Nitrogen Laser

1 Nitrogen Laser* P, Lucht August 1971 r . Ye oe 7 | Partial. Contents Part II} nitrogen laser physics . "1, general considerations ' ‘2. rate equations ' +3.relation ofinversion tocurrent density 4.overvolting and E/p1 Part III: nitrogen laser engineering 1.discharge circuits ' 2.optimising pressure , 3. optimizing laser aésign 4.discharge uniformity 1 5.lasertudedesorption |6.inductance caloulations | Appendix { References i ° :i ' , A Guarantée: All information contained herein isguaranteed tobe less than 234 %acourate. This precaution was taken sothat, intheevent that this highly classified document fell into the wrong hands, the national security wouldnotvetooseriously jeopardized. . i { 1 } !| t 1 PartII:nitrogen laser physics = Seotion 1:general considerations | Forourpurposes here, molecular nitrogen hasthree electronic states: ground, ©and3,messlevels andtheirlifetimes are shown inFig1.(Acomplete energy level diagram maybefound intheappendix) Inthese states, only thebottomost vibrational * Q R=YOmsec‘ aS Fig4evLnBower(opseea= 4a} [eres levels (J=0)areofinterest; higher levels arenotsufficiently populated inanelectric discharge, ordonothavelargeenough matrix elements, to lase. Inthese lowest vibrational levels, several rotational lineshave'sufficient lasing gain,butall these details, aswell asthe details of the fine spin structure ofthe electronic levels, are,not ofdirect import. The lifetimes ofthe Cand Bstates —ashas been noted inevery nitrogen laserarticle sincethediscovery ofnitrogers UVlaser Lines byHeard! in1963—ABBexactly wrong forCWaction, 80 pulsed operation isawayoflice,Forthepurpose ofpumping dyes, pulsed operation isaboon since large peak powers canbedeveloped withonlymodest power supply!requirenents. Also, thermal problens inthedyearecompletelyevo}.Finally,laserspeotroscopy does not require aCW probe afd fares just aswell on apulsed basis. : | | i 2 Section 2: the, rate equations Thepower output ofanitrogeh laser isafunction ofthetotal inversion inthe laser tube, The inversion is, for practical purposes, proportional tothelrate atwhichmolecules are pumped upinto the Cstate. + . ©ANviversums SES q) Ofdourse once amolecule gets tothe Cstate itcan only stay thene forafewtens ofnanosgconds after which itfalls back to soe lower state. ‘Itisnotsurprising, therefore, tofind that the33714 nitrogen laser pulsbs areabout 10nseo induration. i Sinoe itwill beofinterest }omaximize thepower output ofa nitrogen laser fordyepumping purposes, itisnecessary tohave arough idea ofwhat istaking place inside the laser medium so that various geometrical andplectricel factors canbeoptimised ‘ingotual construction. ' 1 ‘ Physically, @transverse-field Nplaser looks something likethat shown inFig. Theelectrodes haveawidth w,length 1,and i ee‘ re or | 4We 4] ; Fig.: s separation s;theyaresnnerspainnitrogenatpressurep.The 3 : endsofthetubearemadeofquartztopassthe33714ultraviolet lasep light which typically pours outinasuperadiant fashion; thatis,thegainofthenstedgenissohighthatfeedbackin theform ofmirrors isunnecessary forlaser action. TheUVbeam has roughly the rectangular ofoss section one would intuitively expect fromtheefetrode geometry. Thebeamdivergence issin-}(w/1) andsin-1(s/1) forthetwobedmdimensions. Whenaplane mirror is placea atone end ofthe lasex, ite length iseffectively doubled 0bothbeamdivergences halv¢. ad TherateatwhichtheCeverlispumped isgivenby i H 'ate=nen,Re Q Wecertainly expect theper-vjlume pumping rate tobeproportional toboth the electron density,}since electrons dothe pumping, atid tothe nitrogen gensity, gince nitrogen iswhat gets pumped. Rg,whichclearly hasthediméngions cm3/seo, issomehow ameasure oftheeffectiveness ofeachplectron-molecule collision inregard tothat collision's ability %excite aground state nitrogen to the €state. Ifthere were on]y one electron and one N2molecule ineachom3, anexcitation woild ocour every (Ro) seconds. i Gross section isperhaps amore graphic conceptualization of collision effectiveness forsbme event, andasdimensions will verify,thesetsticnh/ ReamdcnaAscheTE ———Re= CHE ECeomsare) ©) wherevgistheelectron voiodity. Afanyelectron temperature | i REE ED { 1. Los t . { . : 18 - : Vt 1 s » H -. ” ar | we . i 116 mo 1. ix }. ‘ . oo Loca S07 “ao a0 8080 100-120 40160180 200220400 Hl d . . ELECTRON ENERGY (VOLTS) Sk a as . +0[o> wig.vi-13 Cross section forexcitatioh oftheNjC3xy (v!