (RT) fluid instability, impose an upper limit on this ratio, which results in a minimum pres- sure or absorbed driver h-radiance. For 25<IFAR<35, peak values are - 100 Mbars and --lot5 W/cm2 for megajoule- scale drivers. These minimum values depend on the required implosion velocity, which is determined by the capsule size. Minimum velocities are in the range of 3-4X107 cm/s for megajoule scale lasers. Control of RT-induced mix of hot and cold fuel is crucial to the successful formation of the central hot spot. The convergence ratio C, as defined in Fig. 1 is the ratio of the initial outer radius of the ablator to the final com- pressed radius of the hot spot. Typical convergence ratios to the hot spot for an ignition or high-gain target design are 30-40. If a target with an initial radius RA and average ac- celeration g has a location on its surface with acceleration perturbation Sg, then the deviation from sphericity as it im- plodes is given by cTR=~& t2=:r(Cr--1). An asymmetric implosion will convert less of the available kinetic energy into compression and heating of the fuel. The tolerable degree of asymmetry depends on the excess of available kinetic energy above the ignition threshold, which is discussed later. If we require that this deviation 6R be less than r/4, where r is the final compressed radius, we have sg &I 1 -e-----< g u 4(C,-I)’ Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp TABLE I. Total energy released will determine energy output, but only charged-particle energy is available for self-ignition of ICF-size capsules. E (MeV) E* (MeV) (charged particle) Energy/ firam D+T-+He4(3.52 MeV)+n(14.06 MeV) D+D-+He3(0.82)+n(2.45 MeV) D+D+T(l.Ol MeV)+p(3.03 MeV) D+He3-+He4(3.67 MeV)+p(14.67 MeV) T+TtHe4+n+n 17.58 3.52 3.39x 10” 3.6 2.4 8.67X 10’” 18.34 18.34 3.53x10” Il.32 1.82X 10” where u is the implosion velocity. Since 3OGC,440 is typi- cal, we require accelerations and velocities that are uniform to about 1%. The fuel conditions that must be achieved for efficient burn and a high yield relative to the driver energy can be obtained readily from an analysis of the bum of an inertially confined fuel mass. The number of thermonuclear reactions n per second is given by where (au) is the reaction cross section averaged over a Maxwellian distribution of particles, and for an equimolar DT mixture, where Nais the initial total number density. If we define the burn fraction by +=2nlNo, then we have 4 No ~=-+1-+)2(ou). If we assume that the Maxwell averaged cross section is nearly constant over the burn duration, then we can integrate this equation to obtain -=--2C&), 4 l-4 2 (6) where G- is the confinement time. In inertial confinement, burn of an ignited fuel mass typically is quenched by hydro- dynamic expansion. (For a capsule below the ignition thresh- old, such as those on Nova, electron conduction usually cools the fuel before hydroexpansion occurs, as discussed in Sec. III.) From the outside of the fuel, a rarefaction moves inward at the speed of sound, C,. By the time this rarefac- tion has moved a fraction of the radius Y, the fuel density in most of the fuel mass has dropped significantly, and the fuel no longer burns efficiently. If we choose r 7-- 3’ (7) which would allow time for a rarefaction wave to propagate across the dense main fuel layer in Fig. 1, we can write the burn efficiency as &=,(m) &. s Phys. Plasmas, Vol. 2, No. 11, November 1995 For DT between 20 and 40 keV, which is typical of the burn of ICF capsules, the ratio of the cross section to the sound speed is nearly constant, and we have approximately (p= pr Nor Pr+6(g/cm2) M N,~+5x10*5(s/cm3j’ (9) where we have related number density No to the mass den- sity p by /Vo=6.02x1023 +2.4X10z3, for DT. (10) Equation (9) compares well with detailed numerical simula- tions of most high-gain ICF targets.6Y7 We need pr=3 g/cm2 for a 33% burnup. As indicated in Eq. (9j, the pr require- ment for ICF is equivalent to the Nr requirement generally quoted for magnetic fusion energy (MEE) plasmas. The fac- tor of 5 X 1 Or5 in the Nr formula uses the DT cross section at 20 keV. At 40 keV, the factor becomes 3X 1015. We can use this burn efficiency formula to compare the fusion burn re- quirements of MFE with those of ICF. Both ICF and MFE refer to “ignition” of the plasma, but ignition has different meanings for these two approaches to fusion. In MFE, which requires steady-state or near steady-state operation for most energy production approaches, ignition is defined in terms of power balance. In this approach, ignition occurs when energy deposition from thermonuclear bum products during one energy confinement time equals the en- ergy required to heat the plasma to thermonuclear bum tem- peratures. When this occurs in steady state, the plasma can sustain itself indefinitely with no external heating. The energy per gram required to heat a DT plasma is given by E DT heating =0.1152X 109T (J/g)=2.3X10y (J/g), at 20 keV. with T,=Ti, (11) where T, is electron temperature and Ti is ion temperature. The thermonuclear burn products and energy content of vari- ous thermonuclear fuels is given in Table I. In general, only the charged-particle reaction products are available to heat the fuel since most of the neutrons escape the plasma without interacting. For DT, the alpha particle energy (E,=3.5 meV) from the reaction is about 20% of the total energy produced. If we assume that all of the alphas are deposited, then the energy per gram deposited in the fuel is given by Review Article 3935 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 6.68X 10’Onr E them~onuclear a particle= n T+ 5 x 10 I5 (Jk) t at 20 keV. ( 2) If we set EDT heating=Ethermonuclear a particle in this simple model, ignition occurs for n7>1.7X lOI or pr=0.21 and corresponds to a bum efficiency of about 3.4%. Ignition in this sense is adequate for a MFE plasma if the energy required to maintain the magnetic confinement is much less than the energy to heat the plasma. Since the magnetic-field energy is much greater than the plasma en- ergy in magnetic confinement devices, it is generally as- sumed that superconducting magnets would be used to mini- mize the dissipation of magnetic field energy. As a measure of the fusion power performance for a MFE device, the fusion power gain is defined by Q = Pf/ Pi , where Pf is the fusion power and Pi is the input power. The fusion power is given by and the input power is given by dV- f Pf, where the integrals are over the plasma volume, E,=3.34X lO”J/g is the energy per gram produced by DT fusion reactions, and EDT heat& is the heat capacity of DT from Eq. (11). In Eq. (14), one-fifth of Pf , which is all of the a-particle energy, is assumed to be deposited in the plasma. The energy confinement time 7s characterizes the rate at which energy is lost from the plasma by cross-field transport and radiation. Ignition occurs when P,=O.O or when Q =m. An actual MFE reactor would run somewhat below the igni- tion limit, to maintain a stable operating regime, so that a Q-20 is desirable.’ Recent experiments’ with DT plasmas have achieved Q = a. In ICF, which is inherently pulsed, ignition occurs when energy production and LY deposition from the central hot spot are sufficient to initiate a self-sustaining bum wave that propagates into the surrounding main fuel. To compensate for driver and implosion inefficiencies, ICF targets must have a high bum efficiency, and most of the fuel must be heated by the burn wave propagating outward from the hot spot. Target gain, defined as the ratio of thermonuclear energy produced to driver energy on target,is the closest equivalent to Q in MFR. A described in Sec. XIV, energy production in ICF requires target gains high enough that the product of gain times driver efficiency is -10. Depending on driver efficiency, target gains of 30-100 or more are required to satisfy this condition. Compression of the DT fuel mass makes it feasible, in the laboratory, to achieve the pr =3 g/cm2 necessary for a burn efficiency of 4, about a factor of 10 higher bum effi- ciency than for an ignited MFE plasma. For a sphere, we have Specific energy vs density for cold DT Ideal Fermi fluid Realistic equation of State implosion I I I 1 IO’ TO2 103 104 Density (gkm3} FIG. 3. For densities of interest to ICF, Fermi-degenerate compression fe- quires much less energy than does ignition. (15) Hence, the mass (and also driver energy at fixed coupling efficiency) required for pr =3 g/cm2 scales as l/p’. At a nor- mal liquid density of 0.21 g/cm3, more than 2.5 kg of DT is required. If this much mass were ignited, it would yield about 3X 10’” J or 7Okt. On the other hand, at a density of 400 g/cm3, a spherical shell with a thickness r/2 and radius r would have pr=3 with a mass of 5 mg. This mass would have a yield of about 6X IO8 J and is readily contained. At five to six pulses per second, such targets could drive a 1 GW reactor for power production. As shown in Fig. 3, if the DT remains nearly Fermi degenerate during compression, then compression is eco- nomical because the energy required for compression is small compared to that required for ignition of the same mass of fuel, The Fermi compression energy can be obtained from a simple estimate. Every Fermi particle occupies a phase space volume of h3. Then N particles in a volume V must occupy a phase space volume given by 4rr d3x d3p =(2s+ I) V 3 P;=Nh3. WI The sum is over spin states that are 2 for spin s = f particles. The Fermi energy is defined by ef= Pf2/2m, where Pf is the momentum of the highest energy particle or = 14p2’3(glcm3). (17) The average energy per particle is just 0,6ef, and the specific energy per gram of DT, em, is given by eor(J/g)=3 X 105p2”3(g/cm3). (1% When there is a finite temperature, Eq. (18) becomes” Eor=3X 105p2’3 1 i-0.02 [ ( T$2)] (19) Equation (19) shows that the temperature of DT at a density of 1 g/cm3 must remain below a few electron volts, or the finite temperature corrections start becoming significant. Equations (18) and (19) ignore ion contributions and mo- 3936 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp lecular effects that affect the real equation of state for DT. Equation (18) is plotted in Fig. 3 for comparison with the specific energy from a more accurate equation of state, such as that given in the Sesame Tables.” Although compression is energetically attractive and re- duces the driver size required for efficient burn, high gain also requires hot-spot ignition. For example, it takes 6.5 X IO4 J to compress 5 mg to 400 g/cm3. But to heat that mass to 5 keV would require about 3 X IO6 J. If the implosion had an overall efficiency of 5%, the driver size would have to be about 6X lo7 J. This is near the upper limit of what could be considered for a laboratory driver, yet the target gain for a burn efficiency of f would be only 10. On the other hand, if the target can be ignited from a central hot spot containing about 2% of the total mass, then the energy required to heat this mass would be only about 6X 10” J. The total energy invested in compression and ignition would be about 1.25X 10” J (2.5X IO7 J/g), the driver size would be 2.5X lo6 J, and the gain would be greater than 200. Depending on the driver efficiency, target gains of 30-100 generally are re- quired for most ICF applications. The hot spot forms during compression from material at the center of the fuel, which is on a high isentrope. The hot-spot temperature will increase as long as the energy gained due to the PdV work done by the imploding main fuel material and charged-particle energy deposition exceed energy lost due to radiation and electron thermal conduction,” as described in Sec. III. Once ignition occurs, heating of the surrounding main fuel layer from elec- tron conduction and a-particle deposition results in a ther- monuclear burn wave that propagates outward into the main fuel layer. The typical configuration of the compressed fuel at ignition is shown in Fig. 1. For effective self-heating, the hot spot pr must exceed the a-particle range. The range energy relationship for cr particlesi is approximated by Fraley14 as where the first term is the interaction with electrons and the second term is the interaction with ions. Here V=EJ3.5 MeV and po=0.25 g/cm3 is the density of solid DT. Figure 4(a) is a plot of the a-particle range as a function of T, (keV) at various densities. At low temperature, most of the a-particle energy is deposited into the electrons, as shown in Fig. 4(b). For solid-density DT, most of the energy goes into the electrons below a temperature of about 32 keV Fraley et al. find that the &-particle range pXo (g/cm2) in solid- density DT can be approximated by p&&/cm’)= 1.5x10-‘T,5’4 1+8.2x10-3T;‘4’ (21) where the electron temperature T, is in keV. At 10 keV, for typical hot-spot densities of IO-100 g/cm3, the a particles have a range of about 0.3 g/cm’. As discussed in Sec. III; a 10-z I IO 111rr , I,,,,, 1 1 $f!“) 102 ‘” 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.9 4 (fraction of CL energy into ions) FIG. 4. Efficient alpha capture requires prwO.3 g/cm”. (a) Alpha-particle range pX, vs T, ; (b) alpha-energy absorption. hot spot at a temperature of about 10 keV with a pr=0.3 g/cm2 is required for ignition of a self-sustaining burn wave for typical high-gain ICF capsules. Ignition and propagating burn are discussed further in Sec. XIII for targets being de- signed for the NIF. The implosion of an ICF capsule can be described by a rocket equation: l5 1 TypIcal range of efficiencies for ablation-driven spherical shell 10-2 - 0 0.2 0.4 0.6 0.6 1.0 Remaining rocket mass fraction, mflmO ET x LlG. 5. Subsonic ablation follows an isothermal rocket equation. Radiation- driven implosions typically have an efficiency of 1.5%~~20%. Direct-drive efficiency depends on laser wavelength and illumination geometry, but is typically 5%-10%; x=m/mO is the ratio of the final shell mass mf to the initial mass mn . Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3937 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp In this equation, P, is the ablation pressure, ti is the mass ablation rate per unit area, ma is the initial shell mass, and fnf is the fuel or payload mass. The rocket efficiency versus mflmo is shown in Fig. 5 for both an ideal rocket and an ablation-driven rocket. The peak efficiency of an ablation- driven rocket is typically a factor of 4 or more smaller than that of an ideal rocket because the exhaust is continually heated by the incident flux driving the implosion. This is further discussed in Sec. V on implosion dynamics. ICF capsules rely on either electron conduction (direct drive) or x rays (indirect drive) for energy transport to drive an implosion. LaMI target In direct drive, the laser beams (or charged particle beams) are aimed directly at a target. The laser energy is transferred to electrons by means of inverse bremsstrahlung or a variety of plasma collective processes. This absorption occurs at a particle density equal to or less than the plasma critical density nc(cmm3)= 102’/h2, where X is the laser wavelength in ,um. Electron conduction must transport the energy to the ablation front, which typically has an electron density of about 1024/cm3. Uniformity of the flux must be obtained by direct overlap of a large number of very uniform beams, or by lateral electron conduction smoothing. Until it was shut down in December 1992, the Omega laser16*17 at the University of Rochester Laboratory for Laser Energetics (LLE) was the principal facility for direct-drive implosion experiments in the United States. Omega was a 24-beam, glass laser facility capable of delivering 2-3 kJ of 0.35 ,um light in a 0.6 ns pulse. Lawrence Livermore National Labo- ratory (LLNL), in collaboration with Rochester, is conduct- ing planar experiments on the Nova laser’8*‘9 at LLNL to investigate hydrodynamic instabilities and beam smoothing in direct drive. These experiments use a single beam of Nova delivering 2-3 kJ of energy in about 3 ns. GEKKO XII at Osaka University in Japan is the principal facility outside the United States for conducting direct-drive experiments. The 12-beam GEKKO laser2’ can deliver about 10 kJ of energy in 1 ns at either 0.5 or 0.35 ,um. Rochester has completed construction of a 60-beam upgrade to Omega. The Omega Upgrade21.22 has achieved over 40 kJ of energy in a variety of pulse shapes. The Naval Research Laboratory (NRL) is constructing a KrF laser called NIKE,23,24 which is designed to deliver 2-3 kJ of energy in a 3-4 ns pulse. This laser is primarily intended as a testbed for a NRL beam-smoothing technique called echelon-free ISI and as a technology devel- opment program for kilojoule-scale KrF lasers with the pre- cision needed for ICF applications. NIKE is scheduled to begin target experiments in 1995. FIG. 6. For indirect-drive targets, Nova and National Ignition Facility ex- periments are relevant to both laser and heavy-ion targets. Capsule implo- sion and bum physics, as well as hohlraum energetics and x-ray transport, are essentially driver independent. optimally designed targets, 70%-80% of the driver energy can be converted to x rays. The optimal hohlraum geometry depends on the driver. Schematic hohlraums for a laser and heavy-ion-beam driver are shown in Fig. 6. The specific details of geometry are chosen to achieve flux uniformity on the capsule. The symmetry requirement will dictate driver beam placement and hohlraum geometry, including such issues as the ratio of capsule size to case size, hohlraum internal structure, and various other details, as discussed in Sec. IX. In general, laser-driven hohlraums designed to achieve radiation symmetry with two laser entrance holes (LEHs) are elongated with a length-to-diameter ratio greater than unity. Such a geometry arises from the need to balance the absence of x-ray emission from the LEH by locating the laser beams, which have higher emission than the rest of the hohlraum wall, relatively close to the LEH. In a spherical geometry, proper placement of the beams would result in very high angles of incidence as the beam pass through the LEHs. Such high angles can result in clipping of the beam on the LEH or a very large LEH. Alternatively, in a sphere, the beams can be aimed past the capsule toward the opposite LEH. This can work for short pulses, but capsule blowoff interferes with beam propagation for longer pulses. There are some spheri- cal laser-driven hohlraums that have more than two holes. These designs must balance the increased LEH radiation losses with a potentially smaller case. Ion-driven hohlraums, such as that shown in Fig. 6, are elongated because of the need to place internal shields for symmetry control. Some spherical ion-driven hohlraums, discussed in Sec. XIV, use more than two radiators. Because of relaxed requirements on laser-beam unifor- The target physics specifications for laser-driven mity and reduced sensitivity to hydrodynamic instabilities, indirect-drive ignition targets are shown in Fig. I. Driver- the U.S. ICF Program has concentrated most of its effort target coupling issues, which include laser absorption, x-ray since 1976 on the x-ray or indirect-drive approach to ICE In conversion, and transport, limit the x-ray temperature of indirect drive, the driver energy, from laser beams or ion laser-driven hohlraums. This limitation is primarily the result beams, is first absorbed in a high-Z enclosure, a “hohlraum,” of laser-driven parametric instabilities,25 which result in scat- which surrounds the capsule. The material heated by the tering of laser light and production of high-energy electrons. driver emits x rays, which drive the capsule implosion. For Light scattering degrades symmetry, and high-energy elec- 3938 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 1.0 Laser energy (MJ) FIG. 7. The National Ignition Facility (NIF) is being designed to demon- strate ICF capsule ignition and propagating burn. trons cause capsule preheat, which reduces the achievable compression. For the typical ignition target designs described in Sec. XIII, the hohlraum temperature is limited to about 300 eV or an equivalent x-ray intensity of about 10” W/cm”. As discussed in Sec. XI, “Hohlraum Plasma Conditions,” this temperature constraint limits the plasma density in the laser propagation path to about 10% of the electron critical density for 0.35 ,um laser light. Given the x-ray flux limitations and the implosion veloc- ity required for ignition, the flux onto the capsules must be sufficiently uniform to allow the capsules to converge by a factor of 25-35, as discussed above. For a capsule to con- verge this far and remain nearly spherical, x-ray fluxes must be uniform to 1%-2%. To achieve this level of x-ray flux uniformity requires a hohlraum that is large compared to the capsule dimension. In current hohlraum designs, hohlraum areas are typically 15-25 times that of the initial capsule area. Such a large-area hohlraum limits the coupling efficien- cies of driver energy to the capsule to lo%-15%, as dis- cussed in Sec. VIII. It should ultimately be possible to achieve a coupling efficiency of 20%-25% through the use of optimal driver and hohlraum geometries that minimize hohlraum and LEH area. The achievable implosion velocity, which is the primary determinant of the minimum-size driver for ignition, is de- termined by a combination of the allowable capsule IFAR and the maximum achievable x-ray flux. Shown in Fig. 7 are gain curves at implosion velocities of 3 and 4X10? cm/s, under the assumption of a fixed hohlraum coupling effi- ciency of lo%-15%. If the capsule IFAR is limited to about 30, an implosion velocity of 3 X lo7 cm/s requires a hohlraum temperature of about 225 eV, whereas an implosion velocity of 4X lo7 cm/s requires a higher temperatur+about 300 eV. This near-linear relationship between radiation temperature and implosion velocity is discussed in Sec. V. At any given velocity, capsules below a certain energy will fail to ignite because the hot spot will not achieve sufficient pr and tem- perature. The shaded bands correspond to a minimum cutoff energy, which depends on hydrodynamic instability levels and capsule surface quality. The left-hand edge of each band corresponds to the gain for perfectly uniform implosions. The right-hand edge of each band corresponds to the gain for targets with surface finishes of 500-1000 A. As seen in Fig. FIG. 8. Nova laser bay. 7, capsules on the proposed NIF (described more completely in Sec. XIII), which is being designed to deliver 1.8 MJ of energy, must reach implosion velocities approaching 4X lo7 cm/s, and have hohlraum temperatures of approximately 300 eV. The ICF program has used data from laboratory experi- ments and from underground nuclear experiments. A joint Los Alamos/LLNL program using underground nuclear ex- periments, called Halite at LLNL and Centurion at Los Ala- mos (collectively called H./C), demonstrated excellent perfor- mance, putting to rest fundamental questions about the basic feasibility of achieving high gain.z6 It performed inertial fu- sion experiments using nuclear explosives at the Nevada Test Site at higher energies than those available in the laboratory. Since its completion in 1985, the Nova laser18~1g at LLNL has been the primary U.S. laboratory facility for radiation-driven experiments. Figure 8 is a picture of the laser hall, showing some of Nova’s ten beams. Figure 9 shows the Nova experimental area as it was before any di- agnostics were installed. The laser beams are arranged so that five beams located along the rim of a 100” cone irradiate each end of a hohlraum, such as that shown in Fig. 10. Nova can deliver about 30-40 kJ in 1 ns at an output wavelength of 0.35 pm. This energy can also be delivered with a wide variety of pulse shapes. Figure 10 is a typical 1.6 mm diam hohlraum used on Nova for implosion experiments. For ease FIG. 9. Nova target chamber. Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3939 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Implosion /- capsule - -Formvar Z\PO” FIG. 10. Nova implosion target, illustrating beam geometry. Five Nova beams irradiate each side of the hohlraum. The beams are uniformly distrib- uted around the rim of a 100” cone. of fabrication, the hohlraum wall for this target is made of gold, but other high-2 materials such as tungsten and ura- nium are also used. The capsule shown inside is a plastic microballoon about 5 mm in diameter. Outside of the United States, GEKKO XII and the Phe- bus laser at Limeil have been the primary facilities for ex- periments on radiation-driven ICE Hohlraumsz7 used on GEKKO XII have been about half the scale of the Nova hohlraums shown in Fig. 10. Experiments on Phebus2s which is the equivalent of two beams of Nova, have used a variety of hohlraum geometries, including spheres ranging in size from 1 to 2 mm in diameter and targets with beam shields for implosions, as shown in Fig. 11. In Russia, the ISKRA-5 laser29 at Arzamus-16 has been used for indirect drive. ISKRA-5 is an iodine laser operating at a 1.3 15 pm laser wavelength. In typical experiments, this facility can fo- cus lo-15 kJ in a 0.25 ns pulse into a spherical cavity with six LEHs. Other facilities being used for indirect drive in- & = 0.6 for all sizes e 200 I I I lffO- i F 160 - 3 i c’ 140 - i- 120 - 800 1200 1600 2000 2 4 (w) FIG. 11. Hohlraum drive on the Phebus laser;?’ has been measured at 0.35 pm. Et,,,,= 6 kJ in 1.3 ns. as a function of cavity diameter. 3940 Phys. Plasmas, Vol. 2, No. 11, November 1995 elude the Asterix III laser3’ at Garching and the Shengguang laser facility”’ in Shanghai. The Shengguang facility is a two-beam facility currently capable of delivering up to 800 J in a 0.1 - 1.2 ns pulse at 1.06 ,um. The primary alternatives to laser drivers for indirect drive are ion-beam machines. Sandia National Laboratories has developed a succession of pulsed-power, light-ion driv- ers. The primary challenge for ion beams has been, and con- tinues to be, achieving the required focused intensity. Com- pleted in 1985, the current Sandia facility is PBFA ILs2 which can deliveG3 about 100 kJ of lithium ions at l-2 TW/cm2. Sandia has begun conducting preliminary hohlraum and beam-coupling experiments, Heavy-ion drivers are also being developed for ICE Of the current ICF drivers, both the 1990 National Academy of Science (NAS)26 and the Fusion Policy Advisory Committee (FPAC)34 reviews concluded that because of their potential efficiency, durability, and rep rate, heavy-ion drivers have the greatest potential as drivers for future inertial fusion power plants. The heavy-ion driver work in the United States is supported primarily by the Office of Fusion Energy (OFE). The U.S. program in heavy-ion drivers focuses on induction accelerators. The experimental work has been carried out primarily at Lawrence Berkeley Laboratory. Although induc- tion accelerator technology has had a variety of applications, primarily for electron beams, a heavy-ion driver using space- charge-dominated beams for ICF currently is the least mature of the major driver approaches. In contrast to the laser case, a typical ion-driven hohlraum, which requires a certain mini- mum intensity to achieve good x-ray conversion,35-37 con- centrates the driver into a few radiators, as shown schemati- cally in Fig. 6. This feature, which is attractive from a reactor-design point of view,3s minimizes the solid angle over which beams must be distributed and allows for a wide variety of reactor designs, including liquid waterfall and ce- ramic granule designs, which protect the target chamber wail against the fluence of neutrons, x rays, and debris from the target. Although significant parts of the following discussion apply to both direct and indirect drive, the principal focus will be on indirect drive. II. HISTORICAL DEVELOPMENT OF INDIRECT DRIVE IN THE U.S. ICF PROGRAM We are nearing completion of a two-decade program to develop the data and numerical modeling capabilities needed to accurately specify the requirements for ignition and high- gain, radiation-driven ICF targets. Although research on in- direct drive in the United States has been largely classified throughout this period and some aspects remain classified, a recent DOE declassification decision39 goes a long way to- ward achieving a long-time goal of research scientists in the field for more openness and international cooperation in ICE John NuckoIls’ seminal 1972 Nature paper’ was pub- lished at about the time when laser technology, diagnostic development, and numerical modeling were becoming ma- ture enough so that an expanded ICF program could begin to evaluate the limits and requirements for the success of ICF. This publication grew out of work, initiated by Nuckolls in Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Capsule energy gain plotted vs compression 102 103 104 105 Compression ( x liquid density) FIG. 12. The initial capsule energy estimates for ICF could be met with a factor of 2.5 increase in the achievable implosion velocity compared to velocities predicted for the NE The gains are plotted with the assumption that the fuel is near Fermi degenerate and that the yield is not degraded due to hot electrons, asymmetry, or hydrodynamic instability. The threshold driver energy and implosion1 velocity are obtained from E,,,(MJ)~~(O.O5/~~~)p3'*(V/(3X 107))-‘, with aY,==3%. the late 195Os, to address the challenge of creating the small- est possible fusion explosion. These early calculations were based on radiation implosions and predated invention of the laser. When the laser was invented in 1960, LLNL physicists immediately recognized its utility for inertial fusion. Sterling Colgate, Ray Kidder, and Nuckolls independently calculated various methods of using high-power lasers to implode and ignite fusion target designs.“’ Colgate and Nuckolls calcu- lated implosions in laser-driven hohlraums. Kidder applied a spherically symmetric pulse of laser light to the target with- out the use of a radiation implosion. Other early work in laser-driven inertial fusion was proceeding around the world. In 1963 at the 3rd International Conference on Quantum Electronics (Paris), Basov and Krokhin” evaluated the laser requirements for using a laser to heat plasma to thermo- nuclear temperatures. This evaluation considered just direct heating of a plasma by laser irradiation and did not use an implosion. Nuckolls’ 1972 paper was based on the direct-drive im- plosion of bare drops or shells of DT. But, as indicated, LLNL had shifted by 1975 to radiation-driven implosions for reasons described below. Figure 12 shows Nuckolls’ original gain curves as func- tions of fuel compression. These curves predict that, if suf- ficient compression is achieved, targets driven by lasers as small as 1 kJ could achieve target gains greater than unity. Drivers of about 1 MJ were predicted to be required for high gain. Although today’s estimates of the driver size required for high gain have not changed significantly, we now believe that a driver of about 1 MJ also will be required to achieve ignition. Why has the ignition threshold increased by such a large factor while the requirements for high gain have remained fairly constant? This apparent disparity is explained by the extreme sensitivity of the ignition threshold to the implosion velocity that can be achieved in near spherical implosions in which the fuel remains nearly Fermi degenerate. A simple model for an isobaric implosion”2Z43 would predict that the required energy would scale as @V-lo, where V is the im- plosion velocity and p is the ratio of the pressure in the fuel to the Fermi pressure. Detailed numerical calculations44 pre- dict that this dependency is approximately reduced to E caps.leiMJ~=; (E)P3’2( &‘1-‘. (23) where rihy&, is the hydrodynamic efficiency and V is in units of cm/s. The reduction in the velocity dependence from an ideal isobaric model is the result of several factors, including an increase in the required hot-spot temperature as the target size decreases, and an increase in the fractional mass in the hot spot that self-consistently occurs during compression and results in reduced compression and hot-spot coupling effi- ciency. The effects of hydrodynamic instability and asymme- try will result in an increase above the energy predicted by Eq. (23). As discussed in Sec. VI, these deviations from a uniform spherical implosion result in a factor of 2-3 increase in the minimum capsule energy required for ignition. The strong dependence of the minimum energy on the achievable implosion velocity means that only a factor of about 4 increase in the implosion velocity is required to go from a minimum energy of about 1 MJ to a minimum energy of 1 W, as shown in Fig. 12. The velocity indicated in Fig. 12 depends on the ignition margin required to overcome the effects of mix during the process of assembling the hot spot. The dependence of gain on implosion velocity is much weaker. To lowest order, the reduction in gain with reduction in target size, or increase in implosion velocity, occurs pri- marily because less mass is imploded per Joule of energy coupled to the target. For equal burn efficiency, the gain would scale as V-’ so that there would be about an order of magnitude less gain at 1 kJ than at 1 MJ, as shown in the curves of Nuckolls. Once a target with a DT pusher ignites, it is expected to burn as calculated. In practice, compressions achieved in self-consistent implosions are lower than the op- timal compression indicated in Fig. 12, and the gain is a stronger function of energy as discussed in Sec. VII. We now believe that implosion velocities are limited to between about 3 and 4X lo7 cm/s because of two constraints: (1) the physics governing the hydrodynamic instability of an ICF implosion; and (2) the maximum intensity allowed by efficient laser plasma coupling. Higher implosion velocities are possible in certain types of high-entropy implosions, in which the high-density shell is heated rapidly to high temperature and then explodes. In a so-called “exploding pusher target,” the center of mass of the shell or “pusher” is almost stationary as it explodes. The radius of the boundary between the inner edge of the shell and the fuel typically converges only a factor of 3 or 4. Such targets are quite insensitive to asymmetry. The direct-drive, electron-conduction-driven exploding pusher target45-49 was the most common early ICF target and was the first type of target to produce thermonuclear neutrons.“7Y48 However, it does not scale to high gain, because all of the mass of the target is on a high isentrope, which precludes high compres- sion. Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3941 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp To obtain gain at laser sizes much smaller than about 1 MJ, Nuckollsi used a very optimistic model for RT instabil- ity in the presence of ablation. As described in Sec. VI on hydrodynamic instabilities, this model, coupled with an as- sumption that implosions with absorbed laser intensities ap- proaching lOI W/cm2 would be feasible, was required to obtain ignition at laser energies approaching 1 kJ. In 1972, computers and numerical models were just becoming pow- erful enough to allow detailed evaluation of the effects of hydrodynamic instability and the limits that laser plasma in- stabilities would place on the allowable intensity. Over the next few years, experiments indicated that laser intensities would be limited to between 1014 and a few times lOI W/cm’, depending on the laser wavelength. Numerical cal- culations provided most of the guidance for the growth of RT instability until the quantitative data discussed in Sec. VI became available in the late 1980s and the early 1990s. By 1974, numerical calculation?’ using the LASNEX code5’ indicated that direct-drive capsules would have much higher instability growth rates than were assumed in Nuck- 011s’ 1972 paper. In addition, new experiments using neody- mium glass lasers indicated that reduced absorption and hot electron production would severely degrade direct-drive im- plosions at the high intensities required for ignition with la- sers in the I- 100 kJ range. The quality of the laser beam also was much worse than could be tolerated for the implosion uniformity required for direct drive. For direct-drive implo- sions, beam nonuniformities provide a source of small- spatial-scale perturbations (referred to as imprinting), which are further amplified during the implosion. Much progress has been made since the 1970s toward solving the irradiation-uniformity problem for direct drive. A series of clever optical inventions, both in the United States and Japan,52-54 traded off laser-beam coherence for laser- beam uniformity so that it is now possible to obtain beams that are uniform to a few percent. The overlap of a large number of beams, and further optical innovation should al- low nonuniformity to be reduced to less than l%, estimated to be required for direct drive. With optimization of density gradient stabilization effects, as discussed in Sec. VI, the direct-drive ignition threshold is now estimated to be about 1 MJ.s5 In the United States, the Omega Upgrade lase?‘s22 at the University of Rochester is designed to answer these ques- tions, and the NIF conceptual design (see Sec. XIII) will permit adding a direct-drive option. In Japan, the 300 kJ Kongoh laser project,56z57 an upgrade to GEKKO XII is be- ing proposed to study direct-drive ignition. Although the beam-smoothing techniques that have been developed greatly reduce the level of these effects, imprinting is still a major concern for direct drive. Calculations carried out in 1975 showed that it is pos- sible, with proper design, to achieve high gain with radiation-driven targets5* such as those in Fig. 1. These tar- gets are very similar to direct-drive targets, except that the choice of ablator material must be properly matched to the x-ray drive spectrum in order to control RT instability and ensure that the fuel can be kept in a near-Fermi-degenerate state. From one point of view, implosions driven by soft x rays could be considered as being driven by a laser with a very short wavelength and a very broad frequency band- width. Compared to direct drive, these calculations for indirect drive showed a dramatically reduced growth of perturbations due to RT instability. As discussed in Sec. VI, this reduced level of instability-one of the principal advantages of radiation-driven implosions-occurs because radiation- driven implosions have much higher ablation rates and hence lower growth rates and thicker shells. In addition, because the laser beams are absorbed far from the capsule, as indicated schematically in Fig. 6, radiation-driven implosions are unaffected by small-scale nonuniformities in the laser beam. As discussed in Sec. XII, “Hot Electron Preheat,” indirect-drive targets are less sensitive to the effects of hot electrons produced by laser-driven parametric instabilities because of solid-angle effects and because radiation-driven capsules are thicker than directly driven capsules. A potential disadvantage of indirect drive for lasers, compared to direct drive, is the longer scale length of plasma traversed by the laser as it propagates from the LEH to the hohlraum wall. Under some conditions, very large levels of parametric instabilities can be generated in this plasma. Con- trolling the level of parametric instabilities places limits on laser wavelength and intensity. In practice, both direct drive and indirect drive are optimized by using short-wavelength lasers with XGO.5 pm, and intensities typically are limited to about lOI W/cm2. For indirect drive, the capsules and such issues as radia- tion transport and hohlraum wall loss are essentially inde- pendent of the driver. This means that the ICF Program could use underground experiments driven by nuclear explosives to test aspects of ICF capsules at much higher energy than could be tested by available laboratory sources. As men- tioned previously, the H/C program (from 1978 to 1988) laid to rest fundamental questions about the feasibility of high- gain ICF?6 Because much of the physics of indirect drive is inde- pendent of the driver, many of the results learned with lasers carry over to other drivers such as heavy-ion beams. This synergism is particularly important for heavy-ion-beam driv- ers. Indirect-drive laser experiments provide a key element of the database required to ensure that targets driven by heavy-ion beams will work when the accelerators are available.34’59 Because of the reduced level of hydrodynamic instabil- ity, capsule energy requirements for ignition at a given x-ray intensity are very close to the projections in Nuckolls’ 1972 paper. However, there is a substantial energy penalty in- curred in producing x rays and transporting them symmetri- cally to a capsule. Further, because of limits to the achiev- able x-ray intensity, the minimum driver energy for indirect drive is about 0.5-I MJ, as shown in Fig. 7. The upper edge of the band in Fig. 7 allows for the effects of asymmetry and the mixing of hot and cold fuel while the hot spot is being assembled. Hence, the currently projected minimum energy for ig- nition and burn propagation is quite similar for both direct and indirect drive. However. because of relaxed beam- 3942 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Forerunner target A lao+m gold scattering wire 1Oy.m gold converter and radiation case l-pm Parylena light and electron rhleld I? \ 3aa,w la&pm diagnostic holes 4 ball - 2 ma/cm3 DT fill - I mg/cms No fill (a) W-pm tungsten- 250~pm-diam Parylene light and electron shield A 520 ~III .c ‘x VO-urn-diem 1 0.7~pm-walifuel ball 0.16~mg/cm3 DT fill O.i-mg/cm3 Ne fill Hohlraum / / ‘sf . / \ SO-pm diagnostic holes / FIG. 13. The first indirect-drive, laser-driven implosion was achieved on the Cyclops laser at LLNL in 1976 using a target called a Forerunner. quality requirements and reduced sensitivity to RT instabil- ity, it has been possible over the past two decades to make more rapid progress toward obtaining the radiation-drive da- tabase required to quantitatively specify the driver require- ments for ignition. In the United States, a comparable data- base for direct drive will not be available until the experiments planned for the Omega Upgrade are completed, sometime after the end of the 1990s. Between March and May 1976, LLNL carried out the first series of laser-driven radiation implosion experiments. Target designs for these experiments required about 100 J of 1.06 ,um light. They were fielded on the Cyclops laser6’ at LLNL. Figures 13 and 14 show the two principal types of targets fielded in these experiments.