=0)stateby oan ~ electron impact, ; 8 ; oe Figure. 3. oy - : i ~_ os. {4 i j | there isofcourse aMaxwell-like distribution ofelectron velocities. Since gisafundtion oftemperature (seeFig4), t atagiven mean electron temperature Ryiscalculated by averaging ov, over allvelocities inthedistribution, hence the‘barover Equa 3.This averaging flattens outthesharp peak shown inthe cross section plot sothat aplot ofRo versus electron temperature looks something like that shown invig I. , j ! e | Re x '' H Fig't ' t —Te(ey + From Equa. (2) itieapparent that the Cstate pumping rate isdependent ontheelectron ‘temperature intwoways,(1) through Ro,and(2)through ne: i 1 aM2Me(Te) NoR.(Te),dt fi ' ’ i i Hl 1 t 8 ; 5 Section 3: determination ofelectron density ng, and the relation between inversion and current density inthe nitrogen laser. Inanelectric discharge tnvo}ving largecurrents (spark)the electron density andgasconductivity growveryrapidly asthe thegasbeginstobreakdow."Afteravariable statictical tine laganavalanche occurs,‘rentaftertheso-called formative time lag, streamers form, theconduction channel fills out, ‘and theelectron density is‘thenreadytogrowinamore analyseable fashion. Allthis}takesplaceinlessthana nanosecond ifthere is ahigh, overvoligge. When the channel is formed, ngisstillverysmall, perhaps only10/om3 andthe applied voltage isstidl suppbrted. Nethengrows according to the simple rate equation, . 1 dite=MeeRiz(fe) (4) ~ H This equation isidentical to’the previous excitation equation except Ryisameasureofthecollision effectiveness forionisation. Ry,likeRo,isafunction oftelectron temperature. Ttishelpful toknowhowlarge nggetsandhowngdepends on otherparameters sothateventually laserpowercanbeoptimized. X Equa (4), though interesting, isnotveryhelpful inanswering thosequestions. AllthatcanbeeaiafromEqua(4)iethatas Nggrows,atsomepointthevoltageacrossthedischarge starts todrop,theelectron temperature falls;Rydiminishes inaway i 1 | soos . 6 t i similar toFig(4), andnglevels offatsome peak value. 1 Consideration ofthe electron, drift velodity and ourrent limiting~ provide an alternative anmwer; to the question. According to P.Llewellyn-Jones? electron drift velocity isgiven by H w= aeEL(4) (s)~ Sm.\% where Eiselectric field, uelectronic speed, and}the electron imean free path. Qisroughly given by i . he =i (6)Nett o | where oisthe mean radius ofagas molecule. The relation between pandnoisofcourse justtheequation ofstate, %= f&= (7)Thad‘i wherepisintorr,Tisthegastemperature relative toroom temperature in°K,andGisaconstant, 2x10!6/torr/om}, Thuswecanwrite, i Tor SP and Equa (5) becomes, ol Woose E+(7 (a) Bro bre . ! 1 T ’ Theelectronic meankinetic energy1,oFelectron temperature, isfound tobe, , ‘ = = if=tm -akk =eEL (19)‘ A34 { Where Aisaconstant indicative ofhowmich anelectron is stopped by acollision, : MsA=XM, a Xe ay (Mer™Moy* °i If-Aissmall, theelectron apcumilates energy picked upfrom the electric field over many pean free paths. Replacing {in Equ.(10)withEqua(@)weabt, Feeva'~(E)-2a% (12) =coe\sa t ror &34 P Note that the gas and electron temperatures are not the sane. Thethermalization timeismhlonger thanthetimeittakes foranitrogen laser tolase.|For ourpurposes, then, Tre] is ! just unity, room temperature,'a constant. From Equ. ((2), then, itisapparent that electron temperature andthefractions E/porE/nof areallproportional toone another; theyareallmeasureb ofthesameproperty ofthe electron gas, namely the mean; kinetic energy. ' : t i8 t H : ! . With acertain degree ofmathgmatical looseness, tcan be eliminated from Equas. (1) ata(12) togive, : \wis(aeTatBayx\E ) i Amo Qve P Hf Thedrift velocity isalso seen tobeafunction ofE/p and f hence ofelectron temperature, ‘Nitrogen isnotanidealgas,iandmanylooseassumptions have been made. Nevertheless, the desults for electron temperature and drift velocity asfunctions ofE/p (orE/N) atleast show the correct monotonic relatiotships. Anexperimentally derived plotofthesetwoquattities YersueB/Nfornitrogen at77°K 1 isshown inFig. (5). : i Toget afeel for the magnitude ofsome ofthe quantities that are being thrown around here, ‘some numbers are appropriate. The t caloulations which follow werg allmade from thepreceeding equations using values forEdndpthat might befound during thelaser pulse inanitrogen{laser. =[090 volts/eny E > volts/ong Lo Qn P=QOtow { E2/50eV 6 Tyr2:|Te=10°°K A=Bxio i Z=700 umn/pare ° 5 a=8A(cre)| Wo=Yom/pace th=4x10"/om ! . | { . - i :. J ; i i iaaaAe et ; ‘ !: ye | nt)oa, ; 4,\ 1 i )|[iets are } : { ® : -Yarcen aaParte790) a t : ,j 1|tomstyeer I 3 . ccdeegeenenoeSoees . .* . + | ot ‘Figure’. =| . ‘ an : 4 : ' ; sos.1 1 9 : ' Weare inthe process ofseeking the eleotron density n,. Since the ‘electrons are light, they account for most ofthe current in ‘the discharge, 50 Jy=T3eeW ch) 4 t . J,itturns out, islimited byfactors external tothe nitrogen discharge itself (otherwise itwould become infinite*), Atthe time ofthe laser pulse, the gurrent density J—aswill be shown later —islimited by{he impedances ofthe discharge 1 circuit aswell asbytheslight inductance ofthedischarge itself. Itwill also beBhown that thdelectron temperature, B/p, and hence W.areessentially controlled bythe electrode geometry and externel discharge circuitry. Ifngiseliminated between Equas. (I)and(2), theresult is, i waei Ele) iniversion~dsfexyKele.(is)WwW(&/p) ‘The important conclusion tobédrawn here isthis: for agiven laser geometry anddrive currdnt, 8/pisalready determined (as will beshown). Once anoptimim value ofpressure is ébundy the amount ofinversion perom3 ndhence theamount ofavailable power isdirectly proportional tothecurrent density supplied. *t20torr andwith thedrift velocity caloulated earlier, if every molecule was singly ichised, the current would be 256,000 amperes, alarge ‘though finite current density. | t i i, to ‘ i Section 4:overvolting andE/p : Thesparkprocessresulting i‘theformation ofaconduction channel, asdiscussed above, dcours very quickly when thegas iscvervolted bymorethanofewpercent(fypically inNp x lasersthegasisovervolted ty500%).Verynearthespark potential itmaytakeseveral seconds forachannel toform becauseinthecaseoflowovervolting thestatistical time lagamounts #6waiting foraboomicrayorphotoionization to start anavalanche. : I Avery simple analysis ofionization buildup inadischarge — first done bysuch gas greats asJ.S.Townsend4 andJ.J. "Electron" Thomson? intheearly partofthecentuny —shows that the number ofelectrons reaching pheanode ofadischarge is icMa=We|—<| (16) 4-2( 1) wheren,isthenumberthetshavethecathode,disthelength ofthedischarge, oisthenutber ofionisstiona peromcaused by each electron, and wisthe number of electrons "created" at thecathode peromoftravel beeachelectron anthedischarge as @resultofso-called "seconabry processes.” wisthusseento beasortoffeedback. whenaielarge, ngissomesmallnumber indicative ofthegasLeakage!current. However, whendisreduced toavaluewhichmakestheacponinator approachsero,itislike ' | ‘ wos i ' 1 ! @loop transmission going tounity, andngblows up.This, Thomson tells us, iswhat sparks are all about. The spark condition, or"Townsend criterien," isthus, wds SLe =) 1. Itcanbeshown that o(/p and4)/p areboth functions ofthe familiar variable B/p=V/pa, soEqua. ((7)cantheeberewritten, : wo(\elP®)[Sores i)e4 (\) %(Ve/pds) | ~ oo i SolvingthisequationforVoparte)onegets, ' Vg=VsCP4s), 8) } ! 6 which goes under the name ofPaschen's Law®. For example, Wolff (checkthisfootnote forevidgnoe ofrecentresearch) foundthat, fornitrogen Pasohén's Lawis'approximately (forreasonable préssures), H ‘ ° \g=300|12.08(Pee)+5.0| (Re) where Visvolts, patmospherés, and dmm. Forpraétical purposes, Paschgn's Lawcanbeapproximated as . t Vie=Aes (2») , where Ais-some congtant, andsistheelectrode separation of ; t 5 { i 12 } 1 t t Av @nitrogen laser. Thedischarge circuit with itsinherent ¢i will cause the discharge tooyervolt bysome fattor B,so Vac=BVac =ABps (22) Thus isobtained the result promised earlier that ! Ely=Veo _AB. (22)Pp ps i That is, aslong asthe voltage supplied tothe laser isgreater thanVg,byasufficient factor (A), theratio B/pis determined entirely byexternal circuitry through B,the overvoltage factor. B/p atbreakdown isindependent ofboth pressure and electrode separation. (This ofcourse isonly trué inour simplified zeroth-order analysis. Infact, E/p ! does vary slightly with these’ parameters, but not much.) -' i ‘ 1 ' ‘ f 1 1 i . H 1 1 ' i: 1 Part III: nitrogen laser engineering | Section 1:discharge cirouit analysis 1 Asimple discharge circuit igshew inFig. 