“’ To simplify fabrica- tion, gold radiation cases were used for these targets and for most radiation-driven implosion targets since then. For the first few radiation implosions, leaded glass microballoons were used as radiation cases, but gold was a far superior material and could be shaped easily from available tubing or electroplated onto mandrels of arbitrary shape. For these first radiation-driven targets, with calculated radiation tempera- tures of about 100 eV, thin glass microballoons were used for capsules. The radiation mean-free path in these capsules was comparable to the shell thickness. The targets became nearly isothermal and behaved as exploding pusher targets. The tar- gets shown in Fig. 13 had yields of about lo4 neutrons, whereas the target in Fig. 14, which was designed to couple radiation to the capsule more efficiently, had a yield between FIG. 14. Improved version of Forerunner target: (a) engineering drawing, (b) assembled target, and (c) fuel capsule and Parylene cover mounted on end cap prior to assembly. 1 and 2X105 neutrons. Yields for both types of targets were predicted correctly. These results, which made us optimistic about radiation drive, resulted in a shift of the 20 beam, 10 kJ Shiva laser from a uniform-illumination scheme to a two- sided irradiation scheme for indirect drive and formed the basis for the early optimism about the possibilities for achieving breakeven on a 200 kJ laser operating at 1.06 ,u,m. However, as we attempted the higher drive temperatures needed for high-density implosions and higher yields, laser- driven parametric instabilities in the hohlraum plasmas gen- erated high levels of energetic electrons. Also, coupling dif- ficulties hampered progress in the LLNL program on both Argus62 (a two-beam laser capable of delivering l-2 kJ of 1.06 pm light that served as a prototype for the laser hard- ware in Shiva) and Shiva as we worked to achieve a DT fuel density equal to 100X liquid DT fuel density (about 20 g/cm3). In the initial Cyclops hohlraum experiments, the pres- ence of high-energy electrons, which we later determined were produced primarily by stimulated Raman scattering (SRS), showed up as noise in the neutron detectors.6’ Be- sides the 500 pm diam target shown in Fig. 13, we tested 300 and 400 ,zrn diam versions of this target. The smaller two hohlraums generated such large signals (from high- energy electrons) in the neutron detectors that they could not be used for implosions. Therefore, we did the implosion ex- periments in the larger, lower-temperature hohlraum, which Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3943 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp j Gold hohlraum wall and scattering cone 0 1 0 1 prompt production region photon energy (keV) Prompt sink region photon energy (keV) FIG. 15. Time-resolved x-ray spectroscopy, showing energy loss and temperature gradient between production and sink regions of Cairn targets on the Argus laser at LLNL (1978). had low noise levels. As discussed in Sec. XI, “Hohlraum Plasma Conditions,” laser plasma parametric instabilities strongly limit the hohlraum temperature that can be achieved with a laser of a given size and wavelength. Because we lacked adequate models for certain key pieces of the physics, including non-LTE (local thermody- namic equilibrium) or NLTE atomic physics for the high-Z hohlraum walls, and adequate understanding of the laser- plasma interactions below critical density inside the hohl- raum, we believed that absorption would be high in hohl- raums for 1 pm light and that conversion to x rays would be very high. In addition, we had few measurements to quantify target performance: no quantitative measurement of x-ray drive, inadequate information about high-energy x rays from energetic electrons, and no measurements of the spectral dis- tribution of scattered light that could have identified Raman scattering. We fully expected to achieve 100X liquid density on Argus and go on to more aggressive implosions on Shiva. In 1977 and 1978, hohlraum experiments were performed with increasingly sophisticated targets, as shown in Figs. 15-17. Figures 15 and 16 show 1978 Argus laser targets designed to measure radiation temperature and x-ray preheat.@ Figure 17 shows a hohlraum for capsules designed to achieve 10 to 100Xliquid density65*66 on Argus. Because of high-energy electron production, we were unsuccessful in all attempts to obtain measurable yields from capsules de- signed to achieve a density > loxliquid on Argus. 3944 Phys. Plasmas, Vol. 2, No. 11, November 1995 Throughout 1978 and 1979, we tested a wide variety of targets designed to achieve high density on Shiva. A sketch of the Cairn Mod-B hohlraum, which achieved the highest densities, is shown in Fig. 18(a). The capsules were glass microballoons with diameters of -150 pm and wall thick- L18Qllm~4420”m ---J '8%104 keV x rays T 5-Z shield FIG. 16. Target setup for a coupling experiment on the Argus laser. We measured the coupling of radiation (burnthrough) and superthermals tpre- heat) to a 12 pm slab of glass (100X-like target) in a 100X-like environ- ment (half-cairn). Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp (W Au!U/Nb conical deflector shield f Argus laser Cairn hlgh- density target radiation casa (8-20 m thick) lastlc support/shield , Laser entrance hole, beam d Argus laser --t skewed injactlon Forerunner Lassr beam fl2 optics w/\/+-T Rilaflon case (Au) -//I Y \ TN fuil ball NOW FIG. 17. By 1977, sophisticated hohlraum implosion targets were being fielded on the two-beam Argus laser: (a) Cairn high-density target; (b) Forerunner exploding pusher target. nesses of 5-10 pm. These capsules were coated with either Teflon (CF,,) or CHz. The illumination geometry for the Cairn-B target is shown in Fig. 18(b). Shiva’s inner cone of beams was focused on the gold shine shields, while the outer cone of beams was focused to pass beyond the capsule and illuminate the opposite hohlraum wall and endcap. Figure 19 shows the variety of Cairn hohlraum types tested in the high- density campaigns on Shiva. Figure 20 is a plot of the den- sity, obtained by neutron activation68 of the glass pusher sur- rounding the fuel, and neutron yields obtained with these designs. In general, the neutron yield anticorrelated with density. The more open geometries, which allowed more ef- ficient transport of energy to the capsule, also provided less preheat shielding against the large fluxes of hot electrons produced in these experiments. Most of the Cairn implosion experiments were designed to operate with radiation tem- peratures near 200 eV. Under these conditions, high-energy x-ray measurements indicated that up to 50% of the absorbed laser light ended up in hot electrons. The presence of these high-energy electrons, which generally had a temperature of 50-60 keV, degraded the achievable density and neutron yield. In general, it proved quite difficult to calculate the performance of these targets with large fractions of hot elec- trons, although the trends were understandable. On the basis of an examination of the plasma conditions calculated for the Shiva hohlraums and an improved under- standing of SRS,25 a model was developed for the limitations on hohlraum temperatures based on filling hohlraums to den- sities near i critical density.69 At this density, the Raman instability-which couples an incident photon, a scattered photon, and a plasma wave-is an absolute instability with very high gain. The plasma wave has a high phase velocity and produces energetic electrons when it undergoes Landau damping. A series of scaling experimentsY7’ which varied the hohlraum size and energy, gave hot-electron fractions that scaled well with the fraction of energy remaining in the pulse after the hohlraum filled to an average density of a critical, as shown in Fig. 21. In addition to measuring the hot-electron fraction, we also measured Raman-shifted backscattered light. The magnitude of this scattering, as well as the time delay before large levels of scattering occurred, also were consistent with the model of hohhaum filling as the source of plasma responsible for producing hot electrons. The time de- lay before the onset of hot-electron production is shown in Fig.22 and is consistent with the calculated time delay for filling to 4 critical densityF9 A Cairn scale 1, referenced to the initial Argus experiments, was 500 pm in diameter and 800 pm long. Most Shiva implosion experiments, such as the Cairn-B shown in Fig. 18, were a scale 2. Because of the Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3945 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp FlG. 5beamsfromeach side in inner c 18. (a) Cairn Mod-B, one of a series of targets that use radiation-driven. ablative compression of the fuel c 20-beam Shiva laser. relatively low critical density of 102’ cmw3 for 1.06 pm laser light, hohlraum experiments on Shiva at this wavelength were limited to between 130 and 140 eV before significant levels of hot electrons were produced, with the 1 ns pulses required for implosions. Low-preheat hohlraums are required for imploding cap- sules with fuel regions that remain nearly Fermi degenerate. To test our ability to predict the performance of ablatively driven capsules in a low-preheat hohlraum, we designed the Nova Precursor Implosion Research Experiments (NPIRE)?’ which were designed to implode capsules at 130- 140 eV and that used the two types of hohlraums shown in Figs. 23(a) and 23(b) with the capsules shown in Fig. 23(c). The cap- sules performed as predicted, with a neutron yield of 107, as indicated in Fig. 23. This gave us confidence that capsules driven by radiation ablation in low-preheat hohlraums would behave as predicted. With diagnostic and alignment shields, apsule. (b) Mod-B in geometry for these targets are quite complex to fabricate, as shown by the assembled targets in Fig. 24. From 1976 to 1981, we investigated both single- and double-shell targets as potential high-gain targets. Compared to single-shell targets such as those in Fig. 1, double-shell targets reach ignition conditions at lower implosion veloci- ties. Figure 25 shows a high-gain, double-shell target.72 In all double-shell targets, called “Apollo” targets, the main fuel is part of the outer shell. During the implosion, the outer shell collides with the much lighter inner shell and accelerates it to a higher velocity. In the limiting case of the inner shell’s mass being negligible compared to that of the outer shell and the collision being elastic, the inner shell can reach a velocity twice that of the outer shell. Since compression to the high density required for high gain generally requires a lower ve- locity than that required to ignite the hot spot, this velocity multiplication can, in principle, result in a factor-of-4 higher 3946 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Mod B I 1 I Y- lo’-10’n p,AR-0.02405 g/cm* Mod H I 0 Y-lo8 n p, AR-O.006 g/cm2 Mod I I Y-3xiO’n ppAR-0.01 g/cm* 3 > 0 ’ Y- lo8 n hTodK 0 Y-2xlO’n FIG. 19. Radiation cases for five Cairn targets: the Mod-B, H, I, J, and K. When irradiated, they provided a variety of drive and preheat environments for the Cairn capsules. most of which were SiO, microshells, 5 pm wall thickness, 150 pm diam, overcoated with 15 pm of Teflon, and filled with about 10 mgkm-’ of DT. gain for a double shell compared to a single shell. The inner shell must be high Z for efficient high-density compression of the fuel contained within it. Because this shell starts out at a density of nearly 20 g/cm3, it can tolerate the high-pressure shock generated during the collision and still achieve high density. Because it is high 2, such a shell also contains the radiation emission from the fuel as it compresses and further lowers the ignition threshold. Early projections of ignition on a “200 w, ” 20-beam Nova laser were based largely on 103 I b ’ fi~~~~~, b t 1 ~~*~~, 1 a b 3 Neutron yield FIG. 20. Fuel density at burn time versus neutron yield for various Cairn hohum geometries. Calm hohlraum scale size f lo-’ - (scale 1 D soo-~ dlam x 8W wn long) I Incident energy (kJ) 8 p 10-Z - ; i lo4 s J IO4 I I , 1 , I I I, 1 I , , , , , ,, I , , I 2X10-4 2xX+ 2x10-P 2x10-4 1 f, = 1.0 4’” r, dtU&, FIG. 21. The experimental hot-electron fraction fhot in 1.06 pm hohlraum scales with the fraction of energy remaining in the pulse f, at time i, when the average hohlraum density reaches quarter-critical. double-shell target designs72’73 such as those shown in Fig. 26. The two capsules shown in Fig. 26 are labeled “sub- sonic” and “transonic” to characterize the velocity of the radiation front (Marshak wavej relative to the velocity of the shock generated by the ablation. In the subsonic capsule, the shock propagates ahead of the Marshak wave during most of the ablation process. In the transonic capsule, the Marshak wave and shock propagate through the LiH ablator at nearly the same speed until the radiation wave is slowed by the TaCOH layer. In this transonic regime, the compression caused by the shock in the ablator depends on radiation tem- perature and decreases as the temperature increases. This negative feedback results in a reduced sensitivity to radiation flux asymmetry because the pressure on the TaCOH shell is proportional to psT, where ps is the shocked ablator density and T is the radiation temperature. These transonic capsules could tolerate 5%-10% flux asymmetry, versus 1% for the subsonic capsules. However, the potential advantages of velocity multipli- cation ignore the effects of hydrodynamic instability during the collision of the two shells. When these types of targets were proposed, little was known about the growth of the turbulent instability layer that is produced during the colli- sion and acceleration of the inner shell. More detailed analy- 0 X-ray streak camera l Onedlmenslonal cylindrical calculations 4667 EWJ) FIG. 22. High-energy electron time delay versus energy for Shiva &O-scale Cairn target (1000 pm diam by 1600 ,um long) hohlraum (2 ns pulse). Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3947 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp (a) Type I cylindrical hahlraum (5/E-4.0) Laser entrance hole T 2000 pm 1 4ClO+mdiam diagnostic holes (c) Capsules for NPIRE hohlraums (d) Perfonance summary (b) Type II spherical hohlraum (2.5 8) b-900 umcl 10’ I I .0= ~~~~~~~~ CH ablator 120 130 140 150 5 W FIG. 23. The NPIRE hohlraums on the Shiva laser were designed to operate at a low radiation temperature of C 130- 140 eV) in order to minimize hot- electron preheat problems. sis of this instability, and experiments74 make it clear that the inner shell cannot be pushed the required distance before being penetrated by this turbulent layer. We now believe that the minimum size for successful ignition of double-shell tar- gets makes it uninteresting for ICF applications. On Shiva,75-77 we fielded a few double-shell targets such as those shown in Fig. 27. The inner shell was a 180 pm diam, 20 /*rn thick glass shell, and the outer shell was a 360 ,um diam, 50 ym thick CH shell formed from a pair of hem- ishells glued to the few-hundred-angstroms-thick film that held the inner shell in place. These Apollo targets had a higher calculated density than did the single-shell Cairn tar- gets. However, the low neutron yields of < IO7 resulted in poor statistics for the neutron activation measurement of the glass pusher area1 density, which was our only density diag- nostic. The model of hohlraum temperatures limited by plasma filling predicted that we would be able to achieve the tem- perature required for high-gain, single-shell targets if the proposed Nova laser were built to produce the third har- monic of the neodymium glass laser. This became practical because of efficient conversion schemes, using nonlinear conversion in potassium dihydrogen phosphate (KDP) crys- tals, initially devised by the University of Rochester.78 In 198 1, the improved coupling in hohlraums was demonstrated at the 100 J level in a series of experiments at 0.53 and 0.35 pm on the Argus laser.79 In these experiments, the hot- electron levels dropped to open-geometry levels, and the fraction of the incident light that was absorbed in the hohl- raum increased to nearly lOO%, as shown in Fig. 28(a). These results are consistent with those seen in 1988 experi- ments reported by Sakabe et c~l.,*~,~~ as shown in Fig. 28(b). Hohlraum absorption greater than 90% also has been typical 3948 Phys. Plasmas, Vol. 2, No. 11, November 1995 (W FIG. 24. The NPIRE targets: (a) cylindrical Cairn NPIRE after final bly; (b) spherical NPIRE after final assembly. assem- of most short-wavelength hohlraum experiments on larger laser systems. The limitations to this high absorption are dis- cussed in Sec. XI on hohlraum plasma conditions. Using these estimates of the achievable radiation tem- peratures and an estimate of the hohhaum coupling effi- ciency that could be achieved consistent with the required implosion symmetry, we estimated the single-shell target gains” shown in Fig. 29. These gains are very similar to those now estimated for the proposed NIF. In 1979, when it became clear that ignition would not be achieved on Nova, we devised a strategy for obtaining the database that would be required for ignition on a future facility.” This strategy tests the physics of high-gain targets by using a series of Nova experiments on targets that are as close as possible to being “hydrodynamically equivalent tar- gets” (HETs), and by using a series of underground nuclear experiments (Halite/Centurion) at much higher energy. This combination of experiments and modeling was devised to provide the basis for the facility that ultimately would be required for ignition and high gain. Since 1979. the LLNL ICF program has focused on de- veloping the quantitative modeling tools, diagnostics, and Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp T8”‘-’ ’ 01 FIG. 25. High-gain Apollo double shell. This target had capsule absorbed energy=0.8 MJ, yield=313 MJ, maximum gold pusher velocity= 1.9X lo7 cm/s, peak spark-plug fuel p-0.68 g/cm2, peak Au pusher p-3.6 g/cm’, peak main fuel DT prw0.96 g/cm’, and peak TaCOH prwO.11 g/cm* (pre- heat shield). experimental techniques required to provide this quantitative physics basis. This strategy was endorsed by the Foster Reviewg3 in October, 1979, along with the recommendation that Nova be a smaller, ten-beam laser with 20.1 (0.53 pm wavelength) and 30 (0.35 ,um) capability. These recom- mended changes were implemented, and Nova has proved to be an extremely successtil facility.s4 In 1983, the first two beams of Nova were constructed as a laser test bed in an experimental facility called Novette, which gave us our first multikilojoule experience with 2w 210 160 - 150 B ii % 120 ii LUJ f 9 60 30 0 F , I 1 I I 1CIl 5~ns b I I I I ’ 160 180 200 220 Channel temperature (ev) 240 FIG. 26. Calculations in 1979, which predicted ignition for a 20-beam “200 kl Nova,” required high hohlraum coupling efficiency and near I-D perfor- mance of double-shell targets. Both capsules had E,,=50 kJ, V(TaCOH)=2X107 cm/s, V(Au)=3X107 cm/s. Capsule yields were about 100 kJ. Gold case CH light shield 1, \ \ I /CH second shell Glass fuel capsule Gold scattering cone I I 1000~m---+/ FIG. 27. (a) Apollo version B constructed for laser experiments on the Shiva laser during 1979. (b) Completed Apollo target. Outer shell and inner fuel capsule are visible through a diagnostic hole. light. ICF experiments on this facility lasted only about three months, but indicated that we were very likely to achieve our hohlraum temperature goals on Nova. Implosions on Novettex5@ used hohlraums such as those shown in Fig. 30. With 7-9 kJ of 20 laser light, these hohlraums reached tem- peratures of 150- 160 eV. For hohlraums that were four-fifths the size of those in Fig. 30 (scale 0.8), the temperatures were about 20 eV higher. The most accurate temperature measure- Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3949 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp (a) Argus laser (LLNL) C3oo~m--i 1 0.8 s *- E 0.6 s ‘Z i+ B 0.4 s 0.2 0 1 . (~~~~~~~~ 1 8 0.6 -s E :: $ 0.4 P X 0.44 pm 0 1.3Fm 0.2 0.6 0.8 1 Cavity diameter (mm) FIG. 28. Small-target hohlraum experiments showed efficient coupling with short-wavelength laser light. (a) Results from 1981 Argus laser experiments at LLNL using 0.35, 0.53, and 1.06 pm light. (b) Aster-ix laser (Garching, 1988) results using 0.44 and 1.3 pm light. ment for these hohlraums was obtained by using an alumi- num “witness plate” on a reentrant tube in “megaphone” hohlraums8’ such as shown in Fig. 31. The witness plates used on Novette had steps of two different thicknesses mounted on the end of a gold reentrant tube. By looking at optical emission when the radiation-driven shock breaks through the aluminum step and recording the time difference between the two steps, we obtain a shock velocity that can be related to x-ray drive. As indicated in Fig. 3 1 for a scale-O.8 hohlraum with 7.2 k.J of laser light, the hohlraum tempera- ture reached 172 eV with only about 3% of the absorbed energy in hot electrons. (These results are consistent with the results achieved on the Phebus laser,** as shown in Fig. 11.) Between 1986 and 1990, LLNL made rapid progress on indirect-drive target physics. Nova experiments and quanti- tative modeling demonstrated symmetry contro1,y’~q2 the first quantitative RT instability expetiments,93*94 the expected benefits of pulse shaping,95*96 and the radiation-drive tem- Capsule: 200 x 6-p& glass + 24-p CH 5 or i0-mg/cm DT fill bnes overfilled by 200 cum to compensate for beam-pointing errors We also carried out some 4w (0.265 pm) experiment$’ with greater than 1.5 k.J of energy in a 1 ns pulse. Witness- FIG. 30. Laser-target configuration for the two-beam Novette laser implo- sion campaign in 1983. These dimensions define a scale- I Novette target. 1.0 Laser energy (MJ) FIG. 29. By 1979. “best estimate” gains for single-shell, radiation-driven ta@S were comparable to today’s estimates. plate measurements on the 4w experiments indicated a hohl- raum temperature of 210 eV with only 0.08% of the energy in hot electrons in a half-scale Novette hohlraum (Fig. 32) using 1.63 kJ of energy. Although we did not carry out 30 experiments on Novette (the appropriate KDP crystal arrays were not avail- able), these results gave us confidence that Nova could meet or exceed its temperature goals of 200-225 eV. In principle, Nova could have been configured to produce 40 light instead of 30 , but we concluded that the decreased performance from optical damage would more than offset the benefits of the increased margin of safety in laser plasma interaction effects. The NAS review** chaired by Dr. William Happer oc- curred just as Nova was becoming fully operational at the end of 1985. Soon after its activation, Nova achieved its initial temperature goals of 200-225 eV with low levels of hot electrons.89 We had established this goal as the tempera- ture that would be required for high gain with a 5-10 MJ laser. The DOE labeled such a facility the Laboratory Micro- fusion Facility (LMF).% The NAS review continued to en- dorse the HET approach, but made the H/C program the highest priority. 3950 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp (a) 1 Alumlnum witness plate 64 Vlew of the Cassegrafn telescope 1 2 Time (ns) FIG. 31. Novette Megaphone O.&scale Cairn target used to measure the shock velocity of the drive at the center of the secondary. Target: 2487 pm long, 1198 /*m in diameter, with 696 pm LEH. Laser beam: 7.2 kJ, 5270 A, 1 ns pulse, ,f/4.3 diverging beam spot at cone. Aluminum witness plate for incident flux temperature: 43 pm step, 990 ps; 67 ,um step, 1590 ps; u,=~.OX 10’ cm/s+P=32 Mbars, TH= 172 eV. Hot electrons: 200 J of 34 keV electrons+7’P,,heat= 1.3 eV for 43 pm step, 0.3 eV for 67 q step. X-ray diode reemission tlux temperature: T,=15.5 eV. perature scaling of implosions.“7 These experiments and their more recent equivalent are discussed later in this paper. Based on the Nova and H/C progress, it was recom- mended that DOE begin considering the LMF based on glass-laser technology. This recommendation initiated a se- ries of internal DOE reviews in 1988 and a request from Congress for an external review of the ICF Program, which was carried out by the NAS in 1989-1990. In its January 1990 interim report. the NAS committee, under the chair- manship of Professor Steven Koonin, commended the Rear view b L diagno&lc hole diameter Dank hole FIG. 32. Half-Cairn targets for Novette scaling experiments. Dimensions: d=outside diameter of cylinder=1500 pm for 1.0 scale; l=length of cylinder=(5/6)& a=distance from back wall to center of Dante hole=(13/ 30)d; b=diameter of Dante hole=[4/15)d: c=LEH diameter=0.5d; t,“=wall thickness; R =radius of front comer=OZid; g=back corner angle =90+2°. Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article progress that had been made in ICF, but concluded that the LMF, with proposed yields of 200-1000 MJ, was too large for the next step and encouraged the laboratories to explore a step between Nova and the LMF.26 In addition, Koonin’s committee concluded that the H/C program had achieved its principal objectives and recommended that the remaining is- sues regarding the feasibility of ICF be resolved on Nova. Analysis of the relationship between implosion velocity, hydrodynamic instability, and hohlraum temperature indi- cated that ignition and modest gain would be possible with a l-2 MJ laser if hohlraum temperatures of 300 eV, and im- plosion velocities of aXlO cm/s could be achieved.98.99 At this implosion velocity, the capsule has sufficient ignition margin to accommodate the expected level of degradation from hydrodynamic instability and asymmetry. At a laser en- ergy of 1.8 MJ, which is the NIF baseline, there also is a sufficient margin to account for uncertainty in the achievable hohlraum coupling efficiency. Early in 1990, using the in- creased power and energy that had become available when Nova’s laser glass was replaced with improved platinum-free material, we were able to demonstrate 300 eV hohlraums with less than 1% of the absorbed energy in hot electrons. Based on experimental and modeling results, both the September 1990 final report26 of Koonin’s NAS committee and the DOE Fusion Policy Advisory Committee (FPAC) 3951 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp report34 recommended construction of a l-2 MJ glass laser for demonstrating ignition and modest gain within about a decade. The NAS noted that ignition demonstration is the natural next step in the ICF program. This recommendation was made contingent upon successful completion of a series of experiments to be carried out on Nova. These experiments and modeling in hohlraum and laser plasma interaction phys- ics (HLP) and hydrodynamically equivalent physics (HEP) constitute the Nova Technical Contract (NTC).26 The HLP experiments address the issues of the effects of hohlraum plasma conditions on implosion symmetry, and the scaling of a variety of plasma collective effects (including parametric instabilities) in hohlraums. The HEP experiments address the issues of hydrody- namic instability and mix, as well as the effects of flux asym- metry on capsules that are scaled as closely as possible to ignition capsules (hydrodynamic equivalence). Several im- provements to the Nova laser, including improved power bal- ance and pointing accuracy, were required to carry out some of these experiments. These requirements resulted in the “Precision Nova Project,““’ which was completed in 1993. Except for cryogenic implosions, which are not now planned for Nova, the experiments of the NTC will complete the goals established for Nova in 1981. As part of its conclusions, the Koonin committee recom- mended that Los Alamos become an integral part of the Nova physics program. That work has been pursued jointly by LLNL and LANL since the end of 1990. In early 1993, DOE endorsed the mission need for the NIF and authorized development of a conceptual design re- port (CDR) for the facility. Demonstration of ignition and burn propagation would complete the physics basis for ICF and open the door for ICF applications, including fusion power production. The following sections review in more detail the theo- retical and experimental progress in ICF, with an emphasis on Nova and the NTC, and summarize the expected perfor- mance of the proposed NIF. Included are a wide variety of analytic scaling laws that serve an important role in illumi- nating key physics issues. III. IGNITION PHYSICS Figure 1 shows the typical configuration of the com- pressed fuel at ignition. As a capsule implodes, P dV work and a-particle deposition from thermonuclear bum of DT act to heat the central hot-spot region. Electron conduction from the hot spot to the cold surrounding fuel, as well as radiative losses, act to cool the hot spot. As the shell of main fuel compresses the hot spot, pressure increases, and densities of both the hot spot and the main fuel increase. If conduction and radiative losses from the hot spot are too large, ignition never occurs. To achieve ignition by the time the implosion process has stopped, the hot spot must have a pr equal to about 0.3 g/cm2 and must achieve a central temperature of about 10 keV. Under these conditions, a-particle deposition can overcome electron conduction losses from the hot spot, and a self-sustaining bum wave will be generated. A simple analytic model demonstrates these requirements.‘2*‘0’,‘02 To estimate the rate of mechanical work per unit vohtme, P, , done on the hot spot, we assume that the main fuel acts as a piston on a gas with uniform pressure: P,= P(dVldt) PAv 3Pv =-=- V v r =2,3X 1015 pr’v~107’ (W/cm”), where p is the hot-spot density in g/cm3, P is the pressure, A is the surface area of the hot spot, V is its volume, r is its radius in cm, v is the implosion velocity in cm/s, and T is the matter temperature in keV. Electrons and ions are assumed to be in equilibrium. The thermonuclear heating rate per unit volume P, is obtained from the bum rate and the fractional alpha particle deposition: P,= p&J%, += i( I- ~)no(av)- 1.2x lo*sp(av), ~,=0.67XlO" (J/g), (25) P,=8X 1016p2 In this equation, 4 is the rate of change of the bumup frac- tion, E, is the cr-particle energy per gram of DT, no is the total number density of particles, (crv} (cm3/s) is the Maxwell-averaged cross section, and F, is the &-particle deposition fraction. Efficient a-particle capture requires a pr greater than the a-particle range shown in Fig. 4. The radia- tion loss, P, , is assumed to be bremsstrahlung emission that escapes the fuel: P,=3.OX 10’6p2T*‘2 (W/cm3). (26) Conduction losses P, are obtained assuming Spitzer’03 con- ductivity with a steady-state temperature profile determined by balancing volume heating and conduction losses: Q=-k VT= -9.4x10'2s(z) Z.ln A T5’2 VT ( W/cm2), 4n-r2Q= F r3(Po,+P,-PR)-+Q=constXr, 2 -+T=T, [Ol l- 11. 217 and T512 4 t-0 VT(r,)= 7-gt2 7 7, p 2?!!=~ e V r y-712 =8X lOI 7 (W/cm3), for In A=2,Z=l. (27) Here S(Z)=S(Z)E(Z)/[S(Z=I)E(Z=~)] is from Spitzer. In addition, S(Z) varies from 1.0 at Z= 1 to about 4.0 at Z=m. Table II gives Sand E at several different values of Z. Here To is the central temperature of the hot spot and r. is its outer radius. The subscripts are dropped in Eq. (27). In obtaining the temperature, the implosion velocity within the hot spot is assumed to be proportional to the radius r at each point. This is necessary to maintain a constant density, which is a typical 3952 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp TABLE II. We use Spitzer values of 6 and E for electron thermal conduc- tivity. z 1 2 3 4 a 6 0.225 0.356 0.513 0.791 1 E 0.419 0.410 0.401 0.396 0.4 characteristic of the hot spot, as seen in Fig. 1. The Coulomb logarithm In A is also assumed to be a constant, and the temperature at the edge of the hot spot is taken to be zero for simplicity. The temperature profile obtained under these as- sumptions is close to that seen in detailed numerical simula- tions at ignition for a typical high-gain target. Equations (24)-(27) provide a qualitative picture of the gain and loss terms in the hot spot, but detailed numerical simulations are required for quantitative accuracy. Energy gain in the hot spot occurs for f= P,,,+ Pa- P,- P,>O. The f =0 boundary is a quadratic in pr: (prj2[ ( +)Fa- 2) +pr( T(~~07’) - $-oa8) This boundary separates regions in which the hot spot gains energy as it is compressed from those regions in which it loses energy. The regions of gain and loss are plotted in Fig. 33 for a velocity of 3X IO7 cm/s. At this velocity, there are uninterrupted trajectories in the energy gain region, from low temperature and low pr to ignition conditions. Plotted in Fig. 33 are the boundaries that specify the regions in which the various terms of the energy equation dominate. Above a line given by T= 15.5(pr)2’3 (keV), (29) the electron conduction loss rate exceeds the radiative loss rate. Typical ICF capsule implosions proceed entirely above this line, for DT with no impurities. It is also clear that PdV work is the dominant energy gain term below O.l<pr<0.2 g/cm” and temperatures of several keV. vWm2) FIG. 33. with sufficient implosion velocity, PdV work will implode a hot spot until cr deposition can propagate the bum. The existence of a loss region at high pr and a tempera- ture of a few keV is caused by the fact that radiative losses scale as pz whereas PdV work scales only as p. The ratio of the PdV work to the radiative loss is given by >=0.767 T”2(v/107) r pr * For any given u, this ratio is less than unity at sufficiently high pr. However, at high pr, the radiation no longer es- capes, and the loss rates are not as high as assumed in this model. This region of energy loss at high pr extends only up to the so-called “ideal ignition temperature,” the temperature at which the a-particle production rate equals the radiation loss rate. In DT without any impurities, this temperature is 4.3 keV. Since both the bremsstrahlung and alpha production rates scale as p’ and are independent of r, the alpha produc- tion results in energy gain above this temperature at suffi- ciently high pr. Along the boundaries defined by f=O, the gain and loss terms exactly balance, so a capsule cannot implode exactly along this boundary. For the region in which electron con- duction and PdV work dominate the energy balance, there is an implosion trajectory toward which all possible implosion trajectories will be “attracted. ” lo4 To show this, we write, for the time rate of change of the temperature, c,p g=x P=P,$P,-P,-p,, dT dT d(v) dT -=-- dt d(pr) dt =2pv - dh-) ’ (31) dT BP -= d(pr) 2C,p”v ma g 3.5x lo-3 b= [v/(3xlo7)1~ a=*-0. If we assume T= S2’5(pr)2’5/b, where S= 1 defines f =O for small pr and T, then we have a solution for’ S=l-&=0.60 or 77=0.815 (pr)2’5 4=7.8( b-1 3~lo~)o’4. (321 This solution parallels the f=O boundary, but is 18.5% lower in temperature. Capsules that begin their implosion away from this trajectory gradually tend toward it. For example, suppose a capsule had a pr=O.Ol g/cm2 and T=l keV in Fig. 33. Under these conditions, the ratio of the PdV work to the conduction loss is almost a factor of 10 when the implo- sion velocity is 3X 107, so the implosion would be almost adiabatic. For an adiabatic implosion, we have ;=( EJ”=( -iI)“‘- (33) For a sphere of mass M, we have 1W=(4?r/3)[(pr)~/p~] or for constant mass, prmpu3. From Eq. (33) we then have Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3953 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp FIG. 34. 1 The calculated NIF capsule trajectory in Ti vs pr space is qualitatively consistent with a simple model of fuel energy gain and loss, spot achieves a higher temperature at preignition values of pr. (34) The T vs pr curve would have a slope of unity, which would approach the “stable attractor” curve from below. The tra- jectory could not cross that of the “stable attractor,” since the slope from below asymptotically approaches the same value as the “stable attractor.” The same process occurs in reverse for a capsule that starts out with too high a tempera- ture for a given pr. Most ICF capsules start out on this latter type of trajectory since the shock that sets the initial adiabat often establishes a higher temperature than can be sustained by the corresponding implosion velocity. Figure 34 is an implosion trajectory from a numerical simulation of the NIF capsule (see Fig. 107, Sec. XIII). Time is implicit in the trajectory and increases as the temperature and pr change from left to right across the figure. The con- tours labeled with different velocities are the f=O boundaries at the indicated velocities. This capsule has an implosion velocity of 4X lo7 cm/s at the time it started decelerating. As seen in Fig. 34, the hot-spot temperature increases somewhat more rapidly during compression than this simple model would predict. This is at least partly because electron con- duction losses are not into a surrounding cold heat sink but into DT, which is at a finite temperature so that conduction losses are reduced. Also, during the low-pr hot-spot assem- bly stage, In h-6, which results in smaller conduction loss compared to Eq. (27), which used In A=2. The line in Fig. 34, with V=4X lo7 cm/s and In R=6, is close to the trajec- tory followed by the mass-averaged hot-spot temperature of the NIF capsule. Figure 35 shows the calculated fuel temperature and density versus pr for a 0.2 MJ capsule that could be driven by the NIF and a larger 2 MJ capsule. Although the capsule energies differ by an order of magnitude, the fuel configura- tion in temperature and pr space, the variables that deter- but the fuel hot mine bum propagation are nearly identical. The smaller cap- sule has larger density to make up for the reduced mass and energy in the fuel. A key to the predicted success of capsules that are being designed to ignite on NIF is the use of a pure DT cryogenic fuel pusher. Of all possible materials that could be used for a pusher to compress the central hot spot to ignition condi- tions, DT has the least susceptibility to the effects of mix, which can occur at the hot/cold boundary. This mix of hot and cold material can quench ignition because of increased radiative and electron conduction losses and because of in- creased heat capacity in the hot-spot region. DT will not suffer increased radiative losses compared to the hot spot and will bum to essentially full yield, independent of mix if ig- nition is achieved. As discussed in Sec. VI, DT also has the least amount of hydrodynamic instability growth at the hot/ cold interface during decompression. Once ignition occurs, the bum wave in these DT cap- I I I - J AilDT ,*%!I DT(2iJj-*2' 1000 ,2 c (0.2 MJ); ) H +- - - - - = 300 *\ 'I -200 * /* P / -100 I? E -30 f$) 0.2 0.4 0.6 0.8 1.6 pr (s/cm*) FIG. 35. Laboratory ignition and high-gain capsules have very similar igni- tion conditions. Hot-spot temperature profiles and pr are nearly independent of size at ignition. Smaller capsules must have higher density to achieve the required hot spot pr4.3 g/cm’. 3954 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp prWcm2) F’JG. 36. Burn propagation in small capsules tracks that in larger capsules until decompression begins. Pairs of curves are temperature contours at a series of times as the burn wave propagates through the fuel. sules propagates in pr and temperature space in a way that is essentially independent of size. Figure 36 shows the temperature-versus-pr conditions for a 0.2 MJ NIF and the larger 2.0 MJ capsule as the burn wave propagates into the fuel. The two capsules track each other until the smaller capsule starts to decompress. Thus, a demonstration of igni- tion and burn on the NIF will determine the requirements for high gain with a larger driver. e P id ,/,y/J$pfv N’FgJ;w’ I 100 I- q- ,9gg([4 --- SwMffc entropy (4 1 a)_. 4 103 103 lo-’ 100 10’ ld la3 Denslty (g/cd) PIG. 37. DT isentropes and shock Hugoniot. The initial state for the shock Hugoniot is p=O.25 g/cm3, T=11.6 K. Each isentrope is labeled by its specific entropy(s) relative to that initial state in units of 10’ J/g/keV. IV. PULSE SHAPING Pur(Mbar)=2 exp[0.75(As-4)]p5’3(g/cm3)=2Pp5’3 Precise and flexible pulse shaping is required to achieve the high densities indicated in Fig. 35. To achieve the re- quired hot-spot and pusher densities with minimal energy, the pusher must remain nearly Fermi degenerate. or The change in fuel entropy, As = A Q/T determines its compressibility. The heat AQ can come from a variety of sources, including shocks, electron conduction, photon pre- heat, and hot electrons from plasma instabilities. For ignition capsules being designed for the NIF, shocks are typically the largest source of entropy. /?=exp[0.75(As-4)], (35) where p is the ratio of the pressure at a given density to the Fermi pressure at that density. From Eq. (35), we see that, for every change in entropy of As=1 above As=4, the pressure at a given density increases by about a factor of 2. To avoid this reduction in compressibility, the optimal ICF capsule should have As<4 from all sources. To see how compressibility changes with the addition of entropy, the equation of state tables for DT (e.g., from the Los Alamos Sesame Library”) can be used to generate a family of isentropes’05 in the pressure-versus-density plane, as shown in Fig. 37. The number labeling each curve also gives the specific entropy along that isentrope, relative to the initial cryogenic value, in units of 10’ JlkeVlg. Since only changes in entropy are meaningful, we have, for conve- nience, put s=O when T=11.6 K and p=O.25 g/cm3, the density of solid DT. Also plotted in Fig. 37 is the shock Hugoniot for DT from an initial solid density of 0.25 g/cm3. The shock Hugo- niot represents the set of possible final states reached in a single shock from the initial state. For a y=513 gas such as DT, the density at high pressures asymptotically approacheslo a compression For ~25.0 g/cm3, curves 1,2,3, and 4 are seen to nearly coalesce. This coalescence is just above the so-called Fermi- degenerate adiabat, where the pressure is due almost entirely to the degeneracy pressure of the electrons (kT,~~~,i). (For pG5.0 g/cm3, the As=0 adiabat curves down from P@‘” because the equation of state of DT at these densities and low temperatures is dominated by atomic and molecular binding and is poorly approximated by a Fermi gas.) There is a fairly abrupt transition at As =4. For As <4, the adiabatic compressibility is a very weak function of s. However, above that threshold, the pressure at a given density increases ex- ponentially with increasing entropy: Typical implosion pressures for an ICF capsule are 100 Mbars or more. If the driving pressure were turned on sud- denly, producing a 100 Mbar shock, the entropy generated in the fuel would be As =9, as shown in Fig. 37. From Eq. (35), compression to a given density would require a pressure about 42 times the Fermi pressure. Figure 37 shows that a single shock of 2 Mbars gives the fuel an entropy of As=4. If we start an implosion at this initial pressure, the subse- quent pressure history must be tailored such that almost no entropy is generated as the driving pressure increases from 2 to 100 Mbars or more. If the pressure profile is generated from a series of shocks of increasing pressure, we can use the Hugoniot relationships’06’107 to determine the allowable pressure ratios Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article entro 7P 2JO. (s-4) p=)--..-~ DT shock Hugonlot, 1Q4 F 3955 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Single-shock pressure ratio (E,) FIG. 38. Entropy changes in shocked DT: (a) for single shock; (b) multiple shocks versus individual shock pressure ratio with fixed final-to-initial pres- sure ratio P+P, = 100, (c) multiple shocks versus individual shock pressure ratio with Pr/PI =256. that will result in an acceptable fuel entropy level. For a y-law gas, we have vs= p2 - hc-- 1 Pl 5+17w ’ TI Rr+1)2/2(Y-wf2 ?-2={l+[(Y-1)/2]M2}{[2yl(y-1)]M2-l} 16M2 = (3+M*)(5M2- 1)’ (371 (38) (39) Tz IT, As( lo* J/keV/g)=2.5R In (P2,p,~~y-,~,y =0.96 ln( sd). (40) In these relationships, subscript 1 (2) refers to conditions downstream (upstream) from the shock, and a y=5/3 has been used. Here R is the gas constant per unit mass. The Mach number, M, is the ratio of the shock speed to the sound speed. For a pressure ratio & Eq. (38) can be compared to an isentropic compression: 771=5 I/y- 0.6 -5 * which can be obtained from Eq. (35) (41) These relationships are reasonably accurate for DT above an entropy of 4. Figure 38 shows the entropy gener- ated as a function of the pressure ratio for a single shock. Also plotted is the total entropy change for a series of shocks with a total pressure ratio of 100 and 256 as a function of the single-shock pressure ratio. In the limit of a very large num- ber of shocks for a fixed pressure change, the entropy change approaches zero (i.e., the compression becomes adiabatic). For a pressure ratio of 100, the total entropy change is less than 0.3 for three shocks each, with a pressure ratio of 4.6. If we were to start with an initial pressure of 1 Mbar and pro- ceeded to 100 Mbars with a series of three more shocks, the entropy of the fuel would remain below 4, and the fuel P max h p2 4 PO S( ?ri ies of discrete constant pressure pit1 shocks with - <4 p/ nl Series of discrete decaying shocks Pkl with - < 4 at fuel p/ FIG. 39. A variety of equivalent pulse shapes can provide the required temporal history of pressure on the fuel: (a) continuous pressure variation: (b) a series of discrete, constant-pressure shocks with P, + ,/P, less than about 4; (c) a series of discrete decaying shocks (picket fence} with Pi+ tiPi less than about 4 in the fuel. would remain essentially Fermi degenerate. From Eq. (38), the total compression ratio for three shocks with a total pressure ratio of 100 is given by d=11.5, h’l f w 1 e or a series of six shocks, the compression ratio is 15.1. From Eq. (41), the isentropic compression ratio for a pressure ratio of 100 is given by vI= 15.9 The timing of these successive shocks must be precisely controlled. Since we want to keep all but a few percent of the total fuel nearly Fermi degenerate, all shocks must be timed to coalesce near the inside surface of the fuel. If two or more shocks coalesce before reaching the inner surface of the fuei, the fuel inside the position where they coalesce will see a much larger pressure ratio, with a correspondingly higher entropy change. On the other hand, if the inner region of the fuel has a chance to decompress before all of the shocks have passed through, the region of the fuel within the rarefaction will see a larger pressure ratio and, again, a larger entropy change. A wide variety of pulse shapes, such as those shown schematically in Fig. 39 can be used. The continuously vary- ing pulse in Fig. 39(a) is potentially isentropic, but in prac- tice, the rate of power change is steep enough that the pres- sure pulses generated by different parts of the pulse shape usually steepen into shocks before they reach the interior of the fuel. The series of steps in Fig. 39(b) generates a series of discrete shocks whose pressure ratio and timing are adjusted. In the “picket fence” pulse shape in Fig. 39(c), the laser drive is on for short pulses and off between the pulses. This launches “blast waves” (shocks followed immediately and continuously weakened by rarefactions) into the capsule. The pressure of each blast wave is chosen so that it has the de- sired pressure when it arrives at the fuel. 3956 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Time (=) 20 2pB:; 10 0 -‘- Aluminum thickness 0 1 2 3 0 1 2 3 4 (4 20 Time (ns) Time Aluminum thickness c 0 0 1 2 3 012345 Time (ns) FIG. 40. Shock-wave measurements on Nova demonstrated OUT ability to produce the time-varying ablation pressures required for high-gain ICE NIP capsules, described in Sec. XlTI, require pulses with a contrast that varies from about 10 to 50. The pulse shape for the NIF baseline PT target (see Figs. 106 and 107 in Sec. XIII) generates four shocks that result in an entropy change AS=4 in the main cryogenic fuel. Figure 37 shows the P vs p trajectory for the NIP target main fuel region. That Nova can deliver widely varying, precisely con- trolled pulse shapes has been demonstrated by using a wedge-shaped aluminum “witness plate” in the wall of a hohlraum,‘08-“0 as shown in Fig. 40. Radiation ablation on the hohlraum side of the witness plate generates a shock. When this shock reaches the outside of the witness plate, optical emission is generated, which we view by means of an ultraviolet streak camera at X=280 nm, with the slit aligned along the length of the witness plate. If a constant-velocity shock is generated, position versus time, at which optical emission is first observed in the slit has constant slope, as shown in Fig. 40(a). If the radiative power driving the shock increases with time, causing a time-varying shock velocity, then the slope is not constant, as shown in Fig. 40(b). In general, when measured radiation temperature is used in the calculations, the shock velocities produced by these pulse shapes are well matched by the calculations, as indicated in Fig. 40(c) for a 2.3 ns, 3: l-contrast pulse (labeled ps22), and Fig. 40(d) for a 3.2 ns, 8:1-contrast pulse (~~23). (The dots are from experimental measurements.) In the calculations, the shock position corresponds to the edge of the dark band. These pulse shapes were used in the symmetry experiments discussed in Sec. IX. Pulse-shaped implosions”‘~“2’g5’96 also show the ex- pected increase in density, as shown in Fig. 41 for a constant- power, 1 ns pulse and an implosion using ps22. The capsules were plastic shells with 50 atm DD fuel fill and 0.1 atm argon doping, as shown in Fig. 42. Figure 41(b) shows the size of the 3 keV emission from the imploded core. Some of this emission comes from the plastic pusher, so the size of the x-ray emission does not directly indicate the change in density. A more direct measure of the change in density comes from Stark broadeningn3 of the argon He-/3 x-ray line profile, as shown in Fig. 4l(cj. This measurement shows that the density doubled with this modest level of pulse shaping, in agreement with calculations. Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3957 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp (a) Laser power profile 25 I . c I $ 20 i 15 8 s 10 5 in 1 0- 0 1 Time (ns) 25 $ 20 g 15 t 10 2 5 0 m 0 1 2 3 Time (ns) t 1-ns square 4-- Laser pulse shape ----+ 2.3-ns shaped I-ns square medium drive Wavelength (A) 3:l contrast drive ii s $ 5 c .& t E 3.30 3.35 3.40 3.45 3.50 Wavelength (A) FIG. 41. Implosion experiments with shaped drive demonstrate higher convergences and fuel densities at the same peak drive pressure. V. IMPLOSION DYNAMICS The implosion of an ICF capsule can be described by a rocket equation, as given in Eq. (22). In an ablation-driven rocket, the exhaust, which is the target corona, is continually !i ‘C 0 250 200 150 100 50 0 /--i 0 0.5 1.0 1.5 2.0 Time (I-M) 106w g 180 200 220 240 260 280 180 200 220 240 280 280 Peak drive temperature (eV) Peak drive temperature (eV) FIG. 42. Nova implosion experiments show the expected scaling of yield and fuel ion temperature with radiation temperature. 3958 Phys. Plasmas, Vol. 2, No. 11, November 1995 heated so that it remains nearly isothermal as it expands, instead of having no internal energy, as assumed for the ideal rocket. The ideal rocket has the efficiency (x ln2 x)/(1 -x), as shown in Fig. 5, where x=mlmo is the ratio of the payload mass m to the initial rocket mass mO. The band of achievable efficiencies in Fig. 5 corresponds to the range seen in nu- merical simulations for ICF capsules. The top of the band is typical of radiation-driven implosions, which have hydrody- namic efficiencies of 15%-20%. X rays that drive the implo- sion are deposited at high density near the ablation front. Laser-driven, direct-drive implosions have lower hydrody- namic efficiency than do x-ray-driven implosions because the laser energy is deposited in the target corona at a density and radius outside the ablation front. This energy must then be conducted to the ablation surface. In a spherical target, the efficiency of this conduction process decreases as the dis- tance between the laser absorption region and the ablation front increases.*t4*‘ts This is essentially a solid-angle effect. Hence, lasers with longer wavelengths, which have a lower critical density and are absorbed at larger radius, have lower implosion efficiencies. Direct-drive targets that use a laser wavelength of i-1 pm typically have an implosion efficiency of 5%-IO%, depending on details of the target. The minimum capsule size that will achieve ignition and Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp propagating burn into the main fuel depends strongly on the achievable implosion velocity. This velocity, in turn, is de- termined primarily by the peak pressure that can be gener- ated consistent with efficient coupling of the driver energy to the capsule and by the degree of hydrodynamic instability of the implosion process. The pressure P generated by ablation scales as a power of the incident flux I: P=P,Z"I, (42) where al is less than 1. The mass ablation rate ti is also given by a power of the incident flux: iiz = n&la=, (43) where a:! is also less than 1. If the pusher is imploded adia- batically, then the pressure and density p are related by P=P&'3 p3/5 p;‘5[(3/5h* Or p= p;tsp3/5 = p;i5p3/5 2 (44) where /3 is the ratio of the pressure at a given density to the Fermi pressure P, . Equation (22) for the implosion velocity Viq can be written in terms of the intensity I: Vi-p=: In z= 2 Jai-9 h p”“Ev,, h mo. m m (45) The ablation velocity-the velocity with which the ablation front moves through the shell, Vabl--is given by the mass ablation rate divided by the shell density: v abl jl _ P;‘5p3’5~o p-(3/5)a*= p pz2-(3/5)q* P pgn abl (46) The ablation velocity is a critical quantity for evaluating the hydrodynamic instability of an imploding shell. High ab- lation velocities result in reduced growth from RT instabili- ties, as discussed in Set VI. Equations (42)-(46) are valid for both direct drive and indirect drive, but the coefficients differ significantly. For direct ~ve,15,115,116 we have, approximately, From these two equations, we then have Vimp(CIdS)D,D.= 105X 108(ZX2)“3 In ( i z [email protected].= 4.3x104p3/5~~~l15~-14/15, (50) where we have used PD-r(Mbar)=2pp5’3 (g/cm3) from Eq. (35). Intensity is in units of lOI W/cm2. Laser wavelength X is in micrometers. We assume here that the compressibility of the ablator material has been matched to that of DT (e.g., by pulse shaping or control of x-ray preheat). The AR used in the following analysis is the total shell thickness, although at peak velocity, most of the shell in an optimized target will be fuel. These relationships for direct drive are valid for situations in which the laser absorption occurs predominantly near the critical density. Dependence on laser wavelength will be reduced if the intensity is low enough that significant absorption occurs well below critical density. The exponents of intensity and laser wavelength dependence can be ob- tained from dimensional analysis by using a simple model of the physics involved. We set the incident intensity equal to pressure times blowoff velocity at the sonic point. For direct drive, the sonic point occurs near the critical density pc, so we have 1 z-+LKPcv;E p V&wt$qzh2)1’3, or where V, is the thermal velocity. This matches the scaling in Eq. (47). For the mass ablation rate, we have, at the critical density, jd 1 z 113 rn”pcV*~ p (zhyai~ T;4 ( i . This reproduces the scaling in Eq. (48). The scaling in Eqs. (49) and (50) follow from applying the definition of Vs, and V,, to Eqs. (47) and (48). For indirect drive,‘t7-1’9 we have, approximately, P(Mbar)I,n.=3~.5= 17OZ;;‘, (51) fi&/CIl12/S)~,D,= 3 x 1 05T3 = 1 07z314 r 15 . (52) From these two equations, we then have vi,p(cm/s)r,Dz lo76 In z= 1.8X 107Z::’ (53) (54) These equations, which are written both in terms of the ra- diation temperatures T, (in hundreds of eV, or “heV”) and an equivalent intensity, are valid approximations for capsules for which the capsule ablator albedo (the ratio of the reemit- ted x-ray flux to the incident flux) is near zero. Because it is usually possible to choose a low-Z ablator that has suffi- ciently h&h opacity in its cold state to absorb the incident radiation but still have very low opacity in the heated blow- off region, this approximation is reasonable for much of the capsule implosion history. This approximation is valid longer for a sphere with diverging flow than for a planar sample. When the albedo of the capsule blowoff starts becoming sig- nificant, Eqs. (51)-(54) become time dependent. The expo- nents in Eqs. (51)-(54) also can be obtained by dimensional analysis of a simple model of the physics. We again set the incident flux equal to the pressure times the blowoff velocity Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3959 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp at the sonic point. For radiation drive, the sonic-point tem- perature is proportional to the radiation drive temperature, and the incident intensity is proportional to 7$. Hence, we have or PuT;%~Z~~~. This reproduces the scaling given in Eq. (51). From the rocket equation, we have Vi~p=f In zS”m in z. Hence, we have P mm -ccT~cc[~‘~. Vtb This reproduces the scaling given in Eq. (52). The coeffi- cients in Eqs. (5 1) and (52) can be estimated analytically,1’7 but the exact numerical values depend on details of the ab- lator and the pulse length and shape. The values given in Eqs. (51) and (52) are approximately valid for ablators cho- sen to minimize capsule albedo. Subsonic ablation implosion experiments on Nova, which are described by Eqs. (Sl)-(54), have been very suc- cessful in the 200-300 eV radiation-temperature regime pre- dicted to be required for laboratory capsules that would ig- nite and bum when driven by l- 10 MJ lasers. Figure 42 shows the experimental results and LASNEX simuIations97 for a variety of 1 ns experiments with drive temperatures be- tween about 200 and 260 eV. The capsules had DD fuel. The shells were composed of a polystyrene microballoon, over- coated with a few micrometers of polyvinyl alcohol (PVA) as a permeation barrier. The capsules are then coated by plasma polymerization, with a carbon-hydrogen polymer CH, with n - 1.3 (although the material is generally just referred to as CH). Within the limits of the laser and target diagnostics at the time, features such as bang time, ion temperature, and yield are well matched by calculations, and the predicted strong dependence on radiation temperature is observed. Other experiments on Nova have been used to measure im- plosion symmetry, fuel density and pr, pusher pr, and bum width. There is also a good correspondence between mea- sured and calculated values for these quantities. The shell IFAR, R/AR, the ratio of the shell radius R to its thickness can be related to Viq, v&1, and V,, by inte- grating the rocket equation. The work W done on the implod- ing fuel by the pressure P generated from ablation is given by w= I P dV. w. Most of the work is done while the shell is still at a large fraction of its initial radius. Shell velocities typically ap- proach their peak values by the time the shell reaches half its initial radius. If we assume that the shell is accelerated over half its radius. we have I tl 1 I fl 0 u dt=ZR= 0 V,, In z dt, where ml lnG=ln (55) (55) where f,(x) = [ I - (1 +n)exp(-x)]. In numerical simulations, R/AR varies in time. The maximum in R/AR typically occurs just as the compressed shell begins to accelerate. This maximum is not a represen- tative value for R/AR, because the shell has not moved very far? and the density has not relaxed to a more steady-state distribution. For most high-gain targets, a more representa- tive value of R/AR, for use in comparison with the analysis presented here, is the value at a time when the shell has moved about a of the initial radius. At this time, the shell has moved about 4 of the total acceleration distance and has ex- perienced l/v? of the total number of e-foldings of growth for constant acceleration. For implosions in which most of the mass is ablated, or in other words, if the implosion velocity is greater than the rocket exhaust velocity V,, , then f, is approximately linear in x. Since typical implosion velocities range from 2 to 4X 10’ cm/s, this case generally applies to radiation drive, as seen from Eq. (53), for radiation temperatures of a few hun- dred electron volts. We obtain, for the indirect-drive IFAR, WAR)I,D, 9 -0.56 p, for 4>?>0.8. abl ex (57) If the implosion velocity is less than the rocket exhaust velocity, then fr is approximately quadratic in x. In this case, which applies to direct drive, as seen from Eq. (49) for typi- cal implosion velocities and typical laser intensities of 10’4-10’6 W/cm2, the relationship between the shell IFAR, CRIARID,D, and the rocket parameters is somewhat more complex: en, D,D,= Oh7’ Va,,,Vex’ for 0.8>?>0.1. (58) ex Equation (58) can be rewritten in a way that makes the . . physics clearer. By definrtron, V&l =yizIp. From the rocket equation, we have P/it= V,, . Combining these two, we have pv2 g-o.7 -y. Essentially this same result can be obtained from a simple model for implosion of a shell without ablation. If we apply a constant pressure to a shell with enclosed volume V, then the work done is just PV. If we set this work equal to the kinetic energy given to a shell of thickness Ar and density p, we have 3960 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp PV= P T R3=i MV&,,-~ 4npR2 AR VFmp or R 3 pv2 --‘-- AR 2 P’ To within a factor of 2, this is the same as Eq. (58). Equations (57) and (58) were obtained by assuming an ice block model for the shell density (constant density across the entire shell thickness). In an actual ICF capsule, pressure and density gradients are necessary for the shell to have a uniform acceleration. Within the accelerating shell, we have ,a=vP=$ If the material across the shell has constant entropy, we can use PDT (Mbar)=2/3$‘3 (g/cm3) from Eq. (35) to obtain With the boundary conditions p=po at r=O and Jp dr=po AR, we obtain 63) where p. is the peak density in the shell. The shell thickness is usually defined as the distance between densities that are l/e times the peak density. From Eq. (61), this is about 1:2X that of the ice block model. In general, radiation-driven implosions can be described as high-ablation-rate, low-exhaust-velocity implosions. This results in significant benefits for hydrodynamic stability. Direct-drive implosions are high-exhaust-velocity, low- ablation-rate implosions. In principle, this allows implosions with higher implosion velocity than is the case for radiation drive. For a particular velocity, it is instructive to compare Eqs. (57) and (58). At a velocity of 3X lo7 cm/s, we use Eq. (53) to obtain the following from Eq. (57): R ( 1 21(Vi,,/3X107) 59(V@/3X107) ,hR ID = j?3’5Z9’40 = /33’5T;‘10 - . . (62) Using Eqs. (49) and (50) in Eq. (58), we obtain 80( Viq/3)2 6O(V /3X1O7)2 p3’5(z,5 iii = ‘me 4115 P3’5b 5 , X= f pm. These IFARs have been adjusted by a factor of 1.2 to account for the fact that the shell density is not a constant, as dis- cntssed above. The IFAR scales quadratically with velocity for direct drive versus the linear relationship for indirect drive. If we choose 3 pm light for direct drive, we see that at a velocity of 3X lo7 cm/s, direct-drive shells have IFARs about a factor of 3 higher at an incident intensity of 1015 W/cm’.for a given fuel adiabat. At higher velocities, direct-drive shells have IFARs that are larger by increasing factors. The IFAR of direct-drive shells can be reduced by increasing the fuel adia- bat p, which makes the shell less compressible, although this reduces the target gain and increases the ignition threshold. The IFAR also can be decreased by increasing the intensity, but there is a maximum intensity that is consistent with effi- cient coupling and low levels of laser-driven plasma insta- bilities. Optimizing these two constraints is discussed further in Sec. VI. From Eq. (62), the achievable implosion velocity for radiation-driven capsules at fixed R/AR will be linearly pro- portional to the ablation velocity or nearly linearly propor- tional to the radiation temperature: ( Vimp) I.D. 6 315 R 19/40 =1.4x10 p AR ,5 . (64) Since the minimum energy for ignition depends strongly on the achievable implosion velocity, a great benefit will be derived from operating at the highest possible hohlraum tem- perature and IFAR. This equation also shows that achieving an implosion velocity of 3X lo7 with an IFAR- Fermi- degenerate shell with p= 1 for indirect drive would require a minimum drive temperature of about 200 eV. VI. HYDRODYNAMIC INSTABILITY In general, the RT hydrodynamic instability sets an up- per limit to the value of the shell IFAR, and hence to the peak implosion velocity via Eqs. (62) and (63). As described in Sec. II, Nuckolls’ 1972 paper’ was based on the direct-drive implosion of bare drops or shells of DT. To obtain gain at laser sizes much smaller than about 1 MJ, Nuckolls used a very optimistic model for RT instability in the presence of ablation. This model, described below, with an assumption that implosions with absorbed laser intensities approaching lOI W/cm2 would be feasible, resulted in pre- dictions that ignition at laser energies approaching 1 kJ might be feasible. Since these early optimistic predictions are frequently cited, it is instructive to examine the original as- sumptions and evaluate the changes that have occurred as the experimental database and numerical modeling have im- proved. As described in his 1972 paper, the dispersion relation for RT instability used by Nuckolls was one based on a model of “fire polishing” during the ablation process: y2=ka-k2 5=ka(l-k ARj, (65) P where P, is the ablation pressure, k is the wave number, and AR is the shell thickness. This dispersion relation predicts that all wavelengths shorter than 2rrAR are stabilized and that the maximum number of e-foldings is approximately nmax= Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3961 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp for constant acceleration and (1/2)a t2 = R/2. Equations (23), (63), and (66) can be combined to obtain E ca,,su,e(MJ) = 7 (67) where a typical direct-drive coupling efficiency of 5% into the compressed fuel is assumed. A laser wavelength of X= l/3 ,um was chosen for this example. This transforms the minimum driver energy for direct drive into a relationship that depends only on the maximum allowed growth of hy- drodynamic instabilities and the allowed laser intensity. If we let the maximum number of e-foldings equal 6, we obtain E caps&J)= 261;2’“. (68) If we allow a maximum intensity of lOI W/cm2, then the minimum driver energy is 1 kJ. In 1972, computers and nu- merical models were just becoming powerful enough to be- gin doing detailed evaluation of the effects of hydrodynamic instability and the limits that laser plasma instabilities would place on the allowable intensity. Early experiments indicated that, because of reduced absorption and hot electron produc- tion by plasma collective processes, laser intensities would be limited to lOI to a few times lOI W/cm2, depending on the laser wavelength. Numerical calculations provided most of the guidance for the growth of RT instability until quantitative data be- came available in the late 1980s and the early 1990s. By 1974, numerical calculations5’ using the LASNEX code indi- cated that direct-drive capsules designed for ignition and gain would have much higher instability growth rates than indicated by Eq. (66). The dispersion relations that are most widely used today are still analytic fits to numerical simulations. A widely used formula for the growth of RT perturbations is given by In this equation, k is the mode wave number, a is the accel- eration, L is the density-gradient scale length in the ablation front,-and s is a constant between 1 and 3. Equation (69) with p-1 was obtained in 1983 from numerical simulations for radiation-driven imp_losions. I20 Equation (69) also applies to direct drivei2’ with ,L?= 3. Although p is smaller for radiation drive than for direct drive, ablation velocities at a typical intensity of lOI W/cm’ are about a factor of 10 larger for radiation drive, as seen by comparing Eqs. (50) and (54), so that the stabilizing effects of ablation are larger for radiation drive. The higher ablation rates also result in thicker shells and larger density scale lengths L for radiation-driven capsules. In optimized cap- sules, the ablation and density scale-length effects are about equally important stabilizing effects. There is no simple analytical derivation of the ablation stabilization given in Eq. (69), but a simple physical model reproduces this result. The kV, term can be understood as a simple convective effect due to the fact that RT modes are surface modes. In the absence of ablation, the amplitude 77 of a RT mode is given by ,I,eYnpxO, (70) where y. is the growth rate in the absence of ablation and x0 is position measured relative to the initial surface of the shell. In an ablating shell, the only material that matters to the implosion is the material inside the ablation front. The ablated material disappears beyond the sonic horizon of the shell and no longer affects the implosion. When distance into the shell is referenced relative to the ablation front xA , Eq. (70) becomes yeYO’e -(kxg+kV~t)=,(m-kV~lt,-kx~, (71) and growth is effectively reduced. In this model with a uni- form density shell, it makes sense to define the ablation ve- locity relative to the peak density, as was done earlier. How- ever, in an actual density profile, the RT mode will not necessarily be located near peak density. The coefficient multiplying VA varies by a factor of about 2 in numerical simulations, and this could be due to variations in the posi- tion of the modes relative to the peak density. The factor of 2-3 difference between direct drive and indirect drive could also be due to this effect. A more detailed analysis will be required to better understand the differences in the dispersion relation between direct and indirect drive. The density gradient stabilization modification of the first term in Eq. (69) also occurs because RT modes have a finite spatial extent.‘22,‘“3 If there is not a sharp density dis- continuity at an interface, the effective density difference across the interface is reduced and the growth rate is re- duced. For direct drive, Eq. (69) is a generalization of another formula obtained in 1985 by Takabe et al.:‘24 y=O.9&-jkVA, (721 where p varies in numerical simulations but is usually 3-4. Equation (72) is similar to a form obtained by Bodner*25 from an analytical model of ablation, with a density discon- tinuity at the ablation front. Both Eqs. (69) and (72) have a far weaker form of ablation stabilization than that given by Eq. (65). Direct-drive experiments ‘26~‘27 have now been carried out that agree with the numerical simulations and are in sub- stantial agreement with Eq. (69), although more work needs to be done. Nova Experiments’28-‘“o and calculations for indirect- drive RT instability also are in substantial agreement and are consistent with Eq. (69). Figure 43 shows a typical setup for these experiments. Data are obtained by looking at an x-ray backlighter through a sample placed near the hohlraum wall. By looking face on through a perturbed sample, using either an x-ray framing camera or an x-ray streak camera, one can observe the flow of material from thin to thick regions as an increase in the contrast in x-ray transmission through the sample. Representative data and calculations are shown in Fig. 43(a). Looking edge on to a perturbed sample, one can record the shape of the perturbations on an x-ray framing camera. Representative edge-on data and calculations are shown in Fig. 43(b). By using an x-ray streak camera and 3962 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Data Model Cbowlh of hvmonlca w Om* 2nd KFa harmonlo 4th harmanle - . ima (no) Face-on: streaked Side-on: streaked Time (n*) 1 2 3 xii 0 s wj + loo 40 ;,, 4 60 -8 200 80 I! 250 100 FXG. 43. Experiments 129*130 on planar targets have allowed quantitative evaluation of the growth of RT instability in the presence of radiation ablation. (a) Face-on streaked images provide a 1-D history of the time variation in the spatial distribution of the x-ray backlighter transmission through the perturbed sample, (b) Side-on gated images provide a 2-D record of the spatial distribution of the perturbed foil. (c) Side-on streaked images provide a record of the foil position as a function of time. looking edge on, one can record sample position versus time. Representative data and calculations are shown in Fig. 43(c). Integrating Eq. (69), the maximum number of e-foldings for direct drive is given approximately by iZ= y dt- where I= kR is the Legendre polynomial mode number. A value for the density-gradient scale length L = 0.1 AR has been chosen. This is near the maximum that has been Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3963 achieved in calculations of direct-drive implosions designed to minimize RT instability. In doing the integral, a constant acceleration over a distance x equal to half the initial radius R is assumed. By the time the shell has moved this far, the volume inside the shell has been reduced by almost an order of magnitude, and little more PdV work can be done on the shell. As described in Sec. V, the value for AR in Eq. (73) is an average value of the shell thickness. .hr general, a value for AI? taken from simulations at the time when the shell has accelerated to about i its peak velocity, or when it has moved to about 3 of the initial radius, is representative. The quantity m/m0 comes from the direct-drive rocket Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp I -. , f '. --po =. a 7& ' I - ?Q*, Qfi/ ' &e/q 100 -,ta '. ,@/@ :*; '-. *e*- 2 I% - .z!el, Direct drive -. ,,<’ *e-c c E m '.~~=3.5xlO7am/s,/ cl\ '. P = 31 -. zl -\ !? '\ / -. 'c g IO- .. I .N. -f. I '\ f '. r '. '. '\ '< '. .% I I >\, 0.1 1 .o 10 Laser energy (MJ) FIG. 44. Calculations55 from the University of Rochester that constrain RT growth to 6-7 e-foIdings predict about a 1 MJ threshold laser energy for direct drive. equation, Eq. (49). For direct drive, over the range of veloci- ties and intensities of interest to ICF, (l-~i=l-expi~)-O.2~~il;i”3. (74) Using Eqs. (63) and (74) in Eq. (73) yields the approximate maximum number of e-foldings for direct drive: (75) again choosing h= l/3 ,um as the laser wavelength. If this equation is combined with Eq. (23) for a 5% efficient cou- pling between driver and imploding fuel, the required driver energy becomes 512 1 p4ilf, . 0’6) Equation (76) has a much higher ignition threshold and a much weaker dependence on laser intensity than does Eq. (67) obtained from Nuckolls’ more optimistic model for RT instability. If we allow a maximum amplification of 1000 (6.9 e-foldings), then we have 5/21 &iver(MJ)~.~.~~;5 . (77) This result is consistent with recent calculations55 at the Uni- versity of Rochester, as shown in Fig. 44. For indirect drive, Eq. (73) takes on a particularly simple form that depends only on the shell IFAR, R/AR. Because of the relatively low exhaust velocity, most of the shell mass is ablated in indirect-drive implosions to achieve the required implosion velocity. Hence, we take (l-m/m&-0.8 in the integral and obtain (nI.D.)accel- -/ydty/ ’ AR 1 +0.21(ARIR)-“.XE R’ (78) A constant acceleration over half the shell radius is again assumed, and L = 0.2 AR has been chosen for the density gradient at the ablation front. For indirect drive, values for L typically range from 0.1 to 0.5 AR, depending on the ablator material and the x-ray drive spectrum. Here L= 0.5 AR is the largest gradient scale length consistent with maintaining a given peak shell density and fuel adiabat. As in Eq. (73), AR in Eq. (78) is an average value of the shell thickness. The large reduction in growth for indirect-drive capsules [for Fermi degenerate implosions with p= 1 in Eq. (35)] rela- tive to direct drive was first shown in LASNEX calculations.” This reduction occurs because of the high ablation rates and larger density gradients at the ablation front. From one point of view, implosions driven by soft x rays could be considered as being driven by a very short wavelength, very broadband laser that penetrates to solid density and deposits energy over a significant fraction of the shell thickness. If we limit the maximum number of e-foldings to about six, then Eq. (78) implies that RlAR=30. Instabilities during the deceleration phase also must be controlled. For the case of greatest interest in high-gain ICF targets, the instability during deceleration occurs between the DT hot spot, at high temperature and relatively low density, and the DT main fuel. Although electron conduction pro- vides some ablation stabilization as the hot/cold boundary moves into the cold fuel, stabilization occurs primarily be- cause eIectron conduction establishes a density gradient be- tween the hot and cold material. This gradient is typically 0.1 to 0.2r, where r is the final compressed radius. Without de- celeration, the hot/cold interface would arrive at the origin at about ignition time, so the effective deceleration distance is about equal to the compressed radius r. If just the first term in Eq. (69) is used with L -0.2~ and constant deceleration is assumed over a distance r, the number of e-foldings of growth durmg deceleration ndecel is given by I 9i LL ndecelC 1 -t-0.22’ Because of the density gradient from electron conduction, growth during deceleration typically is limited to about three e-foldings over a broad spectrum of modes, as seen from Eq. (79). The source of perturbation at the hot/cold interface can be either initial perturbations on the inside of the shell, or perturbations that feed through from the outside of the shell. The RT modes are surface modes that decrease away from the surface approximately as rl= vOe-k AR= ‘Iloe-I ARIR. G-30) Hence, the number of e-foldings on the inner surface due to feedthrough is reduced from the number on the outer surface by nfeedthrough= --I$. Because feedthrough decreases exponentially with I, it will be dominated by lower-order modes, The combined effects of acceleration, feedthrough, and deceleration result in a total number of e-foldings of ampli- fication of perturbations given by 3964 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp %cel+ nfeedthmugh+ lldecel = ALigiyl*8l(AR/R)+ ILiz* ‘$2) When the effects of growth during acceleration, feedthrough, and deceleration are combined with the fact that the spectral distribution of perturbations for typical capsules falls off as I increases, the principal modes that contribute to perturbations in the fuel are spherical harmonic mode num- bers less than about 30 or 40. For RIAR=30 the number of e-foldings predicted by Eq. (82) is plotted in Fig. 48(a), which is discussed below. Equation (82) applies to the amplification of perturba- tions that grow initially on the outside of the shell during acceleration. Perturbations initially present on the inside also must be taken into account. However, because the growth of these perturbations is limited by Eq. (79), their initial ampli- tude can be larger before they degrade performance. This does become an important consideration in specifying the cryogenic layer uniformity, as discussed in Sec. XIII. The maximum tolerable capsule aspect ratio depends on the capsule surface finish and the spectral distribution of per- turbations. The effect of a whole spectrum of modes, when all of the modes remain in the linear or only weakly nonlin- ear regime, can be calculated by using the theory of Haa.n.131 This is the case of greatest interest with regard to high-gain ICF capsules. In this regime, the primary nonlinearity is a transition from exponential growth in time to linear growth in time for those modes that exceed an amplitude @2rlk2L= (XIkL). This criterion, which is valid when a full spectrum of modes is present, is a generalization of the single-mode criterion of Layzer,132 which specifies that the transition from exponential growth to linear growth occurs when 7=0.6/k. The factor i/L accounts for the number of similar modes about k that can contribute to the saturation of mode k, including a density-of-states factor with periodic boundary conditions of length L. In amplitude or physical space, this correction occurs because a wave packet with small but finite spectral width cannot be distinguished over short distances from a single mode at k. We expect saturation to occur at roughly the same amplitude in both cases, or when the amplitude of each spectral component of the mul- timode case is given by the Haan criterion. Except for this transition to growth linear in time, all of the modes in a full spectrum of perturbations for most single-shell high-gain ICF capsules with realistic surface finishes can be treated as growing independently. The amplitude generated by a full spectrum of modes with random phases can then be calcu- lated by taking a root-mean-square (RMS) sum over all modes. The best estimates of these effects require the use of a large number of detailed numerical simulations to calculate the growth factors for a large number of individual modes. For a more quantitative description of the model, we define the spherical harmonic modes as R&t)= I di2 Yg(fi)R(fi,tj, (83) where R( a,t) is the radius at solid angle fl and time t, and Yl*, is the complex conjugate of the 1,m spherical harmonic. Initial surface characterization is used to determine R,,(O). Numerical simulations of one mode at a time throughout the linear regime are used to define Ryi( t), the amplitude to which mode 1 would have grown if the evolution were en- tirely linear. This quantity is directly proportional to Rl,(0), with the proportionality factor determined from the simula- tion. Sufficient simulations are run to interpolate to all con- tributing modes. Given the set of quantities R:;(t), ‘we de- termine if the spectrum is nonlinear by comparing R::(t) to S(l)=2R/12, (84) where R is the mean radius. If any modes R&(t) have am- plitude larger than S(Z), they are replaced with an estimated nonlinear amplitude. That is, R yf,( t) if R$t)<S(Z), S(Z){1 +In[R~~(t)lS(Z)]}, if Ryi(t)>S(Z). (85) This construction gives growth linear in time at large ampli- tude, with the appropriate velocity, if Rff,( t) grows exponen- tially. The mix amplitude at any time of interest is deter- mined from the RMS sum of the modes, a”(t)= & 2 hnW12- g ~;kh,zI’ dk = & j- [R(a)-R,]’ dl-in. The bubble amplitude is taken to be v’%, and the spike am- plitude to be (1 +A)v%, where A is the Atwood number.74 Haan has developed a second-order mode coupling theory133 that can be used to determine when this approxi- mation breaks down. This theory is in generally good agree- ment with initial experiments134 that impose multiple initial modes on samples and look at the growth of sum and differ- ence modes. These results confirm that mode coupling is not important for most cases of interest in indirect-drive ICE Significant progress has been made toward experimen- tally verifying this approach to modeling hydrodynamic in- stabilities and the resultant effects of a whole spectrum of modes (mix) in ICF capsules. These experiments exploit controlled variations in initial capsule roughness. Capsules can be roughened intentionally via laser ablation (early ex- periments described later used other techniques to vary sur- face roughness), and the surface can be characterized in de- tail with atomic force microscopy (AFM). As a function of initial surface roughness, model calculations predict observ- ables including (1) neutron yield, pr, as inferred from neu- tron measurements, and (2) spectroscopic emission from dopants in the fuel and pusher. Instability growth can be varied by changing drive profiles and ablator composition. The results shown in Fig. 45 came from a pair of 1991 Nova experiments in which the DD fuel region was doped with argon and the polystyrene pusher was doped with c~o~ne~‘1”‘12’135 One of the experiments used a “smooth” capsule, and the other used a capsule with a deliberately perturbed surface. The smooth capsule had a I2MS surface Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3965 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Scanning electron mlcroscope (SEM) Image of “bumpy-ball” target surface 0 = 1.7 pm Bumpy outer surface 61 t tv, 2.6 2.6 3.0 3.2 3.4 Energy (keV) Smooth outer surface 2.6 2.6 3.0 3.2 3.4 6 5 1.6 2.6 3.0 3.2 3.4 Energy (kev) FIG. 45. Spectroscopic emission measurements I35 from smooth and bumpy-ball targets show the expected differences caused by hydrodynamic-instability- driven mix between the fuel and the surrounding pusher. Because of mix, a bumpy outer surface results in enhanced Cl emission from the pusher and reduced -- Ar emission from the fuel. finish of 300-500 A, and the rough surface had a RMS of about 1.6 pm. In this case, the rough capsule was made by coating the polystyrene mandrel with small polystyrene beads before depositing the CH ablator material. The spec- troscopic signatures of the two capsules were expected to be very different. The smooth capsule was calculated to have little mix between the plastic pusher and the fuel region. In this case, the argon emission would come on early and be quite strong. Chlorine emission would be weak and would come on only later when electron conduction from the fuel region heats up the pusher. In the “bumpy ball” case, sig- nificant mix was expected, and the fuel and pusher emission would come on almost at the same time. In addition, the argon emission was weaker because the fuel was cooled by mix, and the chlorine emission was brighter because of mix. This is what is observed from a streak-camera record of the emission spectrum,“‘~“* as shown in Fig. 46. More work is needed to verify that the Haan model for estimating mix in ICF capsules can be applied to ignition capsules proposed for NIF. This is the ultimate goal of the HEP experiments rec- ommended by the NAS. nitude of instability growth can be adjusted toward that of a NIF capsule. The fuel has argon as a dopant, and the poly- styrene mandrel has a titanium dopant. The variations in neu- tron signatures with surface roughness, as well as dopant spectroscopic signatures, can be used to quantify reduction of capsule performance due to hydrodynamic instabilities. Figure 48(a) shows the number of e-foldings of growth, at peak bum rate for Nova and at ignition for the NIF, as a function of the spherical harmonic mode number for the HEP-4 capsule in Fig. 47 and the NIF capsule shown in Fig. 49. The simple model from Eq. (82) is a good approximation of the number of e-foldings for the modes of interest. Also shown in Fig. 48(b) for the two capsules, as a function of spherical harmonic mode number, is the running integral of the contribution to the total RMS perturbation of the capsule, using the Haan mix model and the modal amplitude spec- trum shown in Fig. 48(c). Because of ablation stabilization, the effects of feedthrough, and the initial modal amplitude decrease with increasing 1, only modes with 1<20 make sig- nificant contributions to the final perturbation amplitude for these capsules. Experiments (HEP-4) are now underway on Nova that A feature of the instability growth of all these capsules is use capsules and pulse shapes (Fig. 47) that have hydrody- an oscillation in the amplification as a function of spherical namic instability growth approaching that expected for NIF harmonic mode number. Oscillation of the initial shock as it capsules. 136*137 These plastic capsules use bromine or germa- propagates across the shell is largely responsible for this ef- nium dopants in the ablator to suppress photon preheat and fect. Perturbations on the shell surface result in perturbations to control the density-gradient scale length at the ablation to the shock generated by the foot of the pulse. These per- front. By varying the dopant level and pulse shape, the mag- turbations are stable and oscillate as they propagate across 3966 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Bumps No bumps 20080110 20061811 FIG. 46. Poor target surface finish increases the amount of mix, causing the Cl dopant in the’ablator to heat and emit early in the compression.“‘S’12 the shell. The phase of these oscillations, when the shock reaches the inner surface of the shell, depend on the shell thickness, wavelength, and shock strength. The rarefaction that propagates backward through the shell is also perturbed and has an amplitude that depends on the perturbation of the shock. When the rarefaction gets back to the ablation sur- face, the perturbation of the rarefaction can add to or subtract from the perturbation at the ablation front. The rapid reduc- tion in growth of the HEP-4 capsule beyond I=30 is caused by this effect. Numerical calculations of amplitude versus 1 oscillate at larger Z’s than those shown in Fig. 48. This effect CH + 0.07% TI W ps26 drtve vs time Time (ns) FIG. 47. (a) The HEP-4 experiments on Nova use doped ablator capsules; tb) pulse shaping (~~26) results in hydrodynamic pertmbation growth jlOO- 300) that approaches that of NIF targets. has recently been observed in experiments on GEKKO XII.138 Perturbations for the HEP-4 capsules are impressed on the capsule surface by a laser ablation process. The initial capsules have a 200-300 a surface finish.‘39 An ArF laser operating at X=0.193 pm is then used to ablate pits on the capsule surface.‘40 By controlling the size, depth, and spatial distribution of these pits, a specified spectral distribution and amplitude can be impressed on a capsule. The spectral dis- tribution shown in Fig. 48(c) arises from a random distribu- tion of 200’pits with a ‘7.5 ,um diam Gaussian spatial profile. (a) NIF and HEP4 ps26 E3r targets (b) NIF and HEP4 ps26 Br targets growth factor at ignition (NIF) normalized running sum of mix and oeak burn (Nova) VI mode amDtitUde usina Haan multimode number model) - 10 20 30 40 50 Mode number Mode number (c) 2-D power spectra for a 5000-A RMS perturbation produced by laser ablation of 200 randomly located, 75-pm-diam pits 0 20 40 60 80 100 Mode number FTG. 48. Growth-factor spectrum for ps26 brominated targets compares well with MF targets. Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3967 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Capsule yield 15 MJ O(l 0 5 IO 15 20 Time (ns) FIG. 49. The NIF baseline target absorbs 150 kJ and has robust ignition and bum-propagation characteristics: (surface finish so.08 pm peak to valley); (b) radiation-temperature input to capsule simulations. Figure 50 shows the yield versus RMS amplitude for cap- sules with this spectral distribution of perturbations. The fall- off in yield with increasing perturbation amplitude is consis- tent with calculations using the Haan mix model. Detailed characterization of these experiments, including drive and symmetry, is still ongoing, but absolute yields are within a factor of 2-3 of that predicted from initial calculations. R Scaling laws for the capsule absorbed power P,, , radius Car,, and pulse length qmp, can be obtained using Eqs. (64) and (87). If we keep the IFAR, RIAR, fixed, we have and Using Eq. (23) with a 15% hydroefficiency typical of indirect drive, and Eq. (64) with RIAR=30, we obtain the minimum capsule energy: E capsu,e(MJ)~.~.~0.03~M~~P-3’2~;;)’8 or Tr i i -4.5 =0.045M,~~- 92 300 eV ’ E,aser(MJ)I.D.=0.23 & M,TP-3’2i;,9’8 i. i where M,, is the margin allowed for the effects of hydrody- namic instability and asymmetry in the compressed fuel vol- ume. Equation (87) gives capsule energies very close to the projections in Nuckolls’ 1972 paper, and in fact scales more favorably with intensity. Equation (87) can be compared to Eq. (77) for direct drive. If we take M,r=2, then the mini- mum capsule absorbed energy is about 90 W, with a radia- tion drive temperature of 300 eV. Since lo%- 15% of the driver energy can be coupled to the capsule, the minimum driver size at 300 eV is 0.6-0.9 MJ, comparable to direct drive. The baseline NIF target, shown in Fig. 49, absorbs 150 kJ. This capsule, with a velocity of 4X IO7 cm/s, can tolerate perturbations that penetrate more than 25% of the capsule radius and are 25% out of round. Below this perturbation fraction, enough hot-spot pr remains for ignition, and the capsule gives a nearly undegraded yield. (88) E cap= G@) R ~ P5E:~p3 cap p3 ’ (904 9 Br-doped c8psules with hydrodynamic growth of 100-300 show clear ybld degradation wlth Increa8lng surface roughness lo7l 0.1 1 Surface roughness RMB (pm) FIG. 50. Quantitative studies of implosions with large RT growth factors are now possible. For the HEP-4 capsules, surface roughness is imposed by precision laser ablation during fabrication. Precision Nova operation has dramatically reduced shot-to-shot yield variations, making these measurements possible. 3968 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp PW P cap+/5T;.93E213. (904 Scaled to the NIF target in Fig. 49, we have approximately R,,(cm)=0.65 pEg T;.m ’ (914 (91b) P,,,(TW)=20p2’5T;.93E(MJ)~;, (914 where r is the energy divided by the peak power. These quantities can be related to the laser energy if the hohlraum coupling efficiency nohl is known: P,aser(TW)= 1 33p2J5T;.93E;;; (93) As before, T, is in units of lo2 eV. VII. CAPSULE GAIN Equations also can be developed for the yield and gain as functions of the driver energy. The yield Y can be approxi- mated by iFIF Y=M&N. --MFET.N. q, b-l,+ 6 where +.N. is the fusion energy per gram for DT and (pr)F is the area1 density of the compressed fuel. The fuel mass MF is given by iW where vH is the hydrodynamic efficiency of an implosion. If we assume constant hydrodynamic efficiency and use Eq. (23), with fixed capsule adiabat, to relate E,, and Vimp, we obtain MFU Eg. (96) For the adiabatic compression of a shell of DT, we have EF= #&=2&“F/3 or PFQ V&, (97) where EF is the specific energy per gram and p is held con- stant. For a sphere with mass M,, we have 1/34!‘5 dnver- (98) Combining Eqs. (94), (96), and (98), we obtain (99) This simple analysis ignores the hot spot, which typically occupies 50%-80% of the compressed radius and reduces the capsule pr for a given compression. Yield from LASNEX calculations scales somewhat more rapidly with energy and more closely follows or Gain-37517 ,?,~h,E~;;,, (100) where aohl is the coupling efficiency between the laser and the capsule. The two dashed lines labeled 10% and 15% in Fig. 7 use s&r= 10% and 15%, which bracket the current NIF target designs. Issues that affect hohlraum coupling ef- ficiency are discussed in Sec. VIII. Equation (100) holds when the capsule at each energy is imploded to a velocity equal to the minimum required to ignite for a given surface finish. This will require a minimum intensity or drive tem- perature at each energy, as given by Eq. (87). At any given energy, it will be possible to meet or exceed the minimum ignition velocity for all intensities or drive temperature above this minimum. For any given implosion velocity, it is possible to calculate capsule gain versus driver energy. Gain curves for indirect drive at velocities of 3X lo7 and 4X lo7 cm/s are shown in Fig. 7. These curves are calculated under the assumption of a fixed 15% hohlraum coupling efficiency of laser energy to a capsule. The shaded band at the left of each set of curves in Fig. 7 corresponds to the uncertainty in the achievable capsule surface finish. The far left edge cor- responds to the gain achievable for perfectly uniform implo- sions. The right edge of the band corresponds to the gain for targets with surface finishes of 500-1000 A RMS. As stated earlier, the best current Nova capsules have surface finishes of about 200-300 A RMS. As the capsule size (or driver energy) increases, the minimum implosion velocity required to ignite a capsule decreases. If we exceed the minimum velocity at any given size, the capsules will still ignite, but there is a performance penalty for operating above the mini- mum velocity. The gain will drop because we will implode less mass and get less yield for a given energy. The capsules also tend to ignite earlier than optimal in the compression process. This results in reduced pr and lower burn efficiency. Hence, the optimum strategy implies operation at the mini- mum implosion velocity consistent with the desired capsule size and yield. This is the strategy that follows the scaling given by Eq. (100). VIII. HOHLRAUM COUPLING EFFICIENCY Both the efficiency of coupling driver energy to a cap- sule and the physics of hohlraum symmetry are largely de- termined by the physics of x-ray absorption in the hohlraum wall. In the following analysis, the hohlraum wall is approxi- mated by a planar surface exposed to a uniform temperature of x rays, and a Lagrangian coordinate system is used for the analysis. The two independent variables are time t and a Lagrangian spatial coordinate m = Sp dx, which is the mass Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3969 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp per unit area of material between the fluid particle and the surface of the hohlraum wall. Conservation of mass and mo- mentum are given by dU dv dt=dm (101) and dv dP -z=dm (102) where U(t,m) = l/p is the specific volume, v(t,m) is the fluid velocity in the rest frame of the hohlraum wall, and P(t,m) is the pressure. Conservation of energy relates the heating T dS of a fluid particle (where T is temperature and S represents specific entropy) to the thermal energy trans- ported out of a fluid element by the energy flux F. Since T dS=de+ P dU, where e(t,m) is the internal energy per unit mass in the slab, the conservation of energy may be expressed as (103) In this analysis, it is assumed that the opacity of the matter is sufficiently high that, on the time scales of interest, matter and radiation are in local thermodynamic equilibrium (LTE). More specifically, the radiation field is assumed to be nearly isotropic and of the same characteristic temperature as the matter. Although the x-ray production region, near the laser critical density, violates this assumption and must be calcu- lated using non-LTE (NLTE) models, the hohlraum wall loss, which is at higher density and lower temperature, is near LTE conditions. The dominant heat-transport mechanism is radiation transport, and the matter is assumed to be suffi- ciently opaque that the diffusion approximationt4’ can be used: (104) where Ka is the Rosseland mean opacity and m is the Stefan-Boltzmann constant. Dimensional analysis of Eqs. (lOl)-( 104) provides use- ful insight. Suppose that the source temperature, applied sud- denly at I =O, is T, . Let ps = 1 /U, be the initial density of the wall, and let P, and e, be the pressure and energy per unit volume that the material would have if it were heated to the full source temperature T, before it could expand to a higher specific volume than II,. Initially, the diffusion process described by Eqs. (103) and (104) will heat the surface of the block so rapidly that the slab material will remain stationary in comparison to the penetration speed of the heat front. When there is no hydro- dynamic motion, these equations lead to a heat front that advances into the slab according to a diffusive law of the form The inertia of the slab material allows the pressure P, to cause disturbances in the slab, which propagate with a sound (or shock) speed that can be estimated from Eqs. (101) and (102): Wt)front- Jp,p,. (106) At early times, the penetration speed of the thermal wave exceeds this hydrodynamic speed, but at later times, the hy- drodynamic speed far exceeds the rate at which the heat wave can penetrate the wall. The critical time scale t, at which the hydrodynamic motion begins to affect the progress of the heat front is easily estimated from the previous two relationships: (107) The depth of the slab that has been heated at this “transition time” t, is estimated by m,=t,JP,p,. (10% For times t4t,, it is safe to assume that p= l/U(t,m)=p, everywhere in the slab, which eliminates the need to solve the mass and momentum equations. (This is Marshak’s “constant density” solution, which is equivalent to the clas- sical nonlinear heat conduction problem.142) When t % f, , something “in between” diffusion-wave behavior and shock-wave behavior occurs. A competition ex- ists between Eqs. (101) and (102), which produce distur- bances that propagate at constant speed, and Eqs. (103) and (104), which produce disturbances that diffusively decelerate as they progress. For example, the pressure of the heated material causes it to explode into the vacuum and decom- press. If the opacity of the heated material decreases as the density drops, more of the radiation emitted by the source reaches the colder, deeper regions of the wall. Thus, the heat front can progress somewhat more rapidly than the nz x dt diffusive behavior, since the heated material becomes less effective at insulating the underlying unheated material. An- other effect occurs if the specific energy increases with de- creasing density. This means that expanding the material at constant temperature requires an energy input. This effect counteracts the effect of a drop in opacity with density. Rosen’43 obtained an approximate similarity solution to Eqs. (lOi)-(104). The following analysis closely follows his solution. First, the energy Eq. (103) is simplified by the assump- tion that, for slow subsonic radiation fronts, the pressure is nearly constant near the heat front. We put P inside the time derivative and deal with the enthalpy h =e + Plp. The en- thalpy and Rosseland mean opacity K are then approximated by power laws of density and temperature: (109) and m2 t i 4&/3 K, T se es ’ (105) front 3970 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp As an approximate solution to the dynamics in the blowoff region, we set the density equal to that of an isothermal expansion in the blowoff region: m P’C,t’ (111) where the sound speed C, is given by --?I2 77112 . (112) From the definition of m, we see that the solution to Eq. (111) is p=exp(-.rlC,t). With these assumptions, the en- ergy equation has similarity solutions of the form m= WtQ (113) and T(m,t)=To ( i ; ‘I(w), (114) with f(W=O)=l and f(W=front)=O as boundary condi- tions. Here To is the temperature at the heated surface when t = to. The parameter W provides a new coordinate system in which the temperature profile is time invariant. By a suitable choice of Q, this enables us to reduce the nonlinear differ- ential diffusion equation for heat transport to a linear differ- ential equation. We obtain by substitution, =wa=pt a D [PP+rtl-Q12+r)]~fa+Lz, dW where D= 16erC;;p&TTf and r=Z(R- E). We can eliminate the time dependence by choosing Q= /3P+l+Z(R-e) PP+l+r 2+Z(R-E) = 2+r . With this choice of Q, Eq. (115) becomes ; Cfp+lz)L s cf~+‘z)‘+QW(fz) -(zpz+z~)p=o. (115) 016) (117) (llf9 Since 1%’ is related to the mass ablated from the surface, it increases as we move through space toward the ablation front. Near the ablation front, W will be large, R is always small, and Z and I are less than unity, so that f’” is small. We expect the gradient (f”)’ to be large near the wavefront, since the nonlinear radiation conductivity must result in a steep-fronted wave. Hence, we neglect the second and fourth terms of Eq. (118). Near W=O, we use, as a trial solution, r / Tar \ al 110 f’w’=p-~+-) J 9 (119) where a=l+RZ. Equation (118) becomes 1 D p+lZ CY -F,,(~)~-‘+Qw][ j#-($-)a]zz’“] = 0. (120) Near the front, the second term cannot be zero, because the gradient is steep. Hence, the first term must be zero. Also, near the front, W= W,. Hence, W, is given by wztr- 4cT 1 4 Tf 0 _--- 3Ko ho QP “GP’T9 t0 wo and the mass penetrated by the radiation wave is then mo= wotQ, Loss E,, -= - = (‘(h)dm= /;‘ho( ;) -‘T;( ;) Plf’(w)dm Area A,,, =hoC~zt~=(mo)l-'Z P;%= P p+ 1z * uw In carrying out the integral, we substituted for p/p0 from Eq. (111) and set m =mo in the resulting term. Here E,, is the energy into the hohlraum wall and A, is the hohlraum wall area. If we do not set m=mo, the right-hand side of Eq. (122) is multiplied by (llcu)Beta[( 1 ---z&a: (1 +Zz)/@J, where Beta(x,y)-r(x)l?(y)lr(x+ y). Similar analytic solutions have been obtained by Kaiser et ~1.‘~~ and by numerically integrating the equation for W.*45 To obtain specific results for gold, we use K,=6X 103Kop0.3T,,eV - l5 cm21g, h=4.2X 106T,$vp-o.‘4 J/g, c,=3.ox 106T$$-O? (123) The Rosseland mean opacity is obtained from the super- transition-array (STA) model’46 and K. is an overall multi- plier on the opacity. Thus, e=O.14, R=0.3, Z=1.6, n=1.5, Z=1.075, r=0.172, p=4.04, and Q=O.54+1.86P. If these quantities are used, the energy absorbed by the hohl- raum wall after a time 7 is approximated by E,,(MJ)=5.2X 10-3K;o.3g(3.44P+ 1)-“.39 x ~:.3#.62+3.3P~ WV (124) where To is the temperature at 1 ns. For a constant hohlraum temperature T,, we have E,,(MJ)=5.2X 10-3K,0.39~.3A,@62. (125) For a constant loss rate k?,,IA,=S, , we must have t-“.38t3.3P=t0. Hence 9 P=O.115 and Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3971 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp (SA)15=F (MJ/cm2/ns)=4.5X 10-3Ti.3:.3/Kt.39, w (126) where (SA)r5 is the absorbed flux in units of lOI W/cm’. This form for the wall loss would be appropriate, for ex- ample, for a constant-power laser pulse with a constant x-ray conversion efficiency if we ignore laser entrance hole loss. Using T= To?.‘15 and (S,),,=O.OlT4, we have T3.3 = 7’;.370.3s = 44.7(S&sz5, where SR is the flux at time 7 emitted from the hohlraum wall. Hence, we can write Eq. (126) as follows: (SR),5=7.0K~.47(SA)f;2’*(ns) . 0.46 (127) From Eq. (127), we see that for time on the order of 1 ns and fluxes of 1014-1015 W/cm2, typical of ICF hohlraums, the reemitted flux from a hohlraum wall is large compared to the absorbed flux. The mass ablated from a hohlraum wall is approximated by mo(g/cm2)= 1.20X 10-3T’.86Kio.46 x(3.44P+ I)- 0.46T(0.54t1.86P) (128) If we take P =O. 115, as required for a constant loss rate, then the depth penetrated in micrometers, for gold, is given by x(,um)= lo4 m(g/cm2)/p=0.53T~~86~~75. (12% Thus, for time and temperature of interest to ICF, a few micrometers of wall material are heated. To obtain the approximate hohlraum coupling efficiency, we write vc.e.E~aser= Ew, + &a+ Eh , (130) where xe. is the laser-to-x-ray conversion efficiency. The LEH losses E, and capsule absorbed energy E,, are esti- mated by .??h= 10-2cA,~, EC,= 10-‘cA,~. The assumption made here is that the capsule absorbs all of the flux incident on it. This assumption is approximately valid for times of interest to ICF capsules for suitably chosen low-Z ablators in spherical geometry. The more general case, for which the capsule will reemit a small fraction of the incident x-ray energy, is discussed below. The hohlraum wall A, (cm’) and entrance hole A, (cm*) areas used are the initial values. The capsule area A, (cm’) used is the initial area of the inside of the fuel layer (or the inside of the ablator if there is no fuel layer). This area is representative of the effective area during the bulk of the energy absorption. Tem- perature T, (heV) is peak temperature, and the time r (ns) used is typically the total energy divided by the peak power. For the case of constant hohlraum temperature, the ratio of the capsule absorbed energy E,, to the energy delivered into the hohlraum by the driver Elaser is then given by’47 4, 17c.e. -= E laSer 1 +A,/A,+(A,/A,)(0.52/~~7~0.38) 17c.e. 77c.e. = 1 -l-ah+ 1.625a,,/N,= 1 +ah+a,/lCiW’ (13% where a,,, and ah are the ratios of the wall or entrance hole area to the capsule area, N, is the ratio of the wall reemis- sion flux to the absorbed flux given by Eq. (127), and N, is the ratio of the energy reemitted by the wall during the pulse to the absorbed energy. Equation ( 132) also can be written in terms of the albedo, which is the ratio of the wall emission to the incident flux and is closely related to N, , E J7c.e. <= 1+ah+1.625a,[(1-a)/@] E 77c.e. = 1 +uh+u,[( l-6)/6] where ctl is the albedo, given by (133) SR 10-2P 1 Ly=-= sR+sA lo-2P+B, = 1 +(0.32/@7ro*38) and U is the average albedo over time 7; given by cy= 10-2T4r 1 10-2pr+ E, = 1 +0.52/Te.7~o.38’ (134) (135) Because the wall albedo is near unity for ICF conditions, or because the ratio of reemitted flux to absorbed flux is large, the hohlraum wall area can be much greater than the capsule and still maintain reasonable coupling efficiency. In the more general case with finite capsule reemission E,,, we can write’48 EC,+ EC,= ( 1 + NJ&,=$ w Ewr=: E,, , or (136) and Eh=g E,,=( 1 +N,)ahEca, w where N, is the ratio of capsule reemission to capsule ab- sorption and n= N,/( 1 + N,.) is the effective ratio of wall reemission to absorption. From Eqs. (130) and (136), we obtain EC, %.e. -= E laser 1 +(%/n)+(l fN,)ah’ (137) When the capsule reemits some fraction of the incident en- ergy, it takes longer to absorb a given amount of absorbed energy. Hence, there is more time-essentially by the ratio (1 + N,)-for energy to be absorbed into the wall and to leak out the LEHs. 3972 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 280 260 $ 240 2M 200 I IASNEX Larer pulses we,* -1 nr mg I 180 I 1 I I t I I 1 0 10 20 30 40 PLWJ FIG. 51. Drive from gold hohlraums is in accord with 2-D LASNFX simula- tions. For capsules that are designed to ignite, we can relate the pulse length and temperature to the capsule energy by using Eq. (87), with a margin of 2 for hydrodynamic instabilities, and Eq. (91b). The hohlraum coupling efficiency from Eq. (132) then becomes EC, ‘17c.c. g&= l+ah+(a,P0.‘4/8.5E~~‘3)’ (138) The coupling efficiency depends primarily on x-ray conver- sion efficiency, and the ratio of LEH and hohlraum wall area to capsule area. The coupling efficiency depends only weakly on capsule energy. The LEHs must be made large enough to avoid signifi- cant absorption and refraction of the laser energy as it enters the hohlraum. The required size scales with the capsule size because the capsule size determines the pulse length. For hohlraums being investigated for ignition, the ratio of hole area to capsule area varies from about 1 to 2. The ratio of hohlraum wall area to capsule area is dictated primarily by capsule symmetry requirements, as discussed in Sec. IX. For ignition hohlraums, the ratio of case area to capsule area varies from about 15 to 30. For this range of sizes for the case and the entrance holes, Eq. (138) gives an overall cou- pling efficiency that varies from about 10% to 20% if the x-ray conversion efficiency is about 70%. Symmetry issues that affect the choice of hohlraum size are discussed in Sec. Ix. Figure 51 shows the experimentally measured and cal- culated hohlraum temperatures as functions of laser power for a series of experiments on Nova.‘49 These experiments used a hohlraum that was 1600 pm in diameter and 2550 pm long with LEH diameters equal to half the diameter. This is a standard scale-l Nova hohlraum. The data are from experi- ments conducted over several years and are for constant- power, 1 ns pulses. The temperatures plotted were obtained from aluminum witness-plate measurements. Temperatures were obtained from shock-velocity measurements similar to those in the pulse-shaping discussion. These are incident flux temperatures that are higher than temperatures that would be inferred from looking through a hole in the hohlraum at wall reemission away from the laser spots. The witness plate 250 200 s si I-- 150 100 /\ 2 9-I Tpeak t &‘5 0.5 1 1.5 2 2.5 Time (ns) FIG. 52. Radiation-temperature profile obtained from soft x-ray diode mea- surements for a hohlraum driven by a 1 ns, constant-power laser pulse. looks at both the hot laser source regions and the cooler reemitting wall. The incident flux temperature, TI, can be related to the reemission flux temperature, TR , from the defi- nition of the albedo in Eq. (134): T J&fW4 I (o*01)‘/4 =$=c( 1+ ;$F38)~” T$’ -T,+O.O8 7. (139) This correction is a weak function of the reemitted tempera- ture. For 1 ns pulses, the source temperature is about 10 eV higher than the re-emission temperature for most cases of interest. Equations (125) (130), and (131) can be used to calcu- late the expected hohlraum temperatures for the Nova experi- ments. The solid lines in Fig. 51 are for constant x-ray con- version efficiencies, v~,~, of 60% and 70%. Also shown are the results of detailed numerical calculations. The experimentally measured hohlraum temperature time history-shown in Fig. 52 for a typical 1 ns, constant- power pulse in a gold hohlraum-implies an x-ray conver- sion efficiency that increases with time during the pulse. If we assume that vc.e=0.70r(ns)0.12, (140) and use this in Eq. (124), we obtain P=O.15 or T=Toto.“, where To is the temperature at 1 ns. As shown in Fig. 52, this gives a good fit to the measured hohlraum temperature- versus-time profile. The temperature history in Fig. 52 is a wall reemission temperature obtained by using the Dantet5’ x-ray diode array to measure x rays emitted from a diagnos- tic hole. As shown in Fig. 53, detailed numerical calculations also predict an x-ray conversion efficiency that increases with time. Equation (140), which is consistent with the nu- merical model results for a 1 ns pulse, is also plotted in Fig. 53. The analysis used for Eq. (132) can be generalized for hohlraums with more complex geometric structure.‘51 The single temperature analysis of Eq. (132) applies to hohhaums that have a single chamber containing all x-ray sources and sinks. More complex multichambered geometries, such as those shown in Fig. 54, frequently are used in ICF experi- ments. In the two chambered geometries shown in Fig. 54, Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3973 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 1.0 , , 1 , ) [ , , , - Conversion efficiency inferred - Oo I I I t , I I I 0.2 0.4 0.6 0.6 1.0 Time (ns) this case, the cap&e is in the sink chamber. The added heat loss of the baffles plus the reduced x-ray transport result in a lower temperature at the capsule. In the hohlraum in Fig. 54(a), however, the capsule is in the x-ray production chamber. Although the baffles absorb energy, they also retard energy transport to the sink chamber, which acts to increase the temperature of the production chamber. This effect can more than compensate for the added heat capacity of the baffles. To be more quantitative in this case, we write the energy balance equation for the production and sink regions as vErp = Ewap + Eps + &a (141) FIG. 53. The conversion efficiency 7 inferred from hohlraum simulations is consistent with QJ derived from T, and wall loss measurements. we define a production or primary chamber (p), and a sink or secondary chamber (s). Although both chambers generally can have both sources and sinks, the p chamber is defined to be the chamber with the dominant source of energy, such that net energy flow is from p to s so that s has the lower tem- perature. Because the internal structure in these hohlraums significantly retards radiation flow between chambers, it is necessary to describe these more complex geometries with two temperatures TP and T, . Both hohlraums in Fig. 54 have more surface area, be- cause of the internal baffles, than would an empty hohlraum of the same size. Since the baffles absorb energy, one might conclude that the capsule in both cases would see a lower temperature. This is true for the hohlraum in Fig. 54(b). In (b) P S P FIG. 54. A multichambered hohlraum can be described as having a produc- tion chamber (P) and a sink chamber (5). In (a) the capsuIe is in the x-ray production chamber, where the light is absorbed. In (b) the capsule is in the sink chamber, which is separated from the laser absorption and x-ray pro- duction chamber by baffles. TEL, + E,, = Ewa, + Et, 7 (142) where E,, and Eh are the capsule and LEH energies, respec- tively, and are given by Eq. (13 I) for a constant temperature. Here E,,, and Ewap are the sink and production wall ener- gies, which are given by Eq. (125) for constant temperature with T,= T, in the sink chamber and T,= Tp in the produc- tion chamber. Here E,, is the energy transported from the production chamber to the secondary and, for constant tem- perature, is approximated by Eps= 10-2A,,,(l;t-~), where A,, is the area of the transport opening between the production and sink chamber. The x-ray conversion effi- ciency is given by v as before. Here E,, is the laser energy deposited in the production chamber and E,, is the laser en- ergy deposited in the sink chamber. If the radiation tempera- ture is not constant, then the energy terms must be calculated as integrals over the time history, as in the example below. Hohhaums such as that shown in Fig. 54(a), which have been referred to as “shimmed hohlraums,” have been fielded on Nova as part of the hohlraum symmetry studies. Figure 78 in Sec. IX shows the results of such an experiment. Without the shims, Nova hohlraums of this size, irradiated with 20 K.I of light in a constant-power, 1 ns pulse, achieve peak drive temperatures of about 230 eV. With the shims, the primary chamber reaches a temperature of 240 eV, and the capsules systematically have a yield that is about a factor of 2 higher. 152 The following solution to Eqs. (141) and (142) below for this specific example reproduces this result. The cylindrical hohlraum in Fig. 78 has a radius of 0.8 mm, a LEH 0.6 mm in radius, and a length of 2.3 mm. The shims are 0.325 mm in radius and are placed on axis 0.65 mm from the hohlraum midplane. The capsule radius is 0.275 mm. Thus, the area of the primary walls (A,,), from shim to shim along the hohlraum wall, including the shim disk area, is 0.072 cm*, the area of the two secondary cham- bers (A,) is 0.074 cm2, the capsule area (A,) is 0.0094 cm2, and each LEH area (Ah) is 0.009 cm2. About 20% of the laser energy (E,) is deposited along the cylinder wall be- tween the axial position of the shim and the end of the hohl- raum. The other 80% of the laser energy is Ep . We use 7,~=0.7, as discussed in Fig. 51. 3974 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp As discussed in Fig. 52, for a constant-power, 1 ns pulse, the hohlraum temperature increases in time as T=To(tlto)o~‘S, so that E/,= lo-,,/ot[ q( ;)““I” dt =6.25X lo-3A& ,$ . i 1 In Eq. (144), T, is the temperature of the secondary region at a time to=1 ns. Also, since the pulse is 1 ns long, the last term is unity, and we have E,,=6.25X 10-3A,,c. (145) Similarly, we have E,,=6.25X lo-“A& (146) and E,,=6.25x10-3A,,(~-~). (147) The primary and secondary chamber wall losses, from Eq. (124) with P=O.15, are given by E ,vap=4.4X 10-“Ap?3p.3 =4.4X 10-3A,T;.3 (148) and E ,pas=4.4X 10-“A,T;.3. (149) If we define T,/T,= y, we can write Eqs. (141) and (142) as 7E,,=4.4X 10-3A,T;~3+6.25X 10-3A,,<( 1 -y”> and -t 6.25 x lo-“A,c gEI,+6.25x10-3A,,(1-y4) =4.4x 10-3A,~~3y3.3+6.25x 10-3A&y”. By adding Eqs. (150) and (151), we obtain .@I = T@Z~ + 4,) =4.4x lo-“A,[1 +(A,/A,)y3.3]T;.3 +6.25x10-3A,[1+(A,/A,)y4]. (150) (151) (152) Inserting the values of the areas and energies into Eqs. (151) and (152) gives 140=3.2Tjp.3(1 +Y~.~)+O.~C( 1+ 1.9~~) (153) and 28=2.14T;t(l-y4)=3.2T;-3y3~3+0.57~y4. (154) Equations (153) and (154) can be solved iteratively to give T,=242 eV and y=O.87 or T,=211 eV. For simple geometry with no shims, we use Eq. (130): 17E1=4.4X 10-3A,T3.3+6.25X 10-3AhT4 +6.25x lo-“ACT? (155) Phys. Plasmas, Vol. 2, No. 11, November 1995 With the total hohlraum wall area A,=0.134 cm2 and Ah and A, the same as above, we obtain 140=5.9T3*3+0.86T4 7 which yields the solution T=230 eV. (156) These calculations show that, although the shims absorb about 500 J of x rays, the primary chamber of the shimmed hohlraum in Fig. 78 is expected to be about 10 eV hotter than the unshimmed hohlraum, as seen experimentally and in more detailed LASNEX hohlraums. This occurs because the shine shield restricts radiation flow to the secondary cham- bers, which are 30 eV colder than the primary chamber. Be- cause of this effect, the tlux onto the capsule in the shimmed hohlraum is increased by (242)4/(230)4=1.225. In other words, the shimmed hohlraum is 22.5% more energy effi- cient than is the unshimmed hohlraum. Although ignition target designs (discussed in Sec. XIII) have not yet used such shimmed hohlraums, they also, in principle, provide a means of increasing the coupling efficiency to the capsule at this scale. Since the hohlraum temperature depends on both the x-ray conversion efficiency and the hohlraum wall loss, we need an independent measurement of the wall loss in order to be confident of both elements of the hohlraum energetics model. Two independent tests of the hohlraum wall loss have been obtained in Nova experiments. In one technique,153 a thin patch of gold is placed on the wall of the hohlraum. The bumthrough time of soft x rays is a measure of the wall loss, which scales approximately as (Ko)-o.47 from Eq. (128). A second, less sensitive technique, uses a wedge of gold or a series of gold steps of different thicknesses placed in the wall of the hohlraum. The shock velocity generated in the gold is approximately proportional to (Ko)-0.25. Both techniques have been used on Nova. Figure 55 shows the results of Nova experiments’54*‘55 using a thin gold patch that has 1, 2, and 3 pm thick sections and an open hole. Emission through the open hole tracks the laser pulse while emission from the gold patch is delayed. The analytical results plotted in Fig. 55 use P=O.15, as dis- cussed previously, in Eq. (128). The predicted burnthrough rate is slightly greater than observed, corresponding to about a 10 eV temperature difference. Also shown are the results of detailed numerical simulations, which accurately match the observed bumthrough rate. Hohlraum temperatures have proven to be reproducible at the major indirect-drive experimental facilities. Figure 56 is a plot of hohlraum temperature versus P,IA, for experi- ments from GEKKO XII,” Phebus,” and Nova.‘49 Here P, is the laser power. The line is T3.3 from the scaling in Eq. (126). The x-ray conversion efficiency in hohlraums for pulses 1 ns or longer is, in general, significantly greater than that measured on flat high-Z disks in open geometry.‘56 Figure 57 shows the x-ray conversion efficiency for a flat disk mea- sured on Nova for 1 ns pulses. For intensities of a few times 1014 W/cm’ to about 10” W/cm” (the intensities on the hohl- raum wall for the data in Fig. 51), the x-ray conversion on disks is clearly lower than for hohlraums and is more inten- sity sensitive. On a gold-coated sphere illuminated with the Review Article 3975 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Streaked XUV imager data at fw = 550 eV Au patches l hv=550eV ohv=225eV Numerical simulation 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Position - Au thickness (pm) FIG. 55. The radiation-wave burnthrough measurements in thin gold foils agree well with numerical simulations and analytical models. 24 beams of the Omega laser, conversion efficiencies com- parable to those in a hohlraum were obtained,‘57 as indicated in Fig. 57. When only six beams from Omega were focused onto a sphere, a conversion efficiency comparable to those seen on Nova flat targets was obtained. These results in open geometry are not well understood theoretically. Although the results obtained in hohlraums are calculated accurately over a fairly wide range of conditions, the inability to predict the results accurately from open-geometry experiments is a con- tinuation of the historical difficulty of calculating the condi- tions in laser-irradiated, low-2 disks.15’ 5001 I 1 400 - n A .O Nova s 0 Phebus s A GEKKOXII includes no hole losses 1 I 10’ 102 103 pL(Ny) T1/2ns A(cm) FIG. 56. Submicrometer-laser-wavelength hohlraum drive experiments from various facilities show general agreement. 3976 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article The soft x-ray emission region around a laser spot in a hohlraum becomes significantly larger than the incident spot during the laser pulse, as shown in Fig. 58. These data are taken by cutting a slot in the hohlraum and imaging the soft x-ray emission around a laser spot on the opposite wa11’59 with a soft x-ray framing camera (zSXRFC).‘~’ The SXRFC can take four frames in each of three different x-ray energy channels. Figure 58 shows the spot size measured at energies of 450 and 1200 eV. The data shown are from three shots with nominally the same conditions. A typical error bar on the spot-size measurements is 20%-30%, based on uncer- tainty in film calibration and the flat-field response of the instrument. As shown in Fig. 58, postprocessed calculations of the emission spot size in hohlraums are consistent with the observed size increase. This increase in size is not seen for a 1 ns pulse in open geometry. Experimentally, the open- geometry data are taken simultaneously with the hohhaum data by focusing one of the laser beams on the outside of the hohlraum. The brightnesses of the laser spot outside the hohlraum and the hohlraum laser spot are roughly equal, so that the increase in hohlraum x-ray conversion efficiency is consistent with this increase in the x-ray emission region. Experiments by Sigel et al. “’ at 300 ps did not show this increase in conversion efficiency relative to disk mea- surements. Figure 59 shows the reemitted flux from their spherical cavity experiments (obtained from x-ray emission through a diagnostic hole) versus the source flux (based on disk measurements) in the hohlraum. The theoretically pre- dicted reemitted flux, as shown, is consistent with the disk Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp a) -2 1 k ZO.8 f ‘zi g 0.6 z 0 ii 0.4 a s a 0.2 2 0 I I I I I $ ‘CA 80 ifi .g 70 a,lu s-3 60 -0 $ cs ZT 40 50 ob 30 o- m 20 $ 10 I Nova (Au disks) LLWLANL spheres (24 beams on Omega) 0 1 2 3 4 5 0 0.5 1.5 2.5 3.5 = (W z (ns) (0.65 ns) LLWLANL sks (1.0 ns) (I&J $5 keV) Nova Au disks (hv <3 keV) 10’3 10’4 10’5 10’6 incident laser intensity (I) FIG. 57. IFme-resolved and time-integrated x-ray measurements from open-geometry experiments show an increase in x-ray conversion efficiency with increasing laser pulsewidth and a decrease with increasing intensity. conversion efficiency and not with a much higher efficiency. The equivalent Nova experiments have not been done. It is difficult to obtain drive measurements to an absolute accuracy better than about 10 eV or 15%-20% in x-ray tlux. 700 g (b) 600 2, 500 400 E 300 2 E 200 z 100 i Data from three shots ’ 0 0.2 0.4 0.6 0.8 1 Time (ns) FIG. 58. Data and postprocessed calculations (circled L) indicate that x-ray source size in hohlraums increases with time: (a) spot size at 452 eV, (b) spot size at 1200 eV. Phys. Plasmas, Vol. 2, No. 11, November 1995 First, the x-ray diodes of the Dante system are calibrated only to an accuracy of about 20%, and the Dante measure- ments are subject to diagnostic hole closure, which is diffi- cult to fully account for. Also, because of the current place- ment technique in the hohlraum wall, there are geometric shadowing effects on the witness plate, which can reduce the apparent temperature. Source flux S, (erglcm2s) FIG. 59. Experiments at Garching with low energy and short pulses do not see significant enhancement of x-ray production in hohlraums compared to open-geometry measurements. Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp gases showed that, except for a time delay compared to pure gold, the x-ray hot-spot image size and the contrast ratio of *bmllc ‘RctlD” Ar the hot spot to the background wall depended only we&y on hohlraum fill.‘65 Hence, the potential effects of self- generated magnetic fields on the laser spot are not readily evident in Nova experiments. However, it is valuable to es- timate the potential importance of magnetic fields for NIF targets. 109 2-D LASNEX neutron yield In LASNEX calculations, it is possible to include the ef- fects of magnetic fields by including the Braginskii transport coefficients’66-‘68 and the magnetic induction equation. The equation for the magnetic field B used in LASNEX is given FIG. 60. Experimental yields for pulse-shaped implosions are one-half to one-third those predicted by current 2-D LASNEX calculations. by’6;=vx,“xB+-$ (VPe-$L?j,, (157) Because capsule yields are sensitive to the drive, they provide additional data for evaluating drive. Figure 60 com- pares the measured to calculated yields for the ps22 symme- try experiments discussed in Sec. IX and the ps26 implosion experiments shown in Fig. 47. The observed yields are about a factor of 2 lower than calculated, which is consistent with about a 10 eV lower temperature’62 or to 15%-20% lower flux if the discrepancy is entirely the result of reduced drive. The calculations were integrated, two-dimensional (2-D) hohlraum calculations that included the capsule, so the ef- fects of flux asymmetry discussed in Sec. IX are included. Detailed mix calculations do not predict any significant yield reductions from hydrodynamic instabilities for these experi- ments, but it is possible that the yield reduction is coming from some effect other than drive. For example, Nova, with only five beams in each ring of beams, has a five-fold azi- muthal asymmetry, which is a three-dimensional (3-D) ef- fect, and cannot be included in 2-D calculations. Also, re- sidual random pointing and power variations between beams result in 3-D perturbations, which are not calculated. ICF3D, ‘63 a new code currently being developed for ICF ap- plications, will be able to address issues such as these in three dimensions. Experiments are currently being conducted to better quantify the drive. Most current calculations do not include the effects of self-generated magnetic fields. Although energy transport in hohlraums is dominated by radiation, magnetic field effects in the vicinity of the laser absorption could affect x-ray pro- duction. The importance of self-generated magnetic fields in hohlraum plasmas is complex both theoretically and experi- mentally. Theoretically, simple scaling arguments can pro- duce fields on the order of a megagauss (MG). Megagauss fields have been observed in open-geometry experiments.‘@ However, magnetic fields are affected by several source and loss terms of comparable importance, which vary differently in different parts of the plasmas. Consequently, it is not clear from scaling arguments alone where these fields are in rela- tion to the regions of large heat flux or radiation generation. The emission spot-size data and calculations in Fig. 58 for pure gold hohlraums on Nova show agreement without including magnetic fields. In symmetry experiments dis- cussed in Sec. IX, using hohlraums filled with a variety of R= -$ (c~,J,+a~JXb)+p, V,T,+/3/\bxVT,. r (159) If we just consider the V X (1In)VP source term, we have aB( MG) dt( ns) = 10e4 h Vn,xVT, (keV), (160) with distance in cm. For nanosecond time scales and gradi- ents typical of ICE targets, megagauss fields are obtained. The cross-field electron conduction coefficient KL is given by 166-169 ntT,Tci Ki=-.--- y;x2+ Y;, m, x4+S1x2+S0' (161) where n, is the electron density and m, is the electron mass and x=a~~~. The 6s and ys depend on z. The electron cyclotron frequency a= 1.76X 10’3Z3(MG), and the electron-ion collision frequency rci= ( 1.09 X 1 O- ’ *)Tz”/ [z In h(n,l102’)], so that 312 x=fi7ri= 1.92X 102 B(MG)Te (keV) 2 In h(n,/102’) ’ (162) In the limit of xz> 1, the transport from Eq. (161) is reduced by a factor K,op 1) r;RY(po) I K(X=O) = (flTei12 w(oT7,i)2* (1631 One way to estimate the importance of magnetic field effects on NIF relative to Nova targets is to examine how the terms in the magnetic field generation equation scale. Since the NIF target has nearly the same plasma densities, tempera- tures, and fluid velocities as discussed in Sec. XI, the scaling of the terms in the induction equation (157) is given by VX( l/n)VP=(l/pt)Vn xVT source term - i/scale2, VXJ diffusion term - 1 /scale2, @-nonlinear functions of B, VX B convection term -l/scale, JX B Hall term -l/scale2, and VT terms -l/scale’. The source terms and dissipation terms have neatly the same l/scale2 dependence. The time available for the mag- 3978 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp netic fields to develop is proportional to scale. If the gradient scale for the magnetic fields is proportional to the hohlraum scale, one would expect NIF to have smaller magnetic fields than Nova targets. However, in some regions of the hohl- raum, the gradient scale depends only weakly on the hohl- raum size. As a quantitative test of the importance of magnetic fields on NIF targets, we have included the magnetic field equation in a detailed LASNEX NIF hohlraum calculation’70 for the baseline PT target described in Sec. XIII. This calcu- lation was run for the duration of the high-power part of the NIF pulse. Throughout the pulse in this calculation, 61r,,<l in the region of heat flow and radiation generation. Magnetic fields had less than a 5% effect on the energy delivered to the capsule. There are regions in the hohlraum with fl~7,,>1, although not in places where electron heat flow to the hohl- raums walls is significant. These results are obviously quite preliminary. However, there is no evidence that magnetic fields cause significant transport effects on Nova or will cause major problems on NIF. Even if magnetic fields became large enough to affect the size of the hot spot or the x-ray production region, they would not affect radiation transport significantly. As dis- cussed in Sec. IX, the radiation distribution in a hohlraum is quite insensitive to the laser spot size, as Iong as its centroid is well defined. IX. HOHLRAUM RADIATION UNIFORMITY The optimal choice for the ratio of hohlraum case area to capsule area is strongly affected by the need to achieve a very high degree of flux uniformity on the capsule. From Eq. (2), we have, approximately, SV 6R 1 r 3 61 v “R<-j-R--T-p 064) where the intensity dependence comes from the rocket equa- tion, Eq. (53), for a radiation-driven rocket. Since 2&R ,,#-<40 is typical, we require energy fluxes to the capsule that are uniform to about 1%. The tolerable degree of asymmetry depends on the ignition margin available. For the NIF ignition capsules, we have allowed a factor of 2 in im- plosion energy to account for the degradation expected from both asymmetry and mix. For asymmetry alone, these cap- sules will ignite with an imploded fuel that has SR>r/2. However, in order to tolerate both the effects of hydrody- namic instability and mix, we specify 6R<r14. If the case radius is large compared to the capsule radius, hohlraums are very effective at smoothing all but the longest-wavelength perturbations. Analytical results can readily be obtained for the example of a spherical capsule of radius R,, inside a spherical case of radius R,, .171p172 If a Legendre polynomial perturbation of order 1 is applied on the inside of the case, the resultant perturbation on the capsule is as shown in Fig. 61. If the case radius is about four times the capsule radius, all modes but the P, component are smoothed by about two orders of magnitude. When RwdllRcap=5, P, passes through zero. If a capsule is chosen so that it passes through this value as it implodes, very small lo outer oph’em LJ%P..b FIG. 6 1. Hohlraums with Rwti/Rcapsule from about 3-S effectively smooth all but the P, Legendre polynomial Hux variations. average levels of P, can be achieved. The’reason for smooth- ing short-wavelength modes is easy to understand. If we as- sume that the channel is thin to radiation transport, then any point on the surface of the capsule averages flux from a large fraction of the hohlraum solid angle. In this process, all high- spatial-frequency modes are averaged out. In practice, a de- sire to maximize hohlraum coupling efficiency often results in Rwd/Rcap<4, at least at early times. Therefore, both P, and P, can be issues. For nonspherical hohlraums, the situ- ation is somewhat more complicated because coupling be- tween modes173 occurs for finite-size capsules. If a pure P2 is applied to the case, P, and all higher modes appear at the capsule. This occurs because different points on the capsule see different solid angles and hence have different smoothing factors. This changes the shape of the perturbation, which is equivaIent to adding harmonics of the applied mode. Figure 62 shows the coupling’74 between P, and P, for a cylindrical hohlraum that has a length-to-diameter ratio of 1.75, typical of laser-driven hohh-aums on Nova or an ignition experi- ment. Figure 62(a) shows the P, and P4 at the capsule for a Pz( P4) applied at the case. The principal effect of this cou- pling is to slightly shift the optimal pointing location for capsule symmetry in the discussion below. In Fig. 6 1, all odd harmonics have been ignored because of an assumed left-right symmetry to the hohlraum. This imposes a power balance and pointing accuracy specification on the laser. (In Sec. XIII, Figs. 116 and 117 show the RMS flux asymmetry in all modes as a function of power balance and pointing accuracy for the NIF ignition targets.) The long-wavelength P2 component must be smoothed by choosing either the appropriate hohlraum geometry or laser geometry. With N rings of beams, it is possible’75 to exactly eliminate all the Legendre moments with 1 Cl <2N - 1. If the number of beams in each ring is equal to 2N- 1 or more, then the spherical harmonic modes Yy with m <2N- 1 are eliminated as well. In a hohlraum with no holes, the rings must be placed at the zeros of the Legendre polynomial of order N. The beams in each ring must be uniformly spaced around the ring, and the intensities of the Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3979 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp P2 applied lo hohlraum (Is 1.7 r,,,,,,,-,) P, applied to hohlraum (I= 1.7 r,,ohl,aum) 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 'csp 'up %ohhum ~h.hl"U" FIG. 62. Coupling occurs between Legendre polynomial spatial harmonic modes in nonspherical hohlraums. rings must be proportional to the Gaussian quadrature weight for that angle. Holes in a hohlraum wall can be treated as a negative source, and a very similar analysis applies. For example, if the hohlraum wall is heated and the laser beams are suddenly turned off so that no flux comes from the beams, then a significant negative P,IP, occurs because of the holes. For a typical laser hohlraum, holes covers about 5% of the solid angle, and P,IPo= -0.227 from the holes. To balance this asymmetry,the centroid of the laser emission must move to- ward the LEHs. Because the hohlraum wall has a time- varying albedo and because of plasma blowoff from the hohlraum wall, which changes the angular position of the laser beams relative to the capsule, symmetry in hohlraums also is time varying. Because the interior of an ICF hohlraum is initially empty or filled with a low-density, optically thin gas and remains largely optically thin during the laser pulse, the dif- fusion approximation used for losses into the hohlraum wall in Sec. VIII does not apply to transport within a hohlraum. When blowoff from the hohlraum wall is important in determining the spatial distribution of sources and sinks of x-ray energy in the hohlraum, or when material in the hohl- raum approaches an optical depth, the coupled hydrodynam- ics and radiation transfer equations’76 must be solved. Sev- eral models-including Monte Carlo, P,, and S-have been developed to solve the radiative transfer equation The Monte Carlo probabilistic methods, which have been consid- ered as the main reference for comparing other approxima- tions, were first applied by Fleck.‘77 The spherical harmonic method, or P,, methodr7* is based on the expansion of the specific intensity into spherical harmonics. When only the first two terms of the expansion are used, the Eddington or diffusion approximation is obtained. The discrete ordinates, OrSNt method’79 solves the transport equation for a series of specific angles. If blowoff is unimportant, a “view factor” calculation’80.‘s’ can be used. This approximation assumes 9 Laser 43 ,’ source A’ ring A./ ,I’ /’ 43 ---_-------- w-4; T- Laser HUH ____ _____ entrance 1 ““‘7@(LEMI* t Hohlraum wall kv, R, FIG. 63. A simplified spherical hohlraum is used to analyze hohlraum sym- metry. vacuum radiation transport between the surface coupled to a wall loss model, such as Eq. (124). However, significant insight can be obtained from an even simpler analytical model that can be used to estimate the required location of the laser spots at various times, as well as the sensitivity of the symmetry to deviations from the optimal position.‘82 The hohlraum is assumed to be spheri- cal, although the analysis also can be done for cylinders.‘83 For purposes of this discussion&he effect of the capsule on hohlraum symmetry is small and is ignored. Although the model is readily generalized, we also assume for most of the analysis that there is a single LEH and a single ring of laser beams on each side of the hohlraum, as shown in Fig. 63, The laser-beam ring is located at an angular location B rela- tive to the capsule axis. The position or relative powers for multiple rings would be chosen so that their power-weighted P, is the same as that for a single ring. The flux at any point on a capsule comes from both the laser-heated region and the x-ray-heated wall. Only the flux from the laser-ilIummated region is sensitive to the pointing accuracy of the laser. The flux from the x-ray-heated wall is essentially independent of exactly where the Iaser hits the wal1. As the wall albedo increases, so does the ratio of the pointing-insensitive flux from the x-ray-heated wall to that from the laser-heated re- gions. We define I, to be the x-ray source intensity provided by the laser, and the blackbody emission from the wall to be I,= 10m2fl, where T, is in units of IO2 eV, as before, and I,, which is in units of lOI5 W/cm2, is assumed to be uni- form throughout the hohlraum. Although this assumption is not strictly valid, the variations within the hohlraum are rela- tively small for typical laser-driven hohlraums. The laser spot intensity is the excess brightness of the wall directly heated by the laser. The excess flux from the laser spots must supply the energy lost to the hohlraum wall, LEHs, and cap- sule. To lowest order, this flux is independent of the size or solid angle of the laser sources, but I, clearly depends on the size of the laser spots. A smaller spot must be more intense in order to produce the required energy. The ratio of the laser spot intensity to the wall intensity depends on the wall al- bedo and the sizes of the LEHs and the laser spot. If we ignore the capsule, we have 3980 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp where A, and A, are the areas of the laser spots and LEHs. The hohlraum wall loss for gold, E,, is given by Eq. (124), and the flux into the wall for constant temperature is dE,v C.3A, -=&,=3.2X 1O-3 Po.3sK,, 3g, dt Ok (165) where E, is in MJ, and A, and 7 are in cm2 and ns as before. The ratio of the laser x-ray intensity to the wall radiation intensity is then 1, 4, -=- Z w A, 066) For a sphere, the ratio of the areas is the same as the ratio of the solid angles, so we can also write (167) where C&, , s1,, and C& are the fractional solid angles of the wall, LEHs, and laser source regions. The ratio of the total power from the wall to that from the laser spots, F, is given by 4&W i 1 F=x= i [(l-CY)/ck!]+(~~ln,) ’ W-38) It is F that will determine the optimal pointing angle and the relaxation of the pointing requirements in a hohlraum. Add- ing a capsule to the analysis has the effect of adding a term C&,/fiw to the denominator, where C&, is the solid angle of the capsule as seen from a point on the wall. At t=O, the ratio of the wall emission to the laser spot emission is zero. But the total wall emission rapidly comes to dominate the emission from the laser spots. For example, for the ignition design, the drive temperature is about 300 eV, while most of the energy is being delivered,, and the pulse width is about 3 ns. The drive temperature is about 100 eV during the foot, a duration of about 10 ns. Figure 64(a) is a plot of F versus time at 100 and 300 eV for a case with LEHs that cover 5% of the total solid angle. Even at 100 eV, the total flux from the wall exceeds that from the laser spot in less than 100 ps. During an interval of a few hundred picoseconds, while the albedo and optimal pointing position are changing rap- idly, the flux symmetry in hohlraums can vary greatly with time, but ignition capsules can tolerate a high degree of asymmetry for times this short (see Fig. 115 and the discus- sion in Sec. XIII for the baseline NIF ignition hohlraum). In the case of a single ring of laser irradiation on each end of the hohkaum, the laser emission region will balance the P, from the hole if we have Z,(x)Pz(x)dx=O, (169) where x=cos 0. Assuming that the emission from the laser sources is uniform and that loss from the LEH is uniform, Eq. (169) is approximately equivalent to 1oor ’ I rlclllt , ( !I,,, 1 o-1 100 IO’ T (ns) 55 F FIG. 64. (a) The hohlraum smoothing factor F versus pulse length. Here F is the ratio of the x-ray flux from the hohlraum wall to the flux from the laser hot spots. (b) The required laser source angular location a to zero P2 versus hohlraum smoothing parameter F. As the hohlraum wall flux in- creases, the laser spot must be closer to the laser entrance hole (LEH) to compensate for the deficit in flux from the LEH. This expression is accurate to terms of order R3/4 in the fraction_al solid angles of the laser sources and LEHs. In Eq. (170), X is the average value of cos 0 for the LEH or the laser source location. Using the expression for F from Eq. (168), we have - QH P~W,A=P~(XH) K F [(I-(y)/a]+(nH/&) (171) The effect of the capsule could be included by adding an- other term, f12,/f&,,, to the denominator in F, as discussed earlier. Figure 64(b) plots the required location of the center of emission for the two-ring case as a function of F for holes that cover 5% of the solid angle. This angle is measured relative to the center of the capsule, so 0’ is the axis of the hohlraum. Only the angle of one of the two rings is given. The other ring is located symmetrically on the other end of the hohlraum. If the holes were smaller, the required shift in angle would be less. One effect that is apparent from Figs. 64(a) and 64(b) is that a rapid change in hohhaum tempera- ture results in a rapid shift in the optimal pointing angle (or power balance for multiple rings). This occurs because there is a drop in albedo, or F, which accompanies a rapid tem- perature change. For example, as seen in Fig. 64(a), it would take 600 ps at 300 eV to reach the albedo, or value of F, that was achieved after 10 ns at 100 eV. Equation (17 1) can be generalized to more rings of laser sources and to higher-order perturbation& With two rings per side, we can generalize F to be (172) Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3981 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp The condition for balancing P, is then given by P2(Xs,)E+P2(Xs*)(1-~)=P*(XH) $+=h,, w (173) where E and 1 -E are the fractional powers in each ring. With two rings per side, the power in each ring can be varied in time so that the location of the centroid of emission is always at the angular location required to eliminate the P, flux variation. If the initial ring positions are at the zeros in P,, at 8=39.23” and 90” relative to the capsule center, then P, as well as P, can be zeroed at time zero. For these locations, the expression for E is given by - QH 0.4-P,(x,) n, F (174) At time zero, the relative powers in the beams must be the Gaussian quadrature weights. To satisfy this requirement, the ratio of the power in the inner ring from each side to that in the outer ring on each side is 0.8 at t=O. Then, P, is con- trolled by changing E and can be zerod as long as the re- quired emission location does not move to a lower angle than the location of the outer ring. The time-varying albedo discussed previously causes a time variation in the optimal pointing angle for the laser beams-or a time variation in capsule flux symmetry-for a fixed pointing angle. Plasma blowoff from the hohlraum wall has the effect of changing the source angle in time, relative to the capsule, for a fixed pointing direction. As plasma blows off the wall, the laser absorption and x-ray emission also move off the wall. This has the effect of moving the angle of the laser source relative to the capsule back toward the LEH. Although the position of the critical surface never moves very far from the original hohlraum wall, the absorp- tion position can move far from the original wall. Inverse bremsstrahlung is very efficient at absorbing the laser light in high-2 material, even at densities well below the critical den- sity. The inverse bremsstrahlung absorption length is given approximately bylg4 h I.B.km) = 0.56X2T~‘2(keV) (nln,)2z In A ’ (175) where h is the laser wavelength in micrometers. In gold or other high-Z hohlraum wall material, the absorption length is less than 0.1 cm for nln,=O.l at a temperature of 4 keV, which is typical for the laser propagation channel, as dis- cussed below. This is comparable to the scale of a Nova hohlraum, but only about $ the scale of an ignition-scale hohlraum. Absorption lengths in gold near nln,=i seldom exceed - 100 pm for a laser with X=0.35 ,um. For both the NIF hohlraum and the Nova experiments described above, the density along much of the laser propa- gation path has nln,=O. 1, and the electron temperature T,=3-5 keV. In both cases, the laser intensity Z-l-2X lOI W/cm’. For Nova-scale hohlraums, the laser is able to propa- gate through this plasma, even in gold, and most of the laser light is absorbed fairly close to the wall in higher-density, lower-temperature gold near n/n,=& In NIF-scale hohl- raums, which are about four times the size of those on Nova, Hohlraum with fnftlal low-Zgas flfl or tow.2 liner FIG. 65. Ignition-scale hohlraums use low-2 liners or gas fill to eliminate excessive wall spot motion. inverse bremsstrahlung in gold at nln,=O.I is large enough that the Iaser absorption and x-ray emission region move- ment from the original wall makes it very difficult to main- tain radiation symmetry. The fix for this effect, recognized in 1978 at LLNL,lg5 is to displace the high-density gold blowoff with lower-density material. Two approaches to this have been tried: (1) a low-Z liner on the gold, which blows off to fill the hohlraum inte- rior with low Z’“6,‘87 and (2) an initial gas fill of the hohlraum. t85.187.188 The effect of such low-Z material is indicated schemati- cally in Fig. 65. With an all-gold hohlraum, the location of the emission region moves below the 40” minimum angle required to balance the negative P2 from the hole, so it would not be possible to achieve symmetry at a late time. With either a low-Z liner or gas fill, the motion of the emis- sion location off the initial hohlraum wall is limited to an acceptable degree. Neither of these approaches stop the high- density gold blowoff, but they displace the low-density gold blowoff (below a density of nln,==O.l on NIF targee de- signs), so the laser beam can propagate close to the initial wall position on NIF targets. As in Nova targets, most of the absorption then occurs in a thin gold layer near n/n,= i. Low Z has little effect on Nova targets because the beam already could propagate to a position near the wall. Initial NIF target designs18’ and Nova experiments to test these designs used a low-Z liner that was viewed as a simpler fabrication approach. As expected from calculations, the Nova experiments with a liner showed the same asymmetry versus pointing as an unlined gold hohlraum with the same pulse length. ‘89 The principa1 purpose of the Nova experi- ments was to see if any adverse plasma coupling effects would be seen when the laser propagated through the low-2 plasma rather than a gold plasma. However, detailed modeling of the NIF targets showed that the NIF capsule symmetry was adversely affected by a hydrodynamic pressure pulse, which was generated by stag- nation of the liner blowoff on the axis of the hohlraum. Our code, LASNEX, is cylindrically symmetric and may exagger- ate this stagnation. Hohlraums also could be designed to pre- vent a focused axial stagnation. This or other hohlraum modifications may result in a target with a liner that can provide a low-Z fill in NIF hohlraums. Because a gas-filled hohlraum, the original approach used in the 1978 calculations,‘@ does not have this stagna- tion problem, it was adopted as the NIF baseline design. This approach also was evaluated in 1988 for the proposed Laser Microfusion Facility (LMF) targets.‘** 3982 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Capsules being designed for ignition can tolerate some time variation in symmetry without performance degrada- tion, but the magnitude of the symmetry swings must be kept below a maximum that depends on the temporal history of the time variations. Without introducing initial spatial varia- tions in composition or thickness, capsules with a time- varying P2 cannot be corrected simultaneously in velocity and position. Azimuthal variations in radial velocity intro- duce azimuthal pressure variations, which generate azi- muthal mass flow. For small-amplitude or short-duration in- tensity variations, these effects are largely reversible if the sign of the flux variations is reversed to give a uniform time- averaged flux. However, after an azimuthal flux variation that persists for a substantial fraction of the pulse, subse- quent reversal of the flux nonuniformity will not entirely remove the effects of the earlier asymmetry. If the effect of the P2 is tuned so that the capsule is spherical at ignition, then velocity and density generally will vary from pole to waist. If the capsule is tuned to minimize velocity and den- sity variations at ignition, then the implosion will be asym- metric. As discussed in the Introduction, an asymmetric im- plosion converts less of the available kinetic energy into internal energy, resulting in lower peak pressure and a higher ignition threshold. The effect of time-dependent, long-wavelength asymme- try was examined in 1988 for the proposed LMF capsules. This work prompted us in 1988 to propose a system (for the LMF and later for the NIF) with two cones of beams on each side in order to ensure control of time-dependent P, asym- metry. Work on NIF ignition capsule implosions was initi- ated in 1990, when the NIF was proposed, and continues today. Excessive time-dependent asymmetry can cause jet- ting of material in the radial direction. Such jetting was seen in 1990 NIE target calculations, in which a single cone of beams per side was used instead of two. In this case, the time-varying P, and P4 asymmetry are bad enough to cause capsule failure. The early-time, positive asymmetry drives material to the waist, and then, upon deceleration, this mate- rial falls as a curtain on the waist plane, quenching ignition. igo This issue is discussed in more detail in Sec. XIII. There are several possible techniques for controlling time-dependent symmetry. For example, a slot could be cut in the waist of the hohhaum to exactly balance the P, effect of the hole. The optimum location of the beam spots is then independent of time. This strategy would cost about 20%- 30% in energy. The same effect also could be accomplished by reducing the albedo over a somewhat larger area near the waist of the hohlraum. Alternately, one could put a high-2 disk in the hohhaum between the capsule and the entrance hole. In the limit that this disk has the same albedo as the rest of the hohlraum and shields the entire capsule from the hole, this eliminates P, caused by the LEH and again gives a time-independent solution to the optimal beam location. However, neither of these approaches, by itself, eliminates the effect of the time-dependent location of the emission re- gion. Other approaches-such as layered hohlraum walls-to provide a space- and time-varying albedo are pos- sible, and additional internal structure can be added to elimi- interior filled with FIG. 66. To provide the required capsule flux uniformity, the NF will use a large number of beamlets arrayed in,two concentric cones on each side of the hohlraum. nate P4, if necessary, to optimize hohlraum coupling efficiency.‘s’ As shown schematically in Fig. 66, for the NIF laser, which has 192 beams in 48 clusters of 4, we intend to control the time-varying flux symmetry by using two rings per side in the hohlraum and by varying the power ratio between the two rings.‘g* This approach has been called “beam phasing.” The current baseline hohlraum design uses a 0.8 mg/cm3 He/Ha gas fill to minimize the motion of the laser spot and to minimize laser absorption in the propagation path of the la- ser. This design is discussed in more detail in Sec. XIII. To estimate the magnitude of the asymmetry at the hohl- raum wall, which would occur from a pointing error, (PdPOLll can be written as 5rP2(Xs)-P2(XH)(~;1H/~Zw)Fl l+F (176) The error introduced by deviations from the optimal angle are reduced by the factor 1 +F, compared to those that would occur at t=O (F=O) or with no hohlraum. For the two-ring example used here, at F =O, P,IPo= 1% for a pointing error S1$~=0.08~. For the case of two rings per side, the required pointing angle of the centroid of emission is obtained by varying the ratio of power in the two rings so that a pointing error corresponds to a power imbalance between the two rings. For the NIF ignition capsule design (see Fig. 107 in Sec. XIII), the time integral of P21Po must be reduced below about 1%. Because most of the energy is delivered while 1 + F= IO, this corresponds to about a 1” placement error in the average position of the rings. For the NIF hohlraum (see Fig. 106 in Sec. XIII), a 1” ring placement error corresponds to about a 100 ,um movement of the ring along the wall at the initial radius for a ring at 50” relative to the capsule. Since many beams will make up the laser rings, the pointing accuracy for individual beams is further relaxed from the average aiming accuracy by a factor of 2 or more, depending on how the pulse shaping is carried out. {Detailed calcula- tions for the NIF ignition targets are discussed in Sec. XIII.) The symmetry for an ignition capsule would be iterated by a variety of techniques, such as imaging the shape of a shock front propagating through a foam ball, as described below, or symmetry capsules specially designed to sample flux uniformity during varying fractions of the ignition- Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3983 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 3-&m-thick-tungstsn hohl!%xim Ten-beam lrradlatlon Laser energy -18 kJ (total) Wavelength = 0.35 pm Pulse length q I ns (FWHM) FIG. 67. X-ray imaging of thin-wall hohlraums shows high absorption and little spot motion or beam spreading for 1 ns pulses (1986 Nova data): (a) relative beam pointing for a scale- 1 .O hohlraum (ten beams); (b) relative beam spot positions, as imaged with a -50 pm resolution pinhole camera. capsule laser pulse. The power ratio of the rings would be adjusted to obtain symmetry for each of a succession of sym- metry capsules that would sample successively longer por- tions of the entire pulse. The beam placement specifications discussed in Sec. XIII are chosen to provide the reproduc- ibility required for such an iterative technique. In addition to direct capsule measurements of symmetry, experimental measurements of the x-ray spot motion and Experiment .c - -\ 1% witness plate (a;One&ded lllumlnatlon (b) Two-sided lllumlnatlon Data Comparison with calculation I 200 -1 > 23 ATf l-b 730.15 CT-, c ,I \ \ I’ \ tl \ \ 0 Experiment - - WALLE / I I I 0 500 1000 x (km) FIG. 68. Knowledge of laser deposition and radiation transport makes possible accurate modeling of wall heating uniformity. 3984 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp hohlraum walI albedo provide significant information on time variation of the capsule symmetry. These experiments, in effect, specify the functional form of the time-dependent symmetry from the LEH and wall motion. The implosion experiments then determine the time average of this func- tional form. Wall-loss experiments, such as those discussed in Fig. 55, are related-through Eqs. (134), (16X), and (171)-to the desired angular location of the x-ray emission. Experiments, such as those on Nova discussed below, can also measure the actual location of the laser-generated hot spots and their motion due to wall blowoff and refraction. With the constraints imposed by such measurements, a time- integrated measurement of implosion symmetry for the igni- tion experiments may be adequate to ensure that the time variations are acceptable. For example, the uncertainty in the wall opacity obtained from wall-loss experiments will result in an uncertainty in the power or pointing required for opti- mal symmetry in an ignition hohlraum. However, a 30% un- certainty in opacity would result in only about a 1” uncer- tainty in the optimal location of the average laser hot-spot position or a 1% uncertainty in the time-dependent asymme- try at the peak of the laser pulse. This is well within tolerable limits if the time-integrated flux is uniform. The Nova spot- motion experiments discussed below have an error bar of about 50 ,um on the measurement of the centroid of x-ray emission. Experiments with this level of accuracy on an ig- nition experiment would result in a < 1% uncertainty in the time-dependent asymmetry from spot motion. With two rings of beams per side, as proposed for the NIF, the relative brightness of the two rings also would have to be determined to a few percent, as indicated in Table VIII in Sec. XIII. A wide variety of experiments have been carried out on Nova to test the control of hohlraum symmetry. Thin-walled hohlraums, which transmit x rays with hv>3-5 keV were used to determine the location of laser light absorption.” Figure 67 shows the results of a thin-walled hohlraum ex- periment with a 1 ns pulse. This experiment demonstrated high absorption and little spot motion at the geometric posi- tion of the laser beam spot. More recent experiments on Nova, lg2 which use a time-gated x-ray framing camera, can be used to obtain time-resolved information about the high- energy x-ray emission from pulse-shaped hohlraums. Uniform-thickness witness plates also were placed in the hohlraum wall” in early Nova experiments to measure tem- perature gradients. As shown in Fig. 68, the time variation in shock breakout is related to the temperature gradient. For a hohlraum with a single ring of beams, the gradient is very large. With two rings, the gradient along the aluminum plate is only a few electron volts. Both results were as expected from calculations. Since Nova has only a single ring of beams per side, as shown schematically in Fig. 10, it is possible to eliminate only the average of P2. The residual time variation in flux uniformity produces the lateral mass motion described above. On Nova, these effects become significant for conver- gence ratios greater than about 10. Since the purpose of the Nova symmetry experiments was to determine only average flux uniformity, convergence ratios were limited to about 10, sufficient for a 1% average flux measurement without the Phys. Plasmas, Vol. 2, No. 11, November 1995 added complexity of the distortion generated by the time dependence of the flux uniformity. Beginning with experiments in 1986,” the time- averaged symmetry on Nova has been demonstrated by im- ploding capsules and imaging the imploded fuel volume. The fuel is imaged by using either an x-ray pinhole framing cameralg3 or a time-integrated ring aperture microscope (RAM).lg4 The RAM uses penumbral imaging with a ring slit to obtain about ten times better signal-to-noise ratio than a pinhole camera with a comparable resolution. The framing camera consists of a series of as many as 16 pinholes that image onto a microchannel plate (MCP). When a 100 ps voltage pulse is propagated across the MCP, the image from any given pinhole is recorded during the time this pulse is propagating across that portion of the MCP that is receiving photons from that pinhole. The time between individual im- ages can be adjusted independently in the camera used to take the images shown in Fig. 69. Capsules used in these experiments are the same as those shown in Fig. 42. The sign and magnitude of P2 can be varied by changing either the hohlraum length or the beam pointing. Figure 70 shows the results of changing the beam pointing. We define the capsule pole as the portion of the capsule on the axis of rotation. The waist is the portion of the capsule along the hohlraum midplane. When the hohlraum is elongated, as in the left image, the position of the laser beams is closer to the LEH than is required to achieve uniform average flux, result- ing in a “pancake” implosion. As the hohlraum is shortened, as shown in the right image, the illumination from the two rings of laser beams approaches the capsule waist, and the average flux delivered to the waist begins to exceed that delivered to the poles, resulting in a “sausage” implosion. Between these two extremes, the laser spots are at the opti- mum position for which the average P, component is zero, and the implosion appears spherical. The center image is spherical within the measurement accuracy of a few percent in flux. An interesting feature of the sausage image is the rotation of the image axis away from the hohlraum axis. This -. .:. Caselcapsule t~1.45 ns area ratio 16 -,yy .: * 7, .:i:...:::: ;,+ :.:y = 0 t =‘I 36 ns tnl.71 ns R t (ns) FIG. 69. The 100 psresolution, x-ray framing cameras are used to observe the imploding capsule and to infer hohlraum drive symmetry. Review Article 3985 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp outwnrd polniing Inward-pointing @I (0) FIG. 70. Nova experiments have used x-ray imaging of imploding capsules to test the modeling of hohlraum drive asymmetries. Observed x-ray image shapes confirm the calculated variation of the implosion shape with beam pointing: (a) outward-pointing shifts produce pole-high fluxes or “pancake” images; (b) symmetric: (c) inward-pointing shifts produce waist-high fluxes or “sausaged” images. The tilted axis in (c) shows the effects of beam imbalance and pointing errors prior to the Precision Nova improvements. type of nonaxial distortion occurred frequently on Nova prior to the power balance and pointing improvements achieved in the “Precision Nova” Project. The pointing accuracy and power balance goals specified for Precision Nova recently have been achieved,“’ with pointing accuracy improved from about 100 ,um to the Precision Nova goal of 30 pm [see Fig. 7 1 (a)]. The power balance has been improved about a factor of 2, to 5%, during the high-power part of the pulse and to less than 10% during the low-power foot of the pulse [see Fig. 71(b)] for the 20 kJ pulse shape used for the high- density, high-convergence HEP- 1 implosions described in Sec. X. With these specifications, Nova implosions can be carried out repeatedly within a 1% variation in the average flux uniformity. Figure 7 1 (c) shows that Nova is now capable of meeting the Precision Nova power balance specifications for a pulse having a 1O:l contrast ratio and delivering more than 40 kJ. Table III lists the different types of pulse shapes and hohlraums that have been used in symmetry experiments. Constant-power, 1 ns pulses: the 3:1-contrast, 2.2 ns, ps22 pulse; and the 8: l-contrast, ps23 pulse have all been used. [The last two pulse shapes and their witness-plate shock tra- jectories were shown in Figs. 40(c) and 40(d).] Gold hohl- raums without liners, hohlraums with CH and nickel liners, and hohlraums with methane gas fill have been tested. Most of the symmetry experiments were carried out with ps22, which produces plasma conditions and spot motion that are very close to those of NIF target designs. The symmetry experiments with liners were carried out before choosing a gas-filled hohlraum as the baseline target for the NIF. Symmetry experiments on gas-filled hohlraums began on Nova during the summer of 1994 and are continu- ing. Because the presence of low-Z material in the hohlraum during the high-power part of the pulse did not adversely affect the low-Z liner experiments, any difference between the lined and gas-filled hohlraums are expected to result pri- marily from startup effects. The gas-filled hohlraums present more of a computational challenge because of the presence (8) i3a8m pointing (10 ban*) &I) PCWW balance (10 beams) -100 -1ikl 0 100 Azlmuthlll affsef @I) Pmlsion NOW goal: 30 WII 2.5 2.0 1.5 1.0 0.5 0 500 low 1500 2ow 25w nme W Pnclsion Nova goal: 5-10s (c) PCWW balance Es, E 41.4 kJ 3, Wme (nr) FIG. 71. The Nova laser power balance and beam pointing were improved by a factor of 2-3 in the Precision Nova project. These improvements were required for high-precision symmetry experiments and high-convergence implosions. of a window on the hohlraum LEH to contain the gas and because of a transient as the laser beam initially propagates through the window and gas. Gas-filled hohlraums also have been used for the plasma scaling experiments described in Sec. XI. For all the Nova experiments discussed below, the hohl- raums were 1600 pm in diameter with a 1200 ,um LEH. Pointing positions refer to the distance between the hohlraum midplane and the plane at which the central ray of all the beams on one side would intersect as they pass through the axis of the hohlraum, as shown schematically in Fig. 72. This distance fixes the angle between the capsme axis and the x-ray emission region and is the principal determinant of the resultant implosion symmetry. In “normal focusing” for most Nova implosion experiments, all beams pass through the origin in the plane of the LEH. For a given LEH size, this gives the greatest clearance between the laser beams and the hohlraum wall. This is the focusing for experiments in which symmetry is changed by varying the hohlraum length. As indicated in Table III, experiments also have been done with constant-length hohlraums in which symmetry is changed by varying the beam focal position relative to the LEH. These two types of experiments give essentially the same results until the laser beams for the constant-length hohhaum ex- periments begin strongly interacting with plasma from the LEH. Most of the symmetry experiments and modeling dis- cussed hereafter were carried out on Nova between 1991 and 1993 as a joint effort by Livermore and Los Alamos.‘g2~‘8g Similar experiments have been carried out on the GEKKO XII laser.27 To date, hohlraums driven with ps22 have been tested under the widest range of different hohlraum and pointing 3986 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp TABLE lII. An extensive hohlraum symmetry database has been developed on Nova. Au, fixed Au, Ni-line Au, Ni-lined Au, CH-lined CH4 gas-filled, length, variable fixed length, variable Au, variable variable variable length, variable length, length, length, focus fixed focus focus fixed focus fixed focus fixed focus E ! ffi x X X X 1 n-3 1 nr ps22 5 m X X X X X X - 3:l 2.2 ns ps23 lImz?l X 6:l 2.6 3.2 ns ns variations. Figure 72 shows the results of experiments and calculations for ps22 in hohlraums lined with 150 nm of nickel. For these experiments, the beam crossing position was in the plane of the LEH, so the beam-pointing position is also the hohlraum half-length, and symmetry is plotted ver- sus hohlraum half-length. The capsule distortion is the ratio of the capsule waist dimension to that along the hohlraum axis. The log of distortion is linearly proportion to average flux nonuniformity. For ps22 implosions, a 2~1 distortion of the fuel corresponds to a 5% average asymmetry. As seen in Fig. 72, the agreement between experiment and the LASNEX calculations is quite good. Most of the data for the symmetry experiments were collected before the Precision Nova improvements were completed, and typical experiments with nominally the same Time (nr) (fj) ‘i oo~oo +%+&¶;;;\ 0.1 900 1100 ,300 ,800 Pointing position (pm) PIG. 72. J.,ASNW[ calculations do an excellent job of modeling symmetry for experiments in which laser pointing is kept fixed at the plane of the LEH as the hohlraum length is varied for pure-gold and lined hohlraums.‘“’ Phys. Plasmas, Vol. 2, No. 11, November 1995 conditions could have a shot-to-shot symmetry variation of several percent. Hovever, with Precision Nova improve- ments, experiments reproducible to within 1% in average asymmetry are possible, as shown in Fig. 73 (again for ps22 experiments). The yield from these Precision Nova experi- ments is also highly reproducible, as shown in Fig. 74. At a temperatures of l-2 keV produced in these implosions, the approximate factor-of-2 shot-to-shot yield variation corre- sponds to a reproducibility within + 10% in ion temperature. The focus of gas-filled hohlraum experiments has been on the ps22 pulse in hohlraums filled with 1 atm of methane.lg5 When ionized, this gas has a density nln,=0.03, about the same as the NIF baseline hohlraum (see Fig. 106 in Sec. XIII). At a later time, the gas compresses to n/n,-0.1, also comparable to the NIF targets (see Fig. 90 in Sec. XI). . . . . . . . . . ..I....... -; . ..1....... I . . . . . . . . . . . i . . . . . . . . . . . . . . . . . . . . . . . . . . 12W 1200 Hohlraum half length (pm) FIG. 73. Precision Nova implosions have shown excellent reproducibility of symmetry. Review Article 3987 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp . P At pointing of e best symmetry m 2:l ablate .’ From ps22 reproducibility series 10’ I I 1200 1300 Pointing position (q) PIG. 74. At best pointing, the scatter in the Precision Nova ps22 yields imply average T, is reproducible to less than I 10%. The work on gas-filled hohlraums is still being analyzed and the symmetry results discussed below are preliminary. De- tailed analysisrg6 of the gas hohlraum energetics experi- ments, indicates that no significant surprises are observed compared to the earlier lined hohlraums when measured lev- els of SBS and SRS are taken into account. A variation of capsule symmetry with hohlraum length for gas-filled hohlraums is reproducible and behaves the same as for lined and unlined hohlraums. However, as shown in Fig. 7.5, the gas-filled hohlraums have optimal symmetry for a target that is lo%-15% shorter than for the lined or unlined Nova hohlraums. Hohlraums with the standard poly- imide 6500 A windows and no gas fill also have optimal symmetry with a lo%-15% shorter hohlraum, as shown in Fig. 75. Optimal symmetry for a thinner, 3500 A window and no gas fill falls between the two cases. LASNEX calcula- tions correctly predict the slope of distortion versus pointing position, but are offset from the data by about 150 pm, about 15%-20% of the laser spot diameter. At a given pointing position, the symmetry shift is equal to about 5% in flux. Such a change in hohlraum length would cause no change in the NIF laser specifications. A promising explanation for this enhanced spot motion effect is refraction of laser beam tila- ments caused by flow of hohlraum plasma transverse to the laser beam propagation direction.1g7 As a laser beam filament is forming, plasma is ejected at the sound speed from the , Gold rime (nr) Pointing posItton (sm) 0 Experlmhnt (0000 h window only) A Exi.wlmsni (CH, 1 atm) +3-LASNEX (CH, 1 atm) PIG. 75. Symmetry experiments with gas-filled hohlraums show the same variations with pointing position as empty hohiraums, but the data are offset from the current LASNEX calculations by 150 ,um. 900 1300 Polnling d beet symmetiy lrum LASHEX ($Un) PIG. 76, LASNEX successfully predicts the pointing of best symmetry for almost all symmetry experiments. Beams must be moved inward for longer pulses to compensate for spot motion caused by hohlraum wall blowoff. The experimental pointing of best symmetry is offset from the calculations by - 150 pm for the methane-gas-filled hohlraums. The cause of this offset is being investigated. filament region. Without transverse flow, this process is sym- metric and the beam propagation direction is unaffected. With transverse flow, the formation process is asymmetric, effectively resulting in a density gradient transverse to the beam which causes beam deflection. The effect is largest near the sonic point, where matter trying to propagate in the upstream direction, persists for a long time. In hohlraums, the sonic point in the flow generally occurs near the laser entrance hole. For Nova’s unsmoothed beams, which are cur- rently used for the symmetry experiments, this plasma is calculated to be unstable to filamentation essentially through- out the pulse for the gas-filled hohlraums. Initially empty hohlraums on the other hand, do not develop enough gain for filamentation until late in the pulse. Experiments are in progress that are designed to determine the source of the shift. A convenient way of portraying the correspondence be- tween experiment and calculation for the symmetry experi- ments is shown in Fig. 76. This figure compares the caicu- lated and experimentally measured pointing of best symmetry for all of the combinations of hohlraums and pulse shapes tested. An interesting feature of Fig. 76 is the fact that, as the pulse length increases, the pointing of best sym- metry moves toward the capsule waist. This occurs because of the increased spot motion caused by the wall blowoff, as the pulse length is increased. To compensate for this in- creased motion, the initial pointing location must be moved inward. This motion of the x-ray emission region also has been measured directly in Nova experiments by cutting a slot in the hohlraum wall and looking at the axial location of the x-ray emission, from a beam on the opposite wall, as a func- tion of time. ‘8g*‘g8 Figure 77 shows a comparison of the ob- served and calculated locations of the emission for a ps22 experiment at an x-ray energy of 450 eV. The observed axial spot motion of about 200 pm agrees with the calculated value. This motion corresponds to a shift in the angular po- sition of emission relative to the capsule center of about 15”, comparable to that calculated for the individual cones of beams on the NIF target. As shown in Fig. 78, Nova experiments also have been 3988 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Position of emission 1; .o w ;B t 27% =lE ?I Time (ns) FIG. 77. The observed axial motion of the centroid of emission for ps22 is close to that calculated. In calculations, Nova beams are assumed to have a Gaussian profile, whereas the actual beam has significant structure, which makes identification of the beam centroid ambiguous.g6 used to determine the effects of putting a high-Z disk be- tween the LEH and the capsule.‘52 As discussed earlier, the high-Z disk reaches about the same temperature as the hohl- raum wall, effectively eliminating the negative P2 from the hoIe. Hence, a beam pointing in a standard hohlraum that gives a sausaged implosion produces a nearly spherical im- plosion when the disk is inserted. Figure 79 shows P21Po for the imploded shape as a function of the shield radius. Be- cause of spot motion, which is largely unaffected by the pres- “-:i -“‘-b z 1 +-yzJ l-q&A ] L J -0.6 I' "I ' "'I ' 'I 'I ' " " ' "" ' 'I 'I ' "'I ' I"' I 0 50 100 150 200 250 300 Shield radius (pm) FIG. 79. The effect of LEH shields on Nova hohlraums can be modeled quantitatively. ence of the disk, these implosions still have a time variation in symmetry. It may be possible to balance the effects of spot motion-which results in a progressiveIy larger flux to the capsule pole-by using a shaped disk or entrance hole that becomes more lossy at late times. The results shown in Figs. 73-79 represent a time- integrated measure of asymmetry. However, for the reasons discussed above, an implosion that has a time-average uni- form flux will have a flux at any instant that may be either pole high or waist high. Figure 80 shows a typical variation for a 1 ns, constant-power pulse. Very early in time, for the pointing chosen, the flux is pole high. Then, as the wall albedo increases, significant flux starts to come from all areas of the hohlraum wall except for the LEHs, and the flux be- comes waist high. As the hohlraum heats up, plasma blows 1-ns square laser pulse; identical pointing FIG. 78. Internal radiation shields modify implosion symmetry, in agreement with calculations. Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3989 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 0 0 0 Compressed core imagat FIG. 80. Time-dependent symmetry from a 1 ns pulse. Symmetry capsules that implode at different times in the pulse show different asymmetries. off the hohlraum walls, and the laser absorption region and x-ray production move inward, moving the x-ray emission more toward the pole, thus again making the flux on the capsule more pole high. Finally, when the laser beams shut off, there is no source to balance the holes, and the flux becomes waist high again. In Sec. XIII, Fig. 115 shows the equivalent time variation for a NIF target without using the “beam phasing” described previousIy to remove the time dependence. Several techniques are being developed to obtain time- dependent symmetry information. One approach uses the full pulse with a series of capsules designed to implode at differ- ent times during the pulse. Those capsules that implode early see only the early-time asymmetry, and a record of the evo- lution of asymmetry can be obtained as indicated in Fig. 80. Los Alamos has begun work on this approach,‘92 as shown in Fig. 81 for Nova experiments that used ps22. A second technique replaces the capsule with a uniform sphere of material, as shown in Fig. 82. The x-ray flux in the hohlraum will drive a shock into this material, which can be imaged by x-ray backlighting. When an appropriate combi- nation of sphere composition and density and x-ray back- lighter energy are chosen, a large opacity contrast is obtained (a) 0 0 35 km wall capsule 20 pm wall capsule W w at the shock. With different choices of x-ray energy or ma- terial, the ablation front rather than the shock front is more easily imaged. Distortion of the shock front is approximately related to the drive pressure nonuniformity by ; (equator-- Qole) = f g (&-I). (1771 For ps22, Fig. 82 shows the calculated ratio of PplJPequator , which can then be compared with the measurement. The av- erage pressure p can be obtained from the shock velocity. Figure 83 shows the results from a Nova experiment.‘* In this figure, A, is the second Legendre coefficient of the po- sition of the shock trajectory and A0 is the average distance moved by the shock. The numerical calculation and the data are in agreement for this experiment. Calculations2m show that, with the current resolution of about 2 pm in the shock position, time variations in NIF target fluxes can be obtained to about 2%. A technique that can be used to obtain early-time sym- metry information is the reemission ba11.201 In this technique, a nonimploding, high-Z sphere is placed at the capsule loca- tion. Reemission from this sphere is related to the incident flux. Figure 84 shows the result of a Nova experiment that used a bismuth-coated sphere and a 2: 1 beam asymmetry in the two Nova rings of beams.‘g2’202 Symmetry experiments on Nova have been a good test of many of the features that will affect symmetry on the NIF. (9 The minimum case-to-capsule ratio (ratio of hohlraum radius to initial capsule radius) is comparable on Nova (2.8) and the NIF (2.5). As described in Figs. 61 and 62, this ratio determines the geometric smoothing of source flux nonuniformities in a hohlraum. It also determines the coupling efficiency of x rays to the capsule, as described by Eq. (132). (ii) The LEH effect on the flux uniformity at the capsule is comparable on Nova experiments and the NIF hohl- (d) (tm)dXPt = 0.92 W~tfrso. = 0.95 -20 0 20 ym FIG. 81. Data from ps22 using the variation in implosion time of capsules with different wall thickness: (a) initial capsule configuration; (b) shaded portion of the drive represents the effective sampling interval for the implosion for the two cases; (c) implosion image data taken orthogonal to the hohlraum axis; and (d) comparison of the measured capsule eccentricity with the calculated value. 3990 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp / TI backllghter disk producing 4.7.keV K-shell emlsslon Backllghter beams: 8.0 kJ, 2 ns pulse at 2~0 delayed -0.5 ns Laser beams: 23.kJ 301 In 8 beams (symmetrically placed) 3:l contrast pulse (ps22) Shock-compressed materlal dlstorted by drive asymmetry absorbs 4quetor backllghter x rays, I Ppd. rpoh p/2 $ Vquator - rpod - 2 Pp0b hquator -1 I 2.0 -1 o.ooL 1 2 f 0-N FIG. 82. X-ray radiography can be used to infer time-dependent asymmetry from imaged shock distortion. 1 0 p P 0.3 g/cm3 SiOz bail 0.5 0.7 0.9 1.1 1.3 1.5 Time (ns) FIG. 83. The foam witness ball technique can measure pressure asymme- tries with nearly 10% accuracy on Nova. Here AZ is the second Legendre coefficient of the shock trajectory. Here A, is the average shock position. FIG. 84. Reemission from a high-2 coated sphere is sensitive to incident flux asymmetry for h&=-T. This technique was proposed by Suter (1984) and has been developed by Los Alamos (1991-1994).‘g2 The reemission concept is sensitive to asymmetry for early times (Kl ns) in the Nova experiments. Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3991 \ J East cone t cone earns) earns) 4KJ 4KJ BI nonlmplodlng target mounted on a Formvar web serves as the signature of symmetry condltlons Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Total laser energy = 21 kJ Foot balance = 8% RMS Peak balance = 4% RUS nmi (ns) Drive spectrum was near Plan&Ian In a uranlum hohlraum 2500 pm length t t t 0 50 100 150 200 Fill pressure (atm) FIG. 85. HEP-l/Precision Nova shots have conservatively measured convergence ratios (from secondary neutron spectra) that are into the NIF range, The experimental measurements and calculations are in good agreement. 2M Fracmix in Cd) is the mix width as a fraction of the distance between the fuel/pusher interface fall line and the unmixed interface postion, raum (see Fig. 106 in Sec. XIII). The P,IPo at the capsule, due to the LEH, is about 10% for the NIF design. Depending on the size of the LEH, this effect ranges from 10% to 20% for the Nova experiments. (iii) The angular change in the location of the source emis- sion due to wall blowoff, which determines the mag- nitude of Rux asymmetry due to spot motion is about lo”-15” on both Nova experiments with the 2.2 ns ps22 pulse and for the gas-filled ignition hohlraum (see Fig. 106 in Sec. XIII). (iv) Refraction effects for both the Nova experiments and the NIF hohlraum are generally fairly small. The re- fraction angle is given approximately by203 (178) where x,(L,) is distance (scale length) along the beam path and xp(Lp) is distance (scale length) per- pendicular to the beam path. Because nln,=O.l and electron conduction results in L,-L,,, refraction is limited to a few degrees. (v) Implosion symmetry reproducibility for Precision 3992 Phys. Plasmas, Vol. 2, No. 11, November 1995 Nova, as shown in Fig. 73 meets the 1% uniformity requirements for ignition experiment time-averaged flux. (vi) Inward and outward pointing on Nova, as shown in Fig. 72, simulates the effects of the inner and outer rings on the NIF hohlraum (see Fig. 106 in Sec. XIII). Although the Nova experiments used only a single ring of beams per side, calculations indicate that the single-ring experiments are a good test of flux asym- metry from the individual ring positions. X. COMBINED TESTS OF SYMMETRY AND HYDRODYNAMIC INSTABILITY A goal of the NAS-mandated Nova Technical Contract (NTC) is implosions have levels of hydrodynamic instability growth and convergence ratios approaching those required for capsules on the NIF. Because Nova has only a single ring of beams per side, elimination of time-dependent symmetry effects has not been possible. Hence, the convergence ratio achievable on Nova is smaller than could be achieved on the NIF. However, hohlraums and capsules can be designed to minimize these effects on Nova. By the use of a smaller Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp capsule-to-case aspect ratio, the higher-order flux asymme- tries are further reduced. Also, a smaller capsule requires a shorter pulse, which results in less spot motion and less time- dependent asymmetry. Capsules being designed to vary hy- drodynamic instability growth in a controlled way are de- scribed in Fig. 47. In the HEP-1z04 experiments on Nova, we have made significant progress toward achieving the combined symme- try and stability-growth levels required for ignition targets by using the capsule shown in Fig. 85(a). This plastic-coated glass microballoon is about half the size of the typical Nova plastic capsule. Because of its small size, the HEP-1 capsule required the relatively short pulse shown in Fig. 85(b). The glass inner shell of the HEP-1 capsule provided ra- diation preheat protection at this scale and was used for a neutron-activation measurement to determine the com- pressed pusher density. Also, as shown in Fig. 85(c), the capsule was placed in a uranium hohlraum, which further reduced preheat. Under the conditions of laser intensity and plasma temperature of this experiment, the uranium M-band radiation at about 4 keV was much smaller than the gold M-band radiation at about 3 keV from a standard Nova hohl- raum. Because the HEP-I capsule was intended for high convergence-ratio experiments, it provided a particularly good test of precision Nova. The 8: 1 contrast pulse shown in Fig. 85(b) was used for the Precision Nova power balance test shown in Fig. 71(b). The convergence ratio of these im- plosions was controlled by varying the initial fill density of the DD fuel from 200 to 25 atm. As seen in Fig. 85(d), the convergence ratio, as inferred from the pr of the compressed fuel, varied from about 10 to 24. At the higher value, the convergence is comparable to that for some of the NIF igni- tion capsules designs discussed in Sec. XIII. The experimen- tally observed values of convergence in Fig. 85(d) were av- eraged over several implosions (2 at 200 atm, 6 at 100 atm, and 10 at 25 atm), and the errors were dominated by the statistical sample size of observed secondary neutrons. With- out the improvements of Precision Nova, the achievable symmetry is inadequate, and the density of the implosions starts decreasing for fills below 100 atm. The pr of the fuel in these implosions was obtained using the Large Neutron Scattering Array (LANSA)zo5 array of 960 single-hit scintil- lator detectors. This detector measures neutrons from the secondary DT reactions that occur in DD fuel: D+D+He3+N, D+D--*T (1.01 MeV)+P, (179) T (O-l.01 MeV)+D-+He4+N (11-17 MeV). The two DD reactions occur with equal probability. When the fuel pr is less than the triton range, the probability of the DT reaction is proportional to the fuel pr. The triton range depends on the fuel temperature, and, near the end of the range, the implied fuel pr for a given secondary fraction is sensitive to temperature.206 Shown in Fig. 86 is the ratio of the DT-to-DD neutrons RDTIRDD~ as a function of fuel pr at different fuel tempera- tures. The size of the HEP-1 capsule initially was chosen to PR Wcm2) FIG. 86. We see R,/R,,, as a function of pr for several fuel electr6n temperatures. u)4 The model used assumes a large uniform density and tem- perature fuel region with a negligibly small central “hot spot,” from which all tritons originate. Curves end at the value of pr where the tritons have thermalized in the fuel. Fuel density used was 21 g/cm3. minimize this problem by limiting the expected fuel pr to a range in which the temperature-dependent effects were rela- tively small. In the HEP-1 experiments, fuel temperatures were l-2 keV, and fuel pr’s were about 0.01-0.015 g/cm’. As seen in Fig. 86, the inferred pr is relatively insensitive to temperature in this range, and it is essentially linear in RDTJRDD~. Neutron energy depends on kinetics and the en- ergy of the reacting triton, which slows down as it traverses the fuel. As the triton slows, the width of the neutron spec- trum narrows. LANSA provides both a secondary neutron fraction and a neutron spectrum, so that the fuel pr can be obtained with- out model-dependent assumptions regarding triton slowing.207 Figure 87 shows the neutron spectrum obtained from summing the spectra from the ten 25 atm shots. Figure 87 also shows the LASNEX-calculated spectrum, including the effects of hydrodynamic instability estimated from the Haan mix model described earlier. From these measurements, we infer an average DT equivalent fuel density, assuming con- stant density versus radius, of about 20 g/cm3. 15 - - Fit to sum of shots Simulation (Haan mix 0 11 12 13 14 15 16 ‘17 18 Energy (MeV) FIG. 87. Shape of composite neutron spectrum of 25 atm experiments (ten shots) is well modeled by simulation with the Haan mix model.*m Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3993 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp ,,,,,,,,,,,, * ,,,, II ,,,,,, II,, Clean, 1-D a 25-atm fill Ou004 - f lti ltttt IIttI IIIII IJIlt IlflL ‘O’o.9 1 01~*~~ ‘)IIl ‘t*BI ‘~t~f’*~l*f-~t~ 1 1.1 1.2 1.3 1.4 1.5 0.9 1 1.1 1.2 1.3 1.4 1.5 c J f t 0.003 - t 1 0.002 - t MIX 40% ml e P - Haan mlx f 0.001 - Secondary neutron width (F&V) Secondary neutron wfdth (MeV) FIG. 88. The combination of the Haan mix model and drive asymmetry somewhat overestimates degradation of 25 atm fill capsules. Figure 88 shows that the LASNEX calculations must add the effects of mix and asymmetry in order to reproduce the observed yield, secondary yield fraction, and secondary neutron-energy width. In these calculations, the P, and P, from residual pointing errors and beam imbalance were added to the calculations. Also, two types of mix modeling were done. First were detailed 2-D calculations of the growth of a wide spectrum of individual modes. This growth, coupled with mode- saturation effects from the Haan model, was folded with the measured surface finish to obtain a mix depth as a function of time at the fuel-glass interface as the capsule decelerated. This analysis results in the point labeled “Haan mix.” For comparison, another series of calculations simply mixed glass and fuel to a certain fraction of the distance between the interface and the “fall line” (i.e., the calculated position of the glass-DT interface if there had been no deceleration). The separation of the fall line and the glass-DT interface is the deceleration distance. Typically, a mix width will be some fraction (“fracmix” in Fig. 88) of this distance. For the calculations shown in Fig. 88, this mix width varied from 10% to 40%. The Haan mix analysis, for this capsule and surface finish, is essentially equivalent to a 40% mix width. Since the fall line is approximately at the origin at the time of peak neutron production, a 40% mix has the effect of mixing 40% of the fuel radius by the time of peak bum. As seen in Fig. 88, the Haan mix analysis plus the effects of asymmetry slightly overestimates the observed performance degradation. In addition to the LANSA data used to obtain the fuel pr, other experiments measured the glass pusher pr. From these measurements, we obtain pusher densities of approxi- mately 1501’50 g/cm3. Table IV compares the measured and calculated values for convergence, fuel, and pusher density and yield. Also listed are the calculated hydrodynamic instability growth and the x-ray-pulse-shape contrast ratio. These quantities ap- proach those required for a NIF capsule, as indicated. XI. HOHLRAUM PLASMA CONDITIONS To control symmetry, reproducible beam-propagation conditions are necessary in the laser channel, and these con- ditions must be consistent with accurate placement of the laser beams. Plasma parametric instabilities such as stimu- lated Brillouin scattering (SBS)” can result in an energy loss or possibly cause a random redirection of energy in the hohl- raum. Stimulated Raman scattering (SRS), in addition to its TABLE IV. For the Nova glass implosions, the calculated implosion parameters agree well with observed values and approach key MF target requirements. Low-convergence High-convergence fill pressure (25 atm) fill pressure Observed Calculated Observed Catculated NIF Convergence CR cspa”telRf”el) Density (g/cm’) (hot spot model) Pusher density mg/cm* (g/cm’) Hydrodynamic instability growth Pulse shape contrast (laser) Yield ( IO7 neutrons) 1410.7 12.3 23.62 1.8 20.7 20-35 1622.4 12.6 19.1 t4.4 14 45-75 73215 53 (140) 602 18 72 (170) (700- 1200) .*. 60- 160 . . . 60-160 400 8 8 8 8 10-50 7.22 1 10 4.220.4 3.8 . . . 3994 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp effects on the energy balance and symmetry, results in the generation of high-energy electrons, which can cause pre- heat, as described in Sec. XII. Plasma that evolves into the hohlraum consists of radiation-driven blowoff and direct laser ablation. The radiation-ablated gold mass is approximated by Eq. (128). The mass ablated by direct laser electron conduction is ob- tained from Eq. (48), in which the laser intensity used should be the intensity that is not converted to x rays. For an igni- tion hohlraum at a radiation temperature of 300 eV, the un- converted incident laser intensity is about 1Or5 W/cm2 on about 20% of the hohlraum area. In this case, direct laser ablation contributes only a few percent of the mass injected into the hohlraum. However, at early times, since the tem- perature of the laser-heated materia1 is higher, the expansion velocity into the hohlraum is higher, and plasma in the laser beam will be dominated by the laser-ablated material. For laser light with wavelengths of 1 ,um and longer, hohlraum plasma conditions can reach a significant fraction of critical density, n,=(1021/cm3)/~2(~m), during this early phase. For all hohlraum experiments on Shiva and earlier 1 ,um lasers, we found that, when hohlraums are calculated to de- velop large regions of plasma near nJ4, they became very efficient at converting incident laser light into hot electrons and Raman-scattered light. As shown in Fig. 21, the fraction of energy left in the laser pulse when the hohlraum is calcu- lated to reach nJ4 corresponds closely to the energy in hot electrons. The observed hot-electron fractions, with a tem- perature of about 50 keV, approached 50% of the incident light, which is the maximum possible level from Raman scattering. A 50% hot-electron fraction is possible only if all of the incident light is scattered in a Raman process at nJ4. The 20~~ process also occurs at n/4 and is an additional potential source of electrons. In this process, an incident pho- ton decays into two plasma waves. The 20~~ instability pro- duces no direct electromagnetic signature and thus is hard to detect. Emission at 1.50,~ can be produced by this instabil- ity. The 20~~ process generally produces higher-energy elec- trons than Raman scattering, and may be responsible for a superhot tail with a temperature above 100 keV, which was generally seen in the Shiva experiments. A model that reproduces the scaling of hot electrons in these 1 pm experiments is based on considering only the time that it takes the directly driven laser blowoff to fill the hohlraum volume to nJ4 and then assuming that all remain- ing light in the pulse is Raman scattered with 100% efficiency.69 Below critical density, the laser heats the blow- off to near isothermal conditions. The time required for suf- ficient material to accumulate to reach nJ4 scales as ~,,,pS/Vs, where V,is the isothermal sound velocity and S is the hohlraum scale size. Since V,K (ZT,) 1’2 and 2~ T”2, then Vs=?‘4. If the temperature in the laser-heated blowoff is determined by the electron flux limit, which is a good approximation for long laser wavelength at relevant intensi- ties, then Imn T V mn T3’2mT3’2/X2 tee ce c 9 or . Shiva 2-i-m 10-i 6 t = pulfelenglh (IIS) s=1~5OOpmdiam x2 0 20 40 60 #/Et FIG. 89. Plots of fhot vs S41Et for 2 ns Cairn experiments on Shiva. A scale-l.0 (s= 1) hohlraum is 500 /*m in diameter and 800 pm long. Tc+t2)2’3 and V,~T~‘4~(Ih2)1’2, where V, is the electron thermal velocity. Using this scaling, we obtain 080) where ~~ is the laser pulse length, E is the laser energy, and Ia Els2rL. This analysis predicts that there should be a time delay before the onset of hot-electron production. From Eq. (1 SO), this time delay should scale with E-‘” for a fixed-size hohlraum and pulse length. This time delay and energy scal- ing were observed on Shiva, as shown in Fig. 22, which is a plot of the time delay in the production of high-energy x rays versus the energy into a scale-2.0 Cairn hohlraum in a 2 ns Gaussian pulse. For closure times at the peak of the laser pulse or later, the fraction of energy left in a Gaussian laser pulse is pro- portional to the error function and scales approximately as exp(-ry/4/72). Figure 89 is a semilog plot of fhot vs S4/E for various 2 ns experiments done to test this scaling. The first number listed near the data is the scale size, and the second number is the laser energy in kilojoules. The scaling is quite good, except for the lowest level point, with much less than 1% of the energy in hot electrons. This plasma filling limited the hohlraum temperatures with low hot-electron levels, achievable with 1 pm laser light on Shiva,to between 130 and 140 eV. The NPIRE71 implosion experiments discussed previously were designed for this temperature, and they worked essentially as calcu- lated. The Cairn experiments discussed above, which were designed for higher radiation temperatures on both the Shiva and Argus lasers, were significantly degraded by hot-electron production. For shorter laser wavelengths with higher critical densi- ties, the blowoff plasma does not reach a significant fraction of critical density until significantly higher hohlraum tem- peratures are reached. At these higher hohlraum tempera- tures, particularly for shaped laser pulses of longer duration, Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3995 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp the radiation-driven blowoff has time to fill the hohlraum and becomes the dominant source of plasma in the hohlraum. The interaction of the laser with the radiation blowoff deter- mines the plasma conditions in the beam path. A combina- tion of inverse bremsstrahlung absorption along the beam path, electron conduction from the beam path into the sur- rounding channel, and pressure equilibrium throughout the channel determines the beam-path density and temperature. By balancing these effects, a near equilibrium in temperature and density is established in the laser propagation channel. A simple model shows how these effects scale and reproduces the average temperature and density from numerical models.99 The inverse bremsstrahlung absorption power per unit volume, PI,,, , along the laser channel, is given by PLmv P,,,(TW/cm3)= ALL ( 1 -e- PLO-W LfAI.B.) c ~ A&LB. ’ (181) where L is the propagation path length, and the absorption is assumed to be small. The inverse bremsstrahlung absorption length Xt,n, is taken from Eq. (175). Here AL is the cross- sectional area of the laser beams and P, is the laser power in Tw. To estimate the electron conduction losses per unit vol- ume from the channel, P,, we use Eq. (27). Although the geometry of the laser beams can be complex, we approxi- mate the conduction loss to be the loss from a sphere of radius I and obtain 16 T;ff2 P,( TW/cm3) = - z In A -;T ‘(‘)’ (182) where S(Z) was defined in Eq. (27). Letting r2=A,/w and equating the conduction loss with inverse bremsstrahlung heating, we have PLUW = 28h2T2(keV) z* In R2(nln,)2 S(Z). (183 Relating laser power to laser energy using Eq. (92), we ob- tain the following relationship: A2 -0.15 In2 h (n&l f Tz- 1 .34T;.93Et’3Z2 S(Z) * (184) A second relationship between temperature and density is obtained by equating the pressure in the hohlraum outside the laser channel with the pressure inside the laser channel. The density in the hohlraum outside the laser channel is taken to be the radiation-ablated mass divided by the hohl- raum volume. For a cylinder of radius Rhohl, the density is given by p=2m,lRh,hI. We use Eq. (128) at constant radia- tion temperature for the radiation-ablated mass and relate time t to the laser energy by using Eq. (93). Assuming that the case-to-capsule-radius ratio is fixed at about 3 in order to achieve symmetry, we have, from Eq. (91a), 113 Rr,,,,(cm) = 1.04 E’Tt(F) r (185) Combining these equations, we have (. 1 -0.153 p(g/cm3)=0.0135T~~86E~o~153K~0~46 & . For radiation temperatures typical of ICF, the average ioniza- tion Z of gold versus radiation temperature is given by Z=23c.45. (187) Combining these factors, we obtain the pressure outside the laser channel: P(Mbar)=96 ; pT =o 15T3.3E-0.153K-0.46 0 i i -0.153 R L 0 0.15 * w-9 The pressure in the laser channel can be written as (n&IT, P(Mbar)= 1.6 hZ , where X is the laser wavelength in micrometers. Equating the two pressures yields n T, 2 -0.09T;3E,O.‘53K;0.4 & -o’153e ac A i. ! (190) Using Eqs. (184) and (190), we obtain the laser-channel den- sity and temperature: -0.09 (191) and n ~=0.16~‘2/7~-2’7(l,, A)-217~iO.323 (192) The assumptions used in this model break down for high-2 plasmas when the channel density exceeds about 102’/cm3. Reemission from the plasma becomes a major factor in the energy transport and the absorbed laser power required to maintain a given temperature increases. This fact is the pri- mary reason that large-scale hohlraums must have low-Z fills to allow the laser to propagate to positions near the hohhaum wall, as required for symmetry. Several interesting conclusions follow from Eqs. (191) and (192). First, the fraction of critical density in the channel scales nearly as the product of the laser wavelength squared and radiation temperature squared. So, for a fixed fraction of critical density, the achievable radiation temperature is in- versely proportional to the laser wavelength. Also, at fixed hohlraum radiation temperature, the channel density is virtu- ally independent of laser wavelength,’ since critical density scales as 1/X2. This is seen in numerical calculations when the channel density remains well below critical density.208 3996 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp TABLE V. A pressure balance model-in which inverse bremsstrahlung absorption and electron conduction establish conditions in the laser beam path, and radiation blowoff establishes conditions outside the laser channel-compares well with a wide variety of LASNEX hohlraum calculations for the hohlraum plasma conditions. Conditions in laser channel Cases examined Pressure (Mbar) n,ln, T, (keV) Liner or LASNEX LASNEX LASNSX Energy T, gas fill calculation Model calculation Model calculation Model Nova (0.35 pm) 20 kI 225 eV Ni 3-4 4.3 0.055-0.075 0.08 3.8 3.6 25 k.I 240 eV CH 4-5 5.5 0.08-0.11 0.12 3.0 2.9 Ignition hohlraum (0.35 pm) 1 MJ 300 ev He gas 4-6 5.5 0.07-0.10 0.10 4-5 3.9 LMF (0.35 pm) 11 MJ 210 eV LiH l-l.2 1.25 0.028-0.04 0.035 2.2-2.5 3.0 The channel temperature is nearly linearly proportional to the radiation temperature and depends only weakly on laser energy, the laser wavelength, or the 2 of the channel. Equations (191) and (192) agree quite well with a vari- ety of LASNEX calculations, as shown in Table V. For calcu- lations using this model with liners, the 2 of the liner is used in calculating the conditions in the laser channel. Gold is still used for calculating the mass in the channel outside the laser path, since the total mass of plasma in the hohlraum is still dominated by the gold blowoff. At 300 eV, the channel den- sity for NIF hohlraums stays below nln,mO.l. For the tem- peratures calculated, Landau damping is quite large under these conditions and plays an important role in the levels of parametric instabilities. For comparison, Fig. 90 shows con- tour plots of electron temperature and density at 14.4 ns from a LASNEX calculation for a NIF hohlraum. This hohlraum calculation had an initial 0.8 mg/cm3He+H, gas till inside the hohlraum (see Fig. 106 in Sec. XIII). Using unsmoothed laser beams, SBS in the low-2 lined Nova hohlraums used for the pulse-shaped symmetry experi- ments is about 5% of the incident light.20g Such hohlraums have extensive regions with nln,=O.l The observed scatter- ing levels, although not a major energy drain, could impact hohlraum symmetry if scattering is significant at angles other than direct backscatter. A major element of the NTC has been the scaling and control of SBS to the larger plasmas of igni- tion hohlraums. Equations (191) and (192) can be used to estimate the scaling of gain for parametric instabilities as hohlraum radiation temperatures are varied. For SBS in a homogeneous plasma, the convective gain in the strong damping limit scales as21o*211 L n/n, 0, -- Qsss=fi2 x T I, ’ & a where L is the path length through the plasma and ( u,Iw,) is the ratio of the acoustic wave damping to its frequency. The damping is primarily Landau damping, which depends on material composition and the ratio of ion temperature Ti to electron temperature T, , as shown in Fig. 91(a). For the NIF, where the ions and electrons have time to nearly equilibrate, v,lo,=O.2-0.4, depending on how much hydrogen is in the hohlraum gas fill. The ion acoustic velocity, which is ap- Phys. Plasmas, Vol. 2, No. 11, November 1995 proximated byJ(ZT,+ Ti)lmi, is largely determined by the electron temperature and the mass mi of the dominant ion species, while ions near the acoustic velocity provide the damping. Damping will be strong if the ion temperature is near the electron temperature, but it will be weak if the ions are cold. Also, the presence of a low-mass minority ion spe- cies increases the damping because these ions have a higher velocity, closer to the acoustic velocity. Hence, hydrogen as a minority species produces higher damping and lower SBS gains. ‘12 In the Nova “gasbag” experiments discussed be- low, plasmas with a significant hydrogen content generally had time-integrated SBS levels below about l%, while plas- mas without any hydrogen, such as pure C02, had average retlectivities as high as 15%-20%, as shown in Fig. 91(b). If we assume that L scales with the hohlraum radius given by Eq. (185) and use Eqs. (191) and (192) for n, and T,, we obtain Qsss=[X 17/7Eo,.077T,O.172-417~0.359. (194) Most of the radiation temperature and laser energy depen- dence of (Lnln,)lT, cancels. Thus, the gain depends on the radiation temperature through the higher intensity required for higher radiation temperature. For a fixed laser geometry, the required intensity scales approximately as c. Thus, the gain for SBS is a strong function of the radiation tempera- ture. The actual situation in a hohlraum plasma is far more complex than that represented by Eq. (193). Phase mismatch because of velocity gradients can reduce the gain length, and laser-beam filamentation can enhance the local intensity from the average intensity. Also, a variety of coherence con- trol techniques-including random phase plates-and tem- poral smoothing-such as smoothing by spectral dispersion (SSD) developed at the University of Rocheste?’ as part of the effort to control symmetry for direct drive-can break up coherent regions in the plasma to reduce the gain length. Figure 92 shows the focal spot of a Nova beam with and without a random phase plate. Although the peak speckle intensities are equally large, with and without a phase plate, the phase plate reduces the spatial scale of the speckles and produces a more uniform focal spot distribution. Distributing the laser energy over multiple frequencies also can be used to Review Article 3997 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 1 0.4 g 0.2 0 0 5 10 15 f W t t Ae3keV Electron temp. B = 4 (f = 14.4 ns) c = 3 c D=6 - 0.2 0.4 2 (cm) 0 0 0.2 0.4 = (cm) W f A = lO’4 W/cm2 B = 3 x 1014 0.4 C = 1015 D~3xlO’~ - _ _ 5 c 0.2 0 0 0.2 0.4 2 (4 FIG. 90. Ignition-scale hohlraums at peak power have large regions in the laser channel with n/n,=O.l and T,-4-6 keV. control temporal coherence times. Detailed numerical models2’3V214 have been developed to study the evolution of The f number of the lens is important because the diatn- filamentation and SBS in the presence of such complex laser eter and coherence length of the speckles is determined by beam temporal and spatial characteristics. the f number. A speckle diameter d, is approximately equal to the diffraction-limited spot for the lens or d,-2 fX. The (4 , I ( I , , ) , , 10 r o.lZ 0 10 20 30 40 50 60 70 Percent hydrogen FIG. 91. Damping rates for helium-hydrogen mixtures in NIF are larger than for Nova CH mixtures: (a) 50/50 mixture of helium and hy&ogeu consistent with a 17 K cryogenic target: (b) protons mixed with CO, or C,D,, reduced reflectivity in Nova experiments. 3998 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp FIG. 92. Although speckle intensities are equally large with and without a random phase plate, a phase plate produces a more uniform focal spot distribution, as shown for a Nova beam. coherence length of a speckle is approximately the Rayleigh range for the lens and is given by I,,-8f’X. This effect is shown in the simulation ‘t4 of an .fl4 beam and an f/s beam (see Fig. 93). Since filamentation and SBS will grow out of these speckles, the f number selects the size and coherence length for the most unstable growth regions in the plasma. If the spatial growth length for filamentation is greater than the length of the filaments, then iilamentation is suppressed. This puts an upper limit on the f number, as given by”3,2*4 *f’s, for NIF, 095) where G is a factor that accounts for thermal effects. Fila- ments also will be stabilized if the growth rate y is less than the bandwidth Ao, or equivalently, A.0 2 w20.0s ~ ,” & G+4X 10-4, c e for NIF. (1961 With a phase plate, the SBS signal levels dropped sig- nificantly in experiments at the University of Rochester, at Rutherford, and at Ecole Po1ytechnique.2’5-217 Similar ef- fects are seen in experiments currently being conducted on Nova. SSD experiments in which phase plates are combined with up to about 0.15% laser bandwidth have begun on Nova. Nova also has the ability to propagate four separate frequencies, separated by up to about 8 A, through a single beamline. These techniques for beam smoothing can both be implemented on the NIF. These experiments are being done with both fl4 and f/S lenses and with a variety of hohlraum 118 f14 500 400 300 200 100 0 FIG. 93. Near “best focus,” the field of a random phase-plate beam consists of long, narrow speckles whose size depends on lens f number and laser wavelength. Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 3999 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp TWWI Yarlws bnndwldth o,Wx,r I cob 1 US besm on No”a I:/:;/ Fouragment KDP array SBSthmugh the fans - Calorlmolfy - TknrrWdWsd r+mrccpy FIG. 94. One Nova beam has been converted to approximate the NIF fo- cusing conditions for measuring SBS. The laser frequency in each of the four KDP segments can be separated by up to 8 8, (at I w). SSD also can be implemented. gas ‘fills. The NIF laser design combines four f/20 beams propagating together as a single f/X cluster. One beamline of Nova has been modified to simulate this configuration, as shown schematically in Fig. 94. To evaluate the limits to the plasma conditions and laser intensities for ignition-scale hohlraums, experiments on Nova are being carried out both in open geometries and in hohlraums, as shown in Fig. 95. Open-geometry plasmas with the required dimensions and plasma density are being investigated by using “‘gasbag” targets,*‘* in which the vol- ume between two films of polyimide is filled with neopen- tane, deuterated neopentane, or CO, at about 1 atm. The gas-tilled hohlraums2’9~220 have a thin (< 1 ,um) plastic mem- brane covering the LEH and are filled with similar gases. Figure 96 and Table VI compare the plasma conditions cal- culated for the Nova experiments and for the NIF hohlraum. Nine of Nova’s ten beams are used to heat the plasma. The tenth beam is used as an interaction beam, delayed until the desired plasma conditions are reached, as shown in Fig. NIF target t---gmm~ TABLE VI. Detailed LASNEX calculations show that Nova plasmas are simi- lar to those expected for the NIF. Nova NIF Gas bags Hohhaums Inner cone Outer cone Path length, f (mm) -2 -2 -3 -2.5 S(n,ln,ldl (mm) -0.2 -0.2 -0.3 -0.15 v,, @m/s) <IO' <IO' <IO' <IO' L, (mm) >6 >6 210 xl TiT, 0.1-0.2 0.1-0.2 0.4 0.3-0.4 97. Figures 98 and 99 show calculated and observed 3 keV x-ray images of the gasbag and hohlraum targets. By about 500 ps, the plasma in the gasbag target is quite uniform. The hohlraum target, which has a ramped pulse, as shown in Fig. 97, has uniform conditions by about 800 ps. Hohiraum eIec- tron temperatures are obtained by using x-ray spectroscopy,22’ as shown in Fig. 100. Electron temperatures are 3-4 keV, in agreement with LASNEX simulations. Time-integrated SBS reflectivities are less than 1% from CJHIz plasmas for both open and closed geometries with f/8 focusing. Figure 101(a) shows the reflectivities for the gasbag2’* experiments. Peak reflectivities are about a factor of 2 larger. These levels are well within the goal of having less than 10% SBS on ignition targets. The calculated linear SBS gain coefficients Q for the Nova experiments are comparable to or higher than those of NIF targets, as shown in Fig. 102. Without nonlinear satura- tion, the predicted SBS scattering, which scales as eQ would be larger than that seen in the experiments. Current models usually include only pump depletion as a saturation mecha- nism. Additional nonlinear saturation mechanisms, such as limitations in the magnitude of ion particle-density fluctua- tions SNIN caused by particle trapping,222 are being evalu- ated. A particular issue not addressed by these low-Z plasmas is the influence of the gold plasma near the hohlraum walI in the generation of SBS. Although most of the laser pathlength in NIF targets is through low-Z plasma, there is a 200-300 pm “shelf” of gold plasma with a density of -0.2&a, in the NIF targets. This scale length is set by inverse brems- Nova targets Open geometry 2.5 mm Closed geometry cyllndrlcal hohlrsum 2.5 mm ---I I--- FIG. 95. Long-scale-length plasma experiments have been performed in both open and closed geometries. 4000 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp --- - 0 1 2 3. 4 Distance (mm) - CiasDa ii f~i ns = #hlra m tzl ns t 3 14.6 ns FIG. 96. Detailed LASNEX calculations show that Nova plasmas are similar to those expected for the NE strahhmg absorption and is about the same for NIF targets and current Nova hohlraums used for implosions. Although the scale lengths are small, the density is relatively high, the velocity gradients are small, and the ion Landau damping is weak, so that significant reflection, such as was seen in the COa gasbag plasmas mentioned above, is possible. In fact, the several-percent levels of SBS seen in the Nova gas-filled hohlraum symmetry experiments are associated with the gold wall plasma. The SBS levels in these experiments drop to about 1% when the gold wall is removed. As was demon- strated for the CO, plasmas, calculations indicate that the level of SBS in the gold can be significantly reduced by doping the gold with a small amount of hydrogen (for ex- ample, the hydrogen could come in the form of CH, cosput- tered with the gold when the hohlraum is constructed) or beryllium. Experiments to evaluate this effect will be carried out on Nova. Initial Nova experiments with alternating 78 A Au and 32 A Be layers show SBS levels reduced to about 1%. The scattered-light experiments on Nova have been ex- tended recently to include Raman-scattered light. These mea- surements indicate that the level of Raman scatter from nln,<O.l can be larger than the SBS. For the range of in- tensities of interest to NIF ignition designs, 5X 1014 to 2X1015 W/cm”, the scattering levels are about 2%-5% with phase plates and 2 A of SSD as shown in Fig. 101(b). This level is well within the NIF specification of <15% for ener- getics. Without SSD temporal smoothing, the level is about 10% at the upper end of the NIF intensity range, but still only about 2% at the lower end. The higher intensity of about Targets filled with 1 atm of C&l,, 3 1.1 x lo*’ ems when fully ionized Volume -12 mm3 for both targets 3 -10 kd to heat to 3 keV Heating beams Interaction beam Interaction beam Interaction beam is delayed until the underdense plasma is heated FIG. 97. Nine of Nova’s beams are used to produce large scale-length plasmas. The interaction beam is delayed until the underdense plasma is heated. Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 4001 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Suwort washer 850 P* Images hv > 3 keV 300 ps LASNEX post- processed images Expetimentd pmhole images mm - FIG. 98. X-ray images and calculations show that the long-scale-length plasmas are 152.0 mm in diameter during the time of the interaction beam. 2X lOI W/cm’ applies to 300 eV peak hohlraum tempera- tures on NIF, whereas the lower intensity applies to 250 eV hohlraums. Ignition designs exist for both temperatures, but there is more margin for hydrodynamic instabilities at the higher hohlraum temperature. Raman scattering from these low densities produces hot-electron temperatures less than 20 keV The NIF capsules have significant self-shielding for these energies, so the low-density SRS is not a preheat issue. The measured Raman scattering is narrowly collimated back into the f/8 incident lens. This observation is consistent with numerical calculations using the F3D code,‘13 which integrate the Raman-scattering equations back through the plasma. The Raman gain is largest in the beam speckles, which geo- metrically favor scattering in a narrow backward direction. Because the SRS is directly back into the lens, this scattering does not adversely affect symmetry. As determined by high- energy x-ray measurements, the fraction of laser energy coupled into hot electrons with a temperature 250 keV, char- 4002 Phys. Plasmas, Vol. 2, No. 11, November 1995 acteristic of Raman scattering or the 20~~ instability near nln,=t, has been consistently less than about 1% for both the Nova implosion experiments and the large plasma experi- ments. Preheat from high-energy electrons is discussed in Sec. XII. Further work on Nova is planned in order to more thor- oughly evaluate Raman scattering levels and the role of laser-beam filamentation. These experiments will help to im- prove quantification of the range of plasma conditions that are accessible for ignition experiments. XII. HOT ELECTRON PREHEAT Understanding the behavior of Raman instability for ig- nition hohlraums is important because high-phase-velocity plasma waves produce very energetic electrons when they are damped in the hohlraum. These energetic electrons are a source of preheat, which can raise the fuel adiabat and make Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Experiment 800~s L Missing interaction beam Ar and Cl doped gas / 9 heater beams Axial image h\ 23 keV LASN EX Interaction beam starts at 600 pS the fuel less compressible, raising the ignition threshold. High levels of Raman scattering were the principal limitation to hohlraum experiments at 1 ,um on the Shiva laser. Above hohlraum temperatures of 130-to 140 eV, significant levels of Raman scattering were observed. Preheat in the DT fuel must be limited to approximately the Fermi specific energy, ea (see Fig. 3), at the density of the fuel during the implo- sion. At this level of preheat, the pressure required to achieve a given density in the fuel doubles. Since the main fuel den- sity during an implosion varies from a few to about 15 g/cm3, the preheat must be limited to between 1 and 5 X lo5 J/g. This preheating limit also can be expressed in terms of the fuel entropy, as presented in Sec. IV. If the preheat comes during the peak-power part of the implosion, while the cap- sule is at or near the peak ablation pressure, then the fuel is at the higher density and the higher preheat level is appro- priate, as assumed below. The preheat E(x)(J/g) inside an ablator of thickness x&/cm”) and area A(cm*) caused by a Maxwellian distribu- tion of electrons with a temperature T,,,(keV) and energy E,,,(J) is given by 223*224 E(J)=$~‘.~ exp(-1.65y0.4)=EOG(y)r (197) where y =x/x0, where x is the thickness, in g/cm*, of the ablator. Here x0 is an approximate mean electron range, in g/cm2, given by 3 x 10-6(A/Z)T;,t x0= Z’12 09% where That is the hot-electron temperature in keV and G(y) is an attenuation factor that occurs because lower-energy electrons are absorbed in the ablator and do not reach the fuel. Here G(y) is derived under the assumption that the hot electrons are not anomalously flux limited. Preheat on witness-plate experiments on Shiva and Novette226 were consistent with these assumptions, but these experiments were not carried out over a wide range of conditions. Using Rq. (197), we can write the tolerable fraction of the laser energy into hot electrons as227 fhot= EFMF W3~)Wsourceha~) ’ (199) where M, is the fuel mass and EL is the laser energy. D(rsource/rcap) is a geometric dilution factor for the hot elec- trons. This factor is significant in hohlraums because the la- ser beams, where the hot electrons would be produced, are at some distance from the capsule. If hot electrons are isotropic, Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 4003 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp A; and Cl dopants-in gas Ti/Cr spectrum from hohlraum - Cr He B ~ I “+ 5.8 6.2 6.6 7.0 hi WV) Cr Hpr a TiHea 0 0 0.4 0.8 I.2 1.6 2 2.4 Time (ns] Hohiraum CrHebfTiHep r.2b ’ ! ’ ’ LASNEX-l 0.5 1 f.5 2 Time (ns) FIG. 100. X-ray spectroscopy indicates T,.-- -3 keV for both open and closed geometries. only those electrons that are in the solid angle subtended by the capsule will hit the capsule. If we take the average loca- tion of hot-electron production as the average case radius, the fraction of hot electrons hitting the case is equal to the ratio of the capsule area to the case area. Some of the electrons that miss the capsule will be reflected off the high-Z case and have another chance to intercept the capsule. For typical high-Z materials, about 50% of the incident electrons will be reflected with about 70% of their original energy. For the discussion below, D =O.l is used. Figure 103 shows the hot- electron fraction that would result in fuel preheat equal to the Fermi specific heat as a function of the hot-electron tempera- ture. The minimum tolerable level, for 40CTh,,G80 keV, is about fh”t=b%. If these hot electrons come from damping of plasma waves produced by Raman backscatter, the hot- electron temperature on the NIF is expected to be 20-40 keV. Raman forward scatter could produce much higher tem- peratures, but at reduced efficiency. direct-drive capsule have less ablator to provide preheat shielding for the fuel. Because of both of these factors, direct-drive capsules are more sensitive to preheat than are indirect-drive capsules. Figure 103 also shows the tolerable preheat fraction for a 1.8 MJ direct-drive capsule such as those now being investigated by LLE.55*228*229 Direct-drive capsules likely will require an adiabat elevated by a factor of 3-4 over Fermi degeneracy to reduce hydrodynamic insta- bility, as discussed in Sec. VI. In this case, direct-drive cap- sules could tolerate a fraction of hot electrons three to four times larger than indicated in Fig. 103 without further deg- radation in performance. Xlil. NATIONAL IGNITION FACILITY AND IGNITION TARGETS Nova hohlraum experiments with 0.35 pm light have all had hot-electron levels, based on high-energy bremsstrah- lung emission, of about 1% or less. This includes the high- temperature, 300 eV hohlraums and hohlraums with long pulses. Experiments to measure Raman scattered light di- rectly have begun on the NIF scale plasmas described in Sec. XI. The proposed National Ignition Facility (NIF) will use modern electro-optic technology, compact segmented ampli- fiers, and multipass laser architecture. Improvements in op- tical manufacturing will enable optical fluences greater than 2-4 times those used on Nova, substantially reducing the total laser aperture (and thus cost) required for ignition per- formance. Figure 104 is a schematic of the NIF from the recently completed conceptual design report.23o Figure 105 is a schematic of the NIF target area. In the case of direct-drive capsules, the beams are ab- The NIF, as currently proposed, is a 192beam, sorbed in the immediate vicinity of the ablator, so there is frequency-tripled (h=0.35 pm) Nd:glass laser system with very little geometric dilution of the hot electrons. In addition, routine on-target energy and power of 1.8 MJ and 500 TW, 4004 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Time integrated SBS reflectivity 0 2 10’5 4 10’5 6 1015 Intensity [W/cm*] SRS reflectivity at peak Te- 3keV 15 g *z 10 ‘E 8 G z5 is 0 Lll”‘l”“[J’“~““l”“I”hlll”l~ ,* .:_ ~. :.a\.?.,-‘,; .* 0 2 10’5 6 4015 intensity w/cm*] FIG. 101. (a) Time-integrated SBS reflectivities are 1% or less in energy from CsH,, plasmas for both open (gasbag) and closed (hohlraum) geom- etries with f/S focusing. Shown is the gasbag data. (b) For the range of intensities of interest to NIF ignition designs, SRS scattering levels are 28-596 with phase plates and 2 A of SSD. Without SSD temporal smooth- ing, the SRS level is about 10% at the upper end of the NIF intensity range, but still only about 2% at the lower end. appropriately pulse shaped.“’ A scientific prototype of one of the NIF beams, the “Beamlet,” is operational and has demonstrated most of the NIF laser requirements, including laser tluence and high-efficiency conversion to 0.35 pm light. The Beamlet will be used to continue to refine the NIF laser design before construction is initiated.132.233 The NIF system design requirements given in Table VII for indirect drive have been determined from the baseline target shown in Figs. 106 and 107. The hohlraum in Fig. 106 uses 1.35 MJ to drive the 150 kJ capsule in Fig. 107 at 300 eV. As discussed in Sec. IX, the light coming in each LEH in Fig. 106 is in two cones, so we can minimize time-dependent FIG. 102. Calculated linear SBS gain coefficients for the Nova experiments are comparable to those of NIF targets. asymmetry in the x rays incident on the capsule by dynami- cally varying the relative brightness of the cones. About a third of the energy must go into the cones near the target midplane. The 192 beams are clustered in groups of 4, so that there are effectively 8 spots in each of the inner cones, and 16 in the outer cones. Each cluster of four beams com- bine to form an effective f/S optic. Each beam is focused to an elliptical spot, which reduces laser intensity without reducing LEH clearance. The spot has a shape approximating a flat top (probably a sixth-order super-Gaussian), again to minimize the peak intensity while maximizing LEH clearance. The nominal spot is 500 pm by 1000 ,um at best focus. Such a spot can be made with re- cently developed kinoform phase plate techniques.234~235 The CH ablator in Fig. 107 contains 0.25 at. % bromine dopant. [The HEP-4 targets discussed in Sec. VI now use bromine-doped or germanium-doped CH.) The dopant, used to control the stability of the ablator/DT interface, reduces the preheat in the CH and eliminates an unstable density step at the CH/DT interface. As seen on current Nova targets, the CH is assumed to contain 5% oxygen as an incidental fabri- cation byproduct. A convenient way to evaluate the laser requirements for ignition targets is shown in Fig. 108. For a given hohlraum 10-3 0 20 40 60 80 100 120 140 fhot WW FIG. 103. The hot-electron fraction fhat resulting in fuel preheat equal to Fermi energy varies from <l% for direct-drive ignition capsules to >5% for the indirect-drive capsules on the NE Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 4005 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Cpntrol room FIG. Beam deliiery system I i I Ffi3quency- conversion Tat&et chamber crystals 104. The NIF is being designed to produce 1.8 MJ of 0.35 pm laser light with 500 TW for defense applications and inertia1 fusion ignition. The NIF be able to explore ignition with both indirect-drive and direct-drive targets. temperature T,, Eq. (92) specifies the relationship between laser power and laser energy. Using the 11% hohlraum cou- pling efficiency calculated for the NIF hohlraum in Eq. (92), we obtain the set of curves labeled at different hohlraum temperatures in Fig. 108. Laser plasma coupling will limit the achievable hohlraum temperature. From Eq. (192), at 400 eV for the long pulses required for ignition capsules, the hohlraum plasma will approach nln,=$. Based on the hohl- raum experimental results at 1 ,um, this is probably an upper- limit temperature for ignition hohlraums. (For short pulses with reduced plasma filling, it should be possible to achieve higher temperatures.) We now are limiting peak hohlraum temperatures to about 300 eV, which limits the plasma den- sities to n/n, ~0.1, as shown in Fig. 90. The minimum capsule energy is proportional to T;4.5, as given by Eq. (87). With a surface finish of about 10 nm, we require a margin in energy of about 1.5 above this mini- mum to ignite with the resultant mix. With a 100 nm surface finish, we require about a factor of 3 above the minimum energy. This gives the pair of curves, at these two different capsule surface finishes, which cut across the hohlraum tem- perature curves. Combining Eqs. (87) and (92), for a con- stant surface finish of 10 nm, gives 4006 Phys. Plasmas, Vol. 2, No. 11, November 1995 will Plaser(TW)= 285@,2,MJ). (200) The region between the NIF laser design performance and the intersection of the achievable hohlraum temperature and achievable capsule surface finishes defines the operating space for ignition targets. We have evaluated a variety of capsules and hohlraums within this region, as indicated by the dots on Fig. 108. Most of the target analysis236-z8 has focused on the baseline 300 eV hohlraum and capsule shown in Figs. 106 and 107. Because this target design (referred to as the PT design) operates near the expected maximum hohl- raum temperature, it is a good design to evaluate the laser power requirements. Also, because the laser-plasma cou- pling is more of an issue at the higher temperatures, as indi- cated in Sec. XI, it is important to investigate the high- temperature designs in detail. At 1.35 MJ, this point design is below the 1.8 MJ, 500 TW NIF laser design performance, and above the ignition energy minimum. This design allows for uncertainty in both laser-capsule coupling efficiency and ignition threshold. The one-dimensional (1-D) capsule simulations de- scribed next are done with the LASNEX code,5’ using PN radiation transport,239 equations of state calculated in line Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp FIG. 10.5. The NF target area is configured for accessibility and ease of maintenance for both laser operations and target experiments. with a “Quotidian EOS” mode1,240 and average-atom XSN opacities.a4r Other radiation-transport schemes predict the same capsule performance. As a source for implosion calcu- lations, non-Planckian frequency-dependent radiation was determined from hohlraum simulations. The spectrum used affects the short-wavelength hydrodynamic instability growth. Other than this effect, which can change perturbation amplitudes by about a factor of 2, the spectrum has little effect on target characteristics. The deposition of a particles produced by the burn is normally calculated with the multi- group diffusion’42 model in LASNEX. Calculations243 of the PT capsule using a Monte Carlo charged-particle transport mode124 produce ignition and burn that are essentially the same as produced by multigroup charged-particle diffusion. tainties in opacity and equation of state, adequate shock tim- ing may not be predictable a priori, but it is achievable with an experimental program that uses techniques currently available on Nova.‘08-“0~‘49 The capsule in Fig. 107 can tolerate moderate deviations from the optimal radiation temperature profile shown in Fig. 106. For example, Fig. 109 shows the yield as the early-time foot and peak drive temperatures are varied. The pulse shape shown in Fig. 106 creates four shocks. The final shock brings the ablator up to peak pressure with sufficiently low DT entropy, as previously shown in Fig. 37. The entropy requirement implies a corresponding require- ment on pulse-shaping precision. For optimal performance, the shocks must be timed within about 200 ps. Given uncer- A lower temperature capsule design is shown in Fig. 110. This capsule was designed with a beryllium ablator, which develops a somewhat higher ablation pressure since it has a lower albedo in this temperature range. Hence, the capsule absorbs more flux at a given temperature, as dis- cussed in developing equation (137). This is important at the lower temperature. Figure 111 shows the sensitivity of the beryllium capsule to pulse-shape variations. A higher- temperature foot to the pulse results in an overall shorter pulse but puts the capsule on a higher adiabat. This reduces the ignition margin and makes capsule performance more sensitive to hydrodynamic instabilities, the resultant mix, and Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 4007 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp TABLE VII. Functional requirements for the indirect-drive NIF laser design. Energy (measured at the entrance hole of the hohlraum) Peak power Wavelength Pulse shape Duration Dynamic range -Continuous -Discrete Capsule irradiation symmetry 1.8 MJ 500 Tw 0.35 ,um Continuous or discrete pulses 20 ns 5o:l lo:1 Hohlraum illumination: Geometry: 2 concentric cones from each side Beamlet energy balance Beamlet pointing accuracy Prepulse Pulse simultaneity Spot size Beam smoothness Cone angles: 27’ and 52’ Beamlet distribution: 3 on outer cone {on inner cone 8% RMS 50 ym < 10’ W/cm2 <30 ps 500 pm at the laser entrance hole Kinoform phase plates at the output Centerline frequencies separated nominally by 1 nm at 1 o in each beamlet of a 2X2 array 2X2 array of beamlets superimposed on target to control intensity fluctuations averaged over a 30 pm circle and 10 ps to less than 25% of average intensity small deviations in the pulse. The shorter duration pulse in Fig. 111 is almost a direct geometric scale of ps22 used in most of the Nova symmetry experiments discussed previ- ously. For the set of curves with the lower-temperature foot, the stepped temperature pulse and the middle continuous pulse give equivalent capsule performance. The initial gas-fill density in the capsule, which can be controlled by varying the temperature of the cryogenic fuel, can be used in turn to control the capsule’s convergence ra- tio, and hence its sensitivity to flux asymmetry. Figure 112 shows the result of varying the initial fill on the convergence ratio for the 300 eV baseline CH capsule. The yield de- creases as the initial gas fill is increased because the total fuel pr decreases. With a CH ablator, the convergence ratio can be decreased approximately from 35 to 25 before the yield drops below 1 MJ. With a 300 eV beryllium ablator capsule, the convergence ratio can be reduced further to about 20, as shown in Fig. 112. As discussed previously, Nova capsules are made largely from plastic. A CH ablator was chosen for the baseline NIF capsule because developing, characterizing, and filling NIF capsules from this material would be more straightforward by means of techniques similar to those already developed for Nova capsules. Techniques are now being evaluated to develop high-quality beryllium shells. nonuniform, differential cooling will result in a higher sur- face temperature and a higher sublimation rate at the thicker part of the layer. Condensation will occur preferentially on the thinner and cooler parts of the layer. This technique pro- duces uniform layers, but the surface quality of the layers depends on many variables that are still being investigated. Calculations indicate that the cryogenic layer must have a RMS surface finish of 0.5 ,um or less in spectral modes be- low L-30. Current estimates from cylindrical player experi- ments carried out jointly by Los Alamos and LLNL indicate that a /3 layer will have a surface roughness about 2-4 times larger then this.247 However, experiments also indicate that additional heating (either from Joule heating of free electrons in the DT driven by a microwave power source or from infrared absorption in the rotational and vibrational absorp- tion bands of DT) can improve uniformity to the required level.248 This latter technique also should apply to DD layers, which will be required for a variety of diagnostic experi- ments. All NIF targets require about a 100 pm cryogenic layer of DT. The physics and technology of thick cryogenic layer formation are quite complex. A prime candidate for thick layer formation is called /3 layering.245*246 Because of tritium ,G decay, DT fuel produces heat at about 1 W/g. If a capsule partially filled with solid DT is held at uniform temperature, the DT will tend to form a uniform layer. If the layer is Alternatively, a uniform layer may be produced by ap- plying a temperature gradient to a liquid cryogenic layer.24g Because both surface tension and evaporation rates are tem- perature dependent, it is possible under some conditions to obtain a uniform layer by adjusting these two properties with an appropriate temperature gradient. In a final technique, a low-density foam is used as a matrix for the cryogenic fuel layer.250 A foam-filled fuel layer has a higher ignition temperature, which depends on the foam density and material composition. Hence, most foam designs require a thin layer of pure DT on the inside of the foam to aid ignition. The Omega Upgrade laser will be used as a test bed for 4008 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 0 5 10 15 20 Ttme (ns) . Outer cone Thickness > 30 pm 8urtace flnlsh I 0.08 wm PTV H+0.25% Br+!f% 0 solld V DT gas 0.3 mg/cm3 Capsule yield 15 MJ FIG. 106. Most of our modeling has concentrated on a 300 eV target, which absorbs 1.35 MJ of light. developing targets with thick cryogenic layers. These experi- ments will begin in 1998. As discussed in the Introduction, initiation of a self- sustaining burn wave constitutes ignition in ICE Beyond a threshold implosion velocity for a given cap- sule size, P dV work can compress the hot spot to the pr and temperature at which a-particle deposition can initiate a burn wave. This occurs when the hot spot’s central tempera- CH + 5% 0 + 0.25% Br 1.11 mm Solld D .95 mm Peak Tr 0.87 mm In-flight aspect ratio Distance moved/AR DT \/ 0.3 mg/cms hip Convergence ratio Peak P V Total ir Tolerates surface finish (PTV, Nova capsule spectrum) Tolerates mlx penetratlon Yield 300 eV 40 25 4.1 x 10’ cm/s 36 1200 g/cm3 1.5 g/cm2 8ooA 91wn 15 MJ FIG. 107. A CH capsule is our ignition point design, and its features deter- mine the requirements for symmetry, stability, and ignition. Hohlraum physks aoe*plahl- Atal energy (M?) FIG. 108. For ignition targets, plasma-physics issues constrain the achiev- able hohhaum temperatures, and hydrodynamic instabilities establish the minimum required temperature. The shaded region constitutes the accessible region in power and energy space, where ignition with indirect-drive cap- sules is predicted. ture reaches about 10 keV with a pr of 0.2-0.3 g/cm2, as described in Sec. III. For NIF-scale capsules, threshold ve- locity is expected to be 3.5-4.0X lo7 cm/s. Ignition results in a rapid increase in yield as implosion velocity is increased gradually beyond the ignition threshold velocity. Experimentally, the implosion velocity can be in- creased, while keeping the fuel on the same isentrope, by varying the peak drive temperature at the end of the pulse or by varying the length of the pulse. As shown in Fig. 113 for the PT capsule, without a-particle deposition and the resulting burn propagation, NIF targets are expected to produce no more than lo-100 KJ, whereas a target with ignition and successful burn propaga- tion will produce l-20 MJ of thermonuclear energy, depend- ing on capsule and hohlraum design. Below a burn-averaged temperature of about 3 keV, neg- ligible a-particle deposition occurs, and the observed in- crease in fusion yield with implosion velocity follows that expected for the purely hydrodynamic increase in the fusion cross section. By the time the fuel temperature doubles due to o-particle deposition, the fusion burn rate has increased by an order of magnitude or more beyond what could be achieved with pure hydrodynamic compression. Target per- formance below a central temperature of a few keV will provide an experimental baseline for determining the purely hydrodynamic increase in fuel temperature as a function of implosion velocity against which the measured departure due to a-particle deposition can be determined. 0 mot temperalure (W FIG. 109. The NIF capsule point design readily tolerates 6% swings in peak or foot temperatures (25% changes in flux). Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 4009 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Surface finish 5 0.06 pm PTV Be, r-dependent V DT gas 0.3 mg/cm3 Capsule absorbs 180 kJ, yields 14 MJ FIG. 110. A capsule with 250 eV peak drive provides a different tradeoff between hydroinstabilities and laser-plasma effects. A slightly higher- energy capsule can be driven by the same laser since the peak power re- quirement is lower. Beryllium is a superior ablator material at 250 eV. This design can tolerate surface perturbations of -600 A, compared to -800 8, for CW300 eV (both peak-to-valley, within the range of current Nova cap- sules). The peak intensity drops from 2X10’5-7X10’4 W/cm*, which re- duces the gain for laser-plasma instability. The convergence ratio is about the same as for a CH capsule at 300 eV. A complementary set of experiments could be done with a nonigniting fuel layer. For example, above or below some ratio of D to T, the targets will not ignite at any implosion velocity reached on the NIF. Assuming a comparable cryo- genic layer quality and a slightly revised pulse shape to ac- count for initial fuel density differences, a curve of yield versus implosion velocity with a nonigniting fuel mixture, normalized for cross section differences, would provide an additional baseline for comparison with the ignition experi- ments. Changing the D to T ratio could affect a cryogenic layering process, which would complicate direct comparison with the 50150 DT case. For example, p layering will not work with a pure D2 fuel layer but might work with a pure or nearly pure Tz layer. The NIF baseline capsule designs absorb 150 kJ, of which about 25 kJ ends up in the compressed fuel. As shown in Fig. 113, the central temperature gets to about 10 keV when the capsule has produced -400 kJ. Therefore, ignition occurs when the fuel energy gain is about 16, or when the a-particle deposition is about three times the initial energy delivered to the compressed fuel. Since the NIF baseline tar- gets are expected to yield up to 15 MJ, these targets would 4 1 MJ 150 F 3 CL 100 50 50 0 250-eV Be capsule 0 5 10 15 t (ns) ‘e capsule 1 FIG. 111. Total pulse length can be varied by adjusting the power in the foot of the pulse. The capsule fails when the foot power is greater than about 130 eV because the fuel adiabat is too high. Nominal 0.3 mg/cm3 - 40 0.5 1.0 1.5 2.0 2.5 Initial gas density (mg/cm3) FIG. 112. Capsule gas fill provides direct control of convergence ratio. Increasing the initial gas fill reduces convergence ratio (and yield). have a fuel energy gain of about 600. A factor of 5-10 higher-energy gain is required for ICF energy production, as discussed in Sec. XIV. ICF target gain requirements can be compared to the Ml% power gain Q discussed in the Intro- duction. The general approach to modeling the effects of hydro- dynamic instabilities on ignition capsules was described in Sec. VI. The ignition targets are designed to remain in the linear or weakly nonlinear regime. Because of this, instabil- ity modehng is based on linear analysis that is as accurate as possible, with an extension into the weakly nonlinear regime =i 1 3 ” $ 0.1 0.01 0 I I I I I I 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Multiplier on peak flux FIG. 113. Ignition could be diagnosed as an increase in yield and neutron- width bum temperature as drive is varied. 4010 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp as necessary. The linear analysis is based on a decomposition of the surface perturbations into spherical harmonics, which are eigenmodes of the linear evolution. Single-mode growth is determined by running many 2-D simulations, each of one single mode in the linear regime throughout the simulation. This provides the most accurate calculation of all known effects, including ablation and density-gradient stabilization, Richtmyer-Meshko? growth, and convergence effects. This set of calculations, combined with a nonlinear satura- tion model,‘31 provides a spectrum of growth factors, as shown in Fig. 48 for the PT capsule. These growth factors are combined with an assumed initial surface spectrum to determine the ignition time perturbation. To test the weakly nonlinear analysis, full simulations of multimode perturbations with realistic initial amplitudes are also run. Currently, simulations must be 2-D, and the number of modes that can be included is limited. A variety of multi- mode simulations have been run on several capsules, at solid angles ranging from relatively small conic sections to half- spheres. Results are consistent with this modeling, although further substantiation is an area of current work. Recent de- velopment of 3-D codes will allow testing of possible differ- ences between 2-D and 3-D evolution.252 The effects of these perturbations on the hot spot are evaluated in a variety of ways. The unstable interface is be- tween relatively cold, dense DT and the hot, lower-density DT of the hot spot. Material mixing of different elements does not occur, only thermal mixing. The actual perturba- tions are 3-D and multimode, and the weakly nonlinear per- turbation growth analysis indicates that the spectrum is strongly dominated by modes around I= 10-20, as shown in Fig. 48. The 3-D character cannot be fully represented in any existing code; available 3-D codes do not include all of the relevant physical processes. There is 3-D calculationalZ2 and experimentalz5” evidence that the multimode 3-D perturba- tion is probably an array of spikes penetrating in toward the hot-spot center surrounding approximately hexagonal bubbles. The effects of perturbations on the hot spot have been modeled in two dimensions in five ways. ti) @> (iii) (iv) W A single bubble of appropriate solid angle surrounded by a curtain of spikes falling along a reflecting bound- ary condition. The circular cone approximately repre- sents a multifaceted 3-D cone of similar size and gross shape. Perturbations with the opposite sign; i.e., a spike on axis surrounded by a circular bubble. Perturbations on the waist that represent long circular ridges and curtains. The multimode 2-D simulations mentioned above, continued through burn time. One-dimensional modeling in which the thermal mix- ing caused by the perturbation growth is represented as an enhanced thermal conductivity in the perturbed region. All of these approaches give similar results as to how large a spike can be tolerated before ignition is quenched: the spikes penetrating the hot spot can be lo-15 ,um in ampli- tude (for the PT), compared to a hot-spot radius of 30 pm. Phys. Plasmas, Vol. 2, No. 11, November 1995 Combined with the modeling described above, this corre- sponds to a maximum tolerable initial ablator surface rough- ness of 50-80 nm RMS. This is to be compared with 20-30 nm RMS surface finish on current Nova capsules. Analysis of the bubble penetration from the outside of the shell gives a surface-finish requirement for shell integrity during acceleration that is comparable to that for ignition. This equivalence depends weakly on the shape assumed for the spectrum of initial perturbations. The modeling described so far pertains to surface pertur- bations that are initially on the outside of the ablator. Of course, there will be perturbations on the other interfaces, as well as material inhomogeneity and other fabrication defects. Any of these can be modeled in a conceptually identical way, using LASNEX simulations based on the assumption that the perturbation of interest exists. These calculations predict that the capsule tolerates perturbations initially on the other inter- faces, which are much larger than tolerable perturbations ini- tially on the outside. Perturbations on the DT/CH interface are very unlikely to be large enough to matter. Perturbations on the DT gas/solid interface need to be smaller than about 0.5 pm. Currently, the best way to model radiation transport and coupling efficiency in ICF hohlraums is with detailed 2-D calculations using a radiation-hydrodynamics code. The cal- culations described here use LASNEX, with detailed radiation transport for the hohlraum/capsule coupling. The simulations are continued all the way through burn. The simulations track the laser beams, calculating inverse bremsstrahlung en- ergy deposition and any refraction that occurs. The calcula- tions typically use XSN non-LTE multigroup opacities,241 although simulations with an opacity table derived from the STA opacity model are also done.‘46 Any coupling to the capsule via hydrodynamic pressure or electron conduction is included. Adequate symmetry and near 1-D burn performance has been achieved in such integrated simulations for a variety of designs at several sizes, including the PT, and beryllium de- signs driven at 250 and 300 eV. Figure 114 shows the 1-D and 2-D yield and burn temperature for the PT target and targets scaled from this design. The 1-D results are from hydrodynamically scaled targets with the required laser en- ergy given by E(MJ) = 1. 35s3, where s is the spatial scale factor compared to the PT. To model asymmetry resulting from imperfect power balance and pointing of me laser beams, we must estimate the effects of fully 3-D asymmetry. This asymmetry and its effects have been modeled in a variety of ways. The asym- metry can be estimated analytically, using laser spot bright- nesses and positions determined from the 2-D LASNJZX simu- lations. Also, the asymmetry can be calculated in three dimensions with a view-factor code. We have used fully in- tegrated calculations, as described above, to confirm the modeling and for some sensitivity studies. The actual 3-D asymmetry on the capsule must be estimated with 2-D simu- lations of the implosion driven with an asymmetric radiation source. Calculations have been carried out with a wide variety of asymmetries on 2-D capsule implosions to ensure that the Review Article 4011 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Yield WJ) and ion tamp Wvt - = ID capsule simulations l o = Integrated simuiations of full target (MJ) 1.0 1.5 Input laser energy (MJ) FIG. 114. Scales of the point design ignite above about 700 kJ. For the I-D capsule simulations, capsule dimensions and times are scaled by s, and the effective laser energy is given by EC&J)= 1.35~~. where s=l is the IT design. For the integrated hohlraum and capsule simulations. dimensions and times are proportional to s, and powers are proportional to s*. specified asymmetry levels are acceptable. Asymmetry can affect ignition in a variety of ways: the obvious kinematic effects of differing velocities; initiation of RT instability growth, especially evident during deceleration; mass flow to- ward less-driven regions, seeding RT instability; irregular hot-spot compression, sometimes forming jets that protrude from the core and disrupt the imploded configuration, as dis- cussed in Sec. IX; and delayed ignition, resulting in more RT growth. The maximum tolerable asymmetry depends on temporal and spatial specifics. In detailed simulations, a P, asymme- try that varies between +4% (constant until switching) and -4% (for the duration of the pulse) produces a marginally acceptable implosion. (In this, and in all of the following, the P, coefficient is quoted so that the peak-to-valley asymmetry in flux is 1.5 times the number quoted.) If the switching time is chosen so that the average asymmetry is zero, the im- ploded configuration is, on average, round but shows a jet. With a swing from +2% to -2%, the asymmetry is small. In this case, the peak pressure generated in the fuel (when no thermonuclear bum is allowed) is reduced by about 12% compared to a perfectly spherical implosion. The yield (in a bum-on simulation) is not reduced by the asymmetry. It is worth noting that, in this simulated implosion with a “2% time-dependent asymmetry, the shell is as much as 10 pm out of round while at radii between 500 and 100 pm. It is as much as 10% out of round (AR= 10 ,um for R= 100 pm) toward the end of the implosion. This degree of asym- metry in the implosion could be measured with a backlighted imaging diagnostic similar to those that have been used on Nova. As mentioned in the Sec. IX discussion on time- dependent asymmetry, the roundness of an imploding shock in a foam shell can be determined on Nova to -2 pm reso- lution. The jetting asymmetry effect is maximized (at a given percent of peak flux asymmetry) by having the asymmetry be constant for the first part of the pulse and then switching to 10 RsdlaUvs &I-’ 300 I 1mperatur* (OV) ,‘- 250 FIG. 115. With a constant power ratio (35% inner cone, 65% outer cone), NIF targets exhibit time-varying asymmetry in the P, and P, Legendre moments of flux. In detailed 2-D calculations, ignition capsules with this degree of time variation ignite and give yields near those seen for spherical implosions with uniform radiation drive. This degree of temporal variation in flux uniformity is near the maximum tolerable and would be reduced by “beam phasing” in which the power fraction in the inner and outer cones is varied in time. another constant value, with the opposite sign, for the re- mainder of the pulse. For that kind of time dependence, the baseline NIF capsule can tolerate 4% P, asymmetry, as de- scribed above. Typical detailed 2-D calculations have a more gradual variation in asymmetry with a lower average pertur- bation for a given peak, as indicated in Fig. 115. If the period of the symmetry swings is shorter, such as would be the case in an experimental program that was de- signed to obtain a uniform average flux over some fraction of the implosion, still larger symmetry swings are tolerable. For example, with a P2 of the form Adt)=Adt)~20 sin[w(t-tu)], (201) where A,(t) is the total flux, w=2?r/(2 ns) (a 2 ns period), implosion symmetry is tolerable with e20 larger than 10%. The time to must be such that the average asymmetry is about 1%. When f. is changed, the principal effect we see is the change in the average P,. If the sinusoidally time- dependent asymmetry is too large, the failure mechanism for this short-duration asymmetry is a jet coming from the center of the implosion outward, as a result of irregular shock con- vergence in the center, rather than the azimuthal mass varia- tion seen for the longer duration asymmetry described above. Although NIF hohlraums certainly have time-dependent asymmetry, current detailed 2-D integrated calculations of NIF targets indicate that, with optimal placement of the two rings of laser beams per side, the time dependence is mar- ginally toIerable for ignition targets, even without indepen- dent time histories for the individual rings. Figure 115 shows the time-dependent asymmetry for the E’T target, with the two cones on each side having a constant power ratio. In this case, 35% of the laser power is in the inner ring and 65% is in the outer ring. The capsule in this integrated calculation achieved nearly the yield obtained in a perfectly spherical implosion, However, the time variation shown in Fig. 115 is near the maximum tolerable. Independent control of the 4012 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 0 Peak max allowable 1 0 r 1 1 I I 0 5 10 15 20 25 Power balance uncertainty (% RMS) FIG. 116. Beam-to-beam energy balance errors can be as large as 15% if beamlet-to-beamlet fluctuations are uncorrelated. power ratio in the separate rings, or “beam phasing,” would be used to reduce the time-dependent asymmetry, as de- scribed in Sec. IX. Since LEH effects and laser spot motion from refraction, wall blowoff, and laser-plasma interaction are the primary causes of time-dependent asymmetry, the issue for the NIF is whether uncertainty in these variations could lead to a failed implosion. Experimental measurements of the wall loss and laser spot position on Nova can establish the time-dependent asymmetry to a few percent, as discussed in Sec. IX. Similar experiments can be done on the NIF. As indicated in Fig. 115, this is well within the tolerable level of time variation for NIF capsules. Further, as described in Sec. IX, several techniques are being developed on Nova that would apply to the NIF for directly measuring the time-dependent asymme- try onto the capsule. We do not find very much variation in sensitivity to asymmetry among the various targets we have designed. Smaller capsules are slightly more sensitive to asymmetries that couple to deceleration RT growth. The difference is not large, and symmetry sensitivity is not an issue that is impor- tant in deciding the overall tradeoffs of laser size and power. Varying the hohlraum size, with a given capsule, is the sym- metry issue likely to be more important in the tradeoffs. Three-dimensional Walle code’80*254 view factor calcula- tions, as shown in Fig. 116, indicate that 10% Rh4S power imbalance between the beamlets results in less than 1% asymmetry at any given time on the capsule, provided the deviations are uncorrelated among the 192 beams. If the power imbalance varies in time, the tolerable power imbal- ance at any particular time can be much larger than this, depending on its time dependence. If correlations exist be- tween the beams’ powers, a much tighter power-balance re- quirement is necessary. For example, groups of eight corre- lated beams, with each group going into the same area of the hohlraum, must be balanced within about 3%. This increased precision requirement is consistent with the assumed reduc- tion in the number of statistically independent power histo- ries. Since the pulse shape can be adjusted for each of the 192 beamlets in the NIF design, any power variations should be statistical. These requirements on the laser are well within current Nova performance parameters of 3% RMS energy imbal- ance, and 5%-10% power imbalance over time scales that Phys. Plasmas, Vol. 2, No. 11, November 1995 tg 0.8 - s 5 0.6 - ii 2?p ---- : $ 0 cL4 - 0.2 - LT SB o Foot l Peak ,------m-w 2 0 J Max tolerable -----..--m^mmm-_ 0 Oo 0 0. l l . OOM 200 Pointing uncertainty (pm, RMS) FIG. 117. Pointing errors can be as large as 200 pm RMS without degrading symmetry significantly. are generally less than half the pulse length.“’ This does not mean that symmetry in Nova hohlraums is as good as in NIF hohlraums; the looser requirements for NIF are a result of the larger number of beams. Three-dimensional Walle view factor calculations indi- cate that with nominal pointing errors-each beam is to point within 50 w RMS of its nominal position, as specified in Table VIII-the resulting additional asymmetry on the cap- sule will be significantly less than 146, as shown in Fig. 117. This pointing specification also ensures more than adequate clearance of the LEH. This requirement is similar to that met by the Nova laser (30 ,um RMS on Nova”’ is 10 wad, but 50 pm RMS on NIF is 7 prad because of the longer focal length). Both view factor and 2-D detailed integrated calcula- tions have been carried out to evaluate the sensitivity of sym- metry to changes in hohlraum geometry and beam cone po- sitions. Table VIII gives the results for the view factor calculations, which are generally consistent with the analyti- cal analysis presented in Sec. IX. Figure 118 shows an example of the 2-D sensitivity de- termined from the integrated calculations, in this case for a beryllium-ablator target driven with a step laser power pro- TABLE VIII. Several parameters are available to control symmetry with two cones of beams. P2 (%)* P4 (%) Power balance inner versus outer change inner power/outer power by 5% Foot 1.7 -0.4 Peak 1.0 -0.1 Hohlraum aspect ratio (fixed hohhaum area and LEH, beams central in LEH) Make hohlraum 100 pm longer Foot 1.8 I.6 Peak 1.6 0.7 Make hohhaum 100 w longer and use Foot *.. 2.0 power to correct P, change Peak a** 0.8 Outer beam pointing Move spots 100 pm out Foot 1.2 1.2 Peak 1.2 0.5 Inner beam pointing Move spots 100 pm out Foot 1.4 -1.2 Peak 0.9 -0.5 “Estimates made using the Walle 3-D view factor radiation transport code. Review Article 4013 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp 12. 10 z* g 6, 4, 2. I I I I I I -400 -200 0 200 400 600 Change in SZparation of spots (AS, pm) FIG. 118. Integrated calculations are being used to confirm acceptable sen- sitivity to pointing. Laser ring separation controls P,. The pointing sensi- tivity is large enough that we can use it to control P, but small enough for the specified pointing accuracy. file. The target can tolerate beam movement of the average ring location of 2200 pm, well outside the expected devia- tion, given the pointing specification on the laser. Figure 119 shows that the integrated calculations of the PT target can tolerate significant variations in the peak power pulse length at two hohlraum lengths, which differ by 400 pm. Asymmetries might also arise from laser-plasma inter- action processes, or other phenomena such as RT instability at the Au/He interface, which are currently predicted not to be significant, but for which uncertainty remains. Light can be scattered, or it can be absorbed more or less efficiently at different positions in the hohlraum. The effect in all cases is equivalent to a power balance change, a movement of the x-ray emission spots, or perhaps a spreading of the laser deposition spots (for small-angle side scattering). Difficulties could arise only if these effects are so large that their irre- producible part is larger than the limits described above. If any of these processes occur but are reproducible and not too large, the effect can be mitigated by changing the hohlraum design parameters. Estimates based on Nova experiments de- scribed in Sec. XI and modeling indicate that these processes can be kept within acceptable limits. If we cannot do this for the 300 eV ET target, our ultimate recourse will be to in- crease the hohlraum size, reduce the laser intensity, and cor- hpln I.ml, amqYlW *--,- ---e ,I 1.37 1.25 JY-1 0.1 ,/I “ohlmml length -1.WMl - -t.occnl 0, I I I 5 2.0 2.5 3.0 3.5 4.0 Main pulse FWHM (ns) FIG. 119. Integrated calculations indicate that the high-power main pulse length can be varied by more than 0.5 ns. 4014 Phys. Plasmas, Vol. 2, No. 11, November 1995 respondingly reduce the hohlraum drive temperature to the 250 eV design, which has significantly less plasma, as dis- cussed in Sec. XI. The remaining uncertainties can be mitigated with changes in the target design that will be made after further Nova experiments, or after the NIF experiments begin. Some of the uncertainties that we have evaluated include the fol- lowing. (9 (ii) (iii) (iv) (VI (vi) A factor of 2 in hydrodynamic instability growth (equivalent to a factor of 2 in surface finish or a factor of 2 in the acceptable size of the bang-time perturba- tions) shifts the ignition cliff from 0.8 to about 1.0 MJ. Improvements in surface finish could probably recover the original margin. The combined uncertainties in x-ray conversion and hohlraum wall loss (energy) are less than about 20%. Stimulated Brillouin scattering should be only a few percent, based on the experiments described in Sec. XI. Depending on the accuracy of the 2-D integrated cal- culations, achieving the correct power balance be- tween the inner and outer cones of beams may require reducing the power in one or the other so that it can- not run at its full power. This may result in a net energy loss of lo%-15%. An error in hohlraum optimization that requires in- creasing the LEH radius 50% would require an in- crease in laser energy of 15% to regain the same hohl- raum temperature. Similarly, increasing the hohlraum area by 35% in- creases the required laser energy by 15%. Several other uncertainties are energetically insignifi- cant. For example, the equation of state and opacity of the CH ablator are sufficiently uncertain that we expect to adjust the details of the pulse shape phenomenologically, but this will not significantly affect the performance requirements of the laser, or the target performance. These errors, in combined effect, are consistent with the factor-of-2 margin provided by a 1.8 MJ, 500 TW laser. Based on all available data and detailed simulations, 1.8 MJ should be adequate for ignition. Although indirect drive is the primary approach to igni- tion on the NIF, developments in direct drive have reached the point where this approach also looks quite promising. With the implementation of additional beam smoothing and more beam ports on the target chamber, the NIF can be con- figured to be capable of both indirect and direct drive. Figure 120(a) shows a schematic of the NIF target chamber with the 48 beam ports configured for indirect drive. By adding 24 more ports, as indicated in Fig. 120(b), and implementing 2-D SSD beam smoothing, the NIF would achieve the beam smoothing currently estimated by LLE55 to be required for direct drive. The NTF will be able to shift rapidly (61 day) between these two geometries if a movable turning mirror is inserted in the NIF switch yard and the additional hardware required for the 24 new beam positions is installed. Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp (a) NIF ID beam geometry (b) NIF DD beam geometry I FIG. 120. The NIF target area beam geometry: (a) NIF baseline target area uses 48 clusters of 4 beams configured for indirect drive; (b) NIF target area building and beam transport system can be reconfigured for direct drive by switching 24 of the 4-beam clusters to alternate positions. XIV. INERTIAL FUSION ENERGY Experiments and analysis conducted over the course of nearly two decades of research have allowed us to establish the hydrodynamics, radiation transport, x-ray production re- quirements, and the plasma-physics limitations of indirect inertial fusion using laser drivers. A demonstration of igni- tion and bum propagation would set the stage for high- confidence development of the applications of ICF, including inertial fusion energy (IFE). Because of their potential efficiency, durability, and rep rate, the NASz6 FPAC,34 and FEAC?’ reviews concluded that, of the current ICF drivers, heavy-ion drivers have the greatest potential for future inertial fusion power plants. For both laser-driven and ion-driven indirect drive, the capsule is radiation driven so that the capsule implosion and bum phys- ics are the same. If the ion-driven hohhaums are heated to the same radiation temperature T, , then the requirements for hydrodynamic instability, implosion uniformity, and pulse shaping to drive the capsule can be applied directly. In addi- tion, at the same radiation temperature, x-ray hohlraum wall losses, radiation-driven hohlraum wall motion, and radiation transport are also directly applicable. Because these are the primary issues that affect coupling efficiency and hohlraum symmetry, the laser-driven hohlraum physics program pro- vides a solid base for calculating heavy-ion (HI) hohlraums. Clear differences exist between HI and laser hohlraums, as indicated in Fig. 6. For example, unlike HI hohlraums, laser-driven hohlraums have holes that affect symmetry, and lasers must contend with laser-plasma parametric instabili- ties and spot motion, which limit hohlraum plasma condi- tions. In current NIF hohlraums, temporal and spatial control of the power is used in a large number of beams to control hohlraum symmetry, whereas in the HI hohlraum in Fig. 6, only two radiators are used. As stated earlier, this geometry is attractive from the point of view of fusion chamber design3* because it is compatible with a variety of protected- wall fusion chambers. Symmetry is obtained by adjusting the internal structure and shape of the hohlraum.723255 The HI hohlraum in Fig. 6 controls P2 asymmetry by controlling the size, shape, and position of the shield directly inside of each radiator, such as in the Nova experiments described in Figs. 78 and 79. Higher-order components to asymmetry, except for P,, are controlled by having a relatively large hohlraum. For hohlraum designs that attempt to maximize coupling ef- ficiency, control of P4 is also required. That is accomplished by an additional shield, as shown in Fig. 6. By using the data and calculational techniques developed for laser-driven hohl- raums, it is possible to calculate the impact of the geometric differences between ion and laser hohlraums. To test the transport issues directly, it is also possible to do laser experi- ments with geometries that mock up HI hohlraums. The physics of ion stopping in hot matter and x-ray pro- duction from a volume-heated radiator are unique to ion hohlraums. Ion stopping in hot matter has been studied by many investigators. 35*36 The physics is believed to be well understood, and the experiments to date,“56 although not at the required matter temperature, match theory. The body of data being developed in the light ion program conducted at Sandia National Laboratories is being extended to higher matter temperatures as the ion-beam intensity on the PBFA II machine is increased. If Sandia is successful in raising the intensity from the current 1-2 TW/cm” to about 5 TW/cm*, PBFA II should be able to reach temperatures of 100 eV. An investigation of a wide range of beam-plasma instabilities,Z7 which could be driven by the ion beam as it propagates through the low-density target corona, also has failed to uncover any mechanism that could transfer a sig- nificant fraction of the beam energy. Simulations of the absorber/radiator geometries shown in Fig. 12 1 indicate that an x-ray conversion efficiency of 50%-80% can be achieved under appropriate conditions.37 Ion beams generally are absorbed in a relatively low-2 ma- terial that heats up and then radiates like a blackbody if the radiator has an optical depth approximately equal to a Planck mean-free path. The energy balance equation for an ion beam can be written as Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 4015 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp (a) Front shield 1 ‘0 J 160 o%bYk-A- Time (ns) cu!50 1O:O Gel’ I 4o 0.1 I I 0 . 2 0.3 0.4 2.5 2.4 2.2 2.0 I- I- L Focal spot radius (cm) 10 20 30 40 Time (ns) RG. 121. With properly designed radiation converters, heavy-ion beam energy can be efficiently converted to x rays. da dEk I=R dt --$ x+(T,T;I, (202) where R is the ion range in g/cm2, E is the specific energy of the absorber, and E, is the kinetic energy of expansion of the absorber. The heat capacity term, R( d eldt), which is propor- tional to the temperature T,, is the dominant term at low temperature. At high temperature, the radiative term domi- nates. The kinetic-energy term generally can be made small by appropriate choice of absorber material. If the intensity is too low, the absorber material never heats up sufficiently to become an efficient radiator before the pulse ends. At high intensity, the absorber heats up quickly and then radiates very efficiently. The intensity required for efficient conver- Ion range I 0.05 g/cm* 2w1 sion increases as the range increases because the longer range resuits in a higher heat capacity of the absorber and a longer time before radiation becomes efficient. Figure 121 shows the results of calculations for a spe- cific radiator geometry. In these calculations, the x-ray power required by a target was specified. As the ion-beam range and focal-spot size varied, the ion-beam power also was var- ied to achieve the required x-ray power. Figure 122 shows the calculated gains (as a function of ion-beam focal-spot radius for two typical HI ranges} for targets with the geometry shown in Fig, 6. The gains given in Fig. 122 are based on an analytical model258 for the various elements of the ion-beam-driven hohlraum. As indicated, Ion range 5 0.1 g/cm* I I I I .” 1 2 4 6 10 Driver energy (Ml) 1 2 4 6 10 Driver energy (MJ) FIG. 122. Energy production using indirect-drive, heavy-ion targets may be feasible with a driver of 2-3 MJ. 4016 Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp these gain curves have used capsules with drive temperatures that vary in the way specified by Eq. (87), with a factor of 2 allowance for nonideal effects. The wall-loss model follows that given by Eq. (124), and the modeling of the radiator components is similar to that given by Ho.37 Detailed 2-D integrated radiation-hydrodynamics calculations, using the’ modeling techniques developed for the Nova experiments and the NIF hohlraums, are being carried out. Initial calculations”59 of this type have achieved a gain of 50 at 8 MJ. Refinements of these calculations are expected to dem- onstrate gains comparable to those in Fig. 122. As shown in Fig, 122, gains are critically dependent on the spot size of the ion beam when it is focused on the target radiators. This dependence arises from the energy required to heat the material in the x-ray converters to a temperature at which they will radiate efficiently. As the ion range de- creases, less mass is heated at a given spot size. This results in a higher gain for a given spot size or a larger tolerable spot size for a given gain. As the range decreases, the radiators cover an increasing fraction of the hohlraum surface area. For some designs, such as those being pursued by Sandia for light ions and some recent HI target designs,260 the ion beams cover the entire surface of the target. Such designs are feasible because the range of relevant ions is much greater than the thickness of high-2 material needed to contain the radiation. An optimal thickness exists for the high-Z case that comes from trading off (1) ion-beam energy lost as the ions penetrate and heat the case and (2) radiation contain- ment. In general, such target designs have lower gain than that given in Fig. 122 for the two radiator designs. The optimal choice of focal-spot size and range is largely an accelerator issue because targets with adequate gain are feasible over a wide range of these choices. In de- signs with larger spot size and lower intensity, the accelerator must be able to transport more current, and the focusing system must be able to focus more current, or the beams must be partially neutralized. Designs such as those shown in Fig. 6 are the current baseline HI designs because the longer range ions, which have lower beam current for a given driver energy, can be ballistically focused without current or charge neutralization. Ballistic focusing is well understood theoreti- cally, although effects such as photoionization of the incom- ing beam by target x-ray emission must be addressed,a6i and it provides HI target point designs with a high-confidence focusing approach. This is viewed as important because of the present lack of data to conclusively support the feasibility of charge-neutralization schemes for focusing. This situation could change because of work being done in the light- and heavy-ion beam programs to investigate charge-neutralization schemes. Beams being produced by the pulsed-power, light-ion beam machines have inherently high current and must rely on current and charge-neutralized fo- cusing schemes.‘“2 The theoretical understanding being de- veloped for these schemes, and the experiments being carried out and planned can provide the information required to base HI designs on neutralized focusing. Since the ability to achieve the required beam intensity is the central issue for both HI and light-ion drivers, depend- ing on the outcome of focusing and transport experiments, the optimal design for HI accelerators may well be ones that have higher-current, lower-energy beams and targets that can accept a lower intensity. The optimal accelerator architecture also could end up being a hybrid between today’s light-ion machines with a single-step particle acceleration and the con- ventional HI accelerator concepts with a very large number of acceleration steps. The following discussion of specific drivers is taken largely from the article by Hogan, Bangerter, and Kulcinski.38 There are two main approaches to HI drivers: radio fre- quency (RF) accelerators and induction accelerators. Physi- cists in Europe and Japan are studying the RF accelerator because of their large body of experience with the many existing high-energy physics accelerators. Physicists in the United States are examining the induction accelerator be- cause of its simplicity and ability to handle high-current beams. In such accelerators, space-charge-dominated beams are accelerated periodically by induction cells and trans- ported by a sequence of alternating-gradient quadrupoles. HI-driven target chambers have the advantage that no material object important to beam propagation or focusing need be in a direct line of sight with the target. The beams can be bent out of the direct path with magnets that are themselves out of the line of sight. Line-of-sight “get lost” (nonreflective and nonscattering) dumps handle the x rays, neutrons, and debris, while fast-closing valves and differen- tial pumps isolate the accelerator vacuum from the vapors in the target chamber. Central to the economics of any inertial fusion power plant is the fusion cycle gain.38 The fusion cycle gain is the product of the driver efficiency 71 (the ratio of the energy delivered to the target and the energy supplied to the driver), the target gain G (the ratio of the thermonuclear yield and the driver energy), the nuclear energy multiplier A4 (the en- ergy change due to neutron reactions, principally in the lithium-bearing blanket used to produce tritium), and the thermal-to-electric energy conversion efficiency E. In any in- ertial fusion power plant, the net electricity P, is related to the gross electricity P, through the power balance equation: P,=P,-Pa-Pd=Pg(l-fa-lhjGAk), NW where P, is the power used for auxiliary equipment and f a = P,IP, is typically a few percent of the gross electricity. Here P, is the driver power, and the driver’s recirculating power fraction PdIP, is the reciprocal of the fusion cycle gain ?JGME. Since the nuclear energy multiplier M is typically 1.05- 1.15, and the conversion efficiency E is typically 0.35-0.45, the product gG must be greater than about 10 to keep the recirculating power fraction below 20%-25%. If the recircu- lating power fraction much exceeds this fraction, the cost of electricity escalates rapidly. Because of their projected high efficiency, HI accelera- tors can tolerate a significant uncertainty in the target gain that is ultimately achievable. HI accelerators are projected to have efficiencies of 20%-35%, and point designs for giga- watt reactors use drivers of 5-7 MJ. Figure 122 shows clearly that, in this range, HI-driven targets can tolerate a Phys. Plasmas, Vol. 2, No. 11, November 1995 Review Article 4017 Downloaded 26 May 2009 to 199.104.125.63. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp drop in gain of a factor of 2 or more and still meet the VG requirements for energy production if the ion beam can be focused to a radius of 2-3 mm. This target margin is com- parable to that of the NIF, which is being designed with approximately a factor-of-2 margin in energy, as indicated in Fig. 108. This margin is considered adequate, given the cur- rent state of knowledge about laser indirect-drive targets. HI targets should not have a larger uncertainty than laser targets, because part of the NIF margin is to account for uncertainties in coupling efficiency due to plasma-physics effects as the laser propagates through the hohlraum. Ion-beam targets will not have this problem. For ion beams, the primary uncer- tainty is the spot size achievable with a given accelerator design. It is generally believed that a conservative accelera- tor could be designed that would achieve the desired spot size with high confidence. However, the cost impact of such a conservative design could make energy production unat- tractive. The purpose of the HI driver development program funded by the Office of Fusion Energy (OFF), is to deter- mine the requirements of an accelerator that would deliver the required beam power, energy, pulse shape, and focal spot at minimal cost. Pulse-power technology can compress large quantities of electricity into reasonably short pulses efficiently and at rela- tively low cost. In a light-ion accelerator, an electrical pulse of the required energy is progressively shortened by a variety of pulsed-power techniques. The ions are generally acceler- ated in a single step, although multigap light-ion accelerators have been proposed. As stated earlier, obtaining the required focused intensity is the major challenge for light-ion beams. Laser drivers also have been identified that are candi- dates for fusion energy production. Diode-pumped solid- state lasers (DPSSL) and KrF lasers both have the potential efficiency and rep rate required for power production. Solid-state lasers initially were discounted for fusion en- ergy production because of the characteristics of flashlamp- pumped Nd:glass lasers-in particular, their inefficiency and low pulse rate. However, the diode-pumped, gas-cooled, solid-state laser may overcome these problems.263T264 One current candidate is an InGaAs diode array and an ytterbium- doped fluorapatite crystal-Yb:Ca,(PO,)sF. The estimated wall-plug efficiency of such a laser could exceed 10%. For a DPSSL to be economical, the cost of the diode arrays must decrease from a current cost of between $1 and $10 per peak watt to between 1~ and lo@ per peak watt when they are produced in volume. The DPSSL laser has an attractive de- velopment path because it is highly modular, like the NIF. All of the operational features of the laser can be demon- strated at an aperture scale of only lo-15 cm. In excimer lasers using gases such as KrF, the gaseous lasing medium is pumped by an electric discharge or an elec- tron beam. The lasing gas flows through heat exchangers to remove waste heat. The 0.26 ,um wavelength and broad bandwidth of KrF lead to good coupling to the target. The use of the KrF laser is complicated by its very short sponta- neous emission lifetime-that is, it does not store energy in the excited state for times longer than the desired extraction time. Thus, for good efficiency, light must be extracted dur- ing the entire pumping time. The anticipated pumping time, as dictated by pulsed-power requirements, is several hundred nanoseconds. Therefore, the pulse must be shortened by about a factor of 100 by using such techniques as angular multiplexing, in which short seed pulses pass through the amplifier sequentially for the entire duration of the pumping, each at a slightly different angle. These beams are then trans- ported through paths of different lengths so they arrive at the target simultaneously. Recent studies265.266 of KrF lasers found net wall-plug efficiencies of 6%-8%. The relatively low efficiency of both DPSSL and KrF lasers puts a premium on high target gain in order to achieve an vG-10. As indicated by Fig. 7, the gain for indirect- drive targets is inadequate for a KrF laser unless the hohl- raum coupling efficiency can be increased. The indirect-drive gain is marginal for the DPSSL laser, even at a driver energy of 10 MJ. The higher gains projected for direct drive, as shown in Fig. 44, are marginal for K.rF and adequate for DPSSL lasers. If the effects of hydrodynamic instabiiity are less severe than currently estimated, direct-drive target gains could be higher. The durability of optical components facing the neutrons, x rays, and debris from the fusion explosion also poses a major challenge for lasers. Since the NIF will be configured to test both indirect drive and direct drive, it will be able to test both target options for laser-driven IFE. ACKNOWLEDGMENTS A significant number of the references in this review are to Livermore or Los Alamos internal documents that are not yet publicly available (listed as “unpublished” in the refer- ence list), but many are in the process of review for declas- sification as a result of the December 1993 decision by DOE to declassify large portions of the U.S. ICF Program. 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