1.Gisatriggered spark gap having avery fast rise time ofperhaps 10usec. Dis thedischarge tube. Thesumofallcircuit inductances isL. Capacitor Cisinitially charged uptosome high voltage Vo, the ewitch istriggered byanexternal circuit, and apulse ofourrent 1 G , c; p Fiqua 1.‘tO isdelivered tothegas. i i After thespark gaphasswitghed onandwhen thedischarge hasbroken down enough sothat its resigtance issmall compared toreactances, theoircuit canberoughly approximated byasimple LCcircuit. ‘Thépeakourrent ofsuchanLCcircuit iseasily shown tobe Iwan=\eVo. a) Thecurrent density Jinthedischarge isproportional toI,#0 toincrease Jandhencethejmountofinversion wecan(1)increase C,(2)increase Vp,or(3)dporease L.Once apower supply is selected, Vpisfixed.Theaarginal benefitofaddinganextra capacitor tobank Cdrops off fast when there are already 10or s0capacitors, and more capacitors also increases circuit ‘ - oe 2 i t inductance. The best thing todoistodesign the discharge circuit evohetaysothatthevarious‘inductances areminimized. Thetotal inductances however, cannever beless than that ofthe spark gapt Typical numbers are | : L =30 wh Cc=20mF |No=$0 KV That (8 KA. Inorderthatthepowerbeagpivereamostlytothedischargeratherthan tothe gap itself, the gap must ewitch onspeedily. This necéssitates itsoperation athigh pressure (several atmospheres). High pressure sparks are long and narrow, sothey have high inductance. Theself inductarice ofaround conductor is,bythe fayways 11 ‘ ; wis(nw)=a0[be2-2]. @ sothattheinductance ofa4omspark,Immindiameter, isabout 15AE. H 1 i Usingthecirouit ofFigure 1,theonlywaytoreduce inductance . i below that ofthe gap istouse many gaps inparallel sothat l Ltotal =Lgap/a. Typically ne20 andLyoy,; =1nH.Themultiple gapapproach iseffective butexpensive, andanalternative is : tousethecircuitshowninhears2. 1 i Before leaving circuit 1,however, oneother observation should H 7 f : 1 ' beadewhich applies toali'arive circuits. Ascanbe.seen from the,plot oftheexcitation rete R,inFigure 4(Part II)andfrom equation’ 15(Part12),theijversion increases withincreased electron temperature, which istosay,withincreased E/p.Back onp.12ofPart [it wasshéwn thet B/p=ABwhere Awas2 Paschen constant andBwastheovervoltage factor. Thefaster the voltage risesontheaieoharge, themoreitwilltendtoovervolt though there isnostrict linear comnection. InFigure 1,since thedischarge hasvery small'capacitance, d¥/dt isvery large; thisisanadvantage ofcircuit1.FaotorBisthuslange,electron temperature ishigh, and pumping ofthe Cstate isefficient. t “imcironit 2because ofthe“presence ofcapacitor Cy,aV/atis somewhat sacrificed asacostofobtaining increased discharge current, Experimental evidence seems téshowthatincreasing avV/at beyond 1500 volts/nsec does not infact improve the overvolt .u zQ.!5fonte a qe : cS) 1Fique2. &) ' factor B,sowithsmall C,tliere isnosacrifice. Thereason for thisisprobably aneffectobthefiniteswitching timeofthe sparkgap.Thatthecircuit vfFigure 2candeliver ahigher peak current can bedemonstrated asfollows. After the gap has 1 1 ' ' i , : 4 { t + ; ow |switched, buf before the discharge begins tobreak down, the rs YONcircuitisthetshowinFigure$fCdeinitially chargedtot Voy the current inthecirouit is . g : TU=(WEY sin (tet u Nuch (3) and the voltage rise onCpis; 4 aq aMy= RLV, sie €).Ve.)=2onYot(3ucu (4) i IfGpissmallcompared toCy,(perhaps 1:4orless), eyee and then 1 Ce . t Lex “oe uiS& jug (5) 2h is 6 %Vesok( . (6) Ye,ANe Som GOTTG t j Whereas the voltage rietine for circuit mam 1was nearly sero, hereitisseentobe2\LC; «Ascompensation, though, C,is chargingtowardtwicetheeubtyvoltageandthistendstoimprove av/at. H WhenVo2reaches theovervoltage Vac=BVag, thedischarge very quickly begins tobreakdom,|thecircuit isthatshominFig3. | Li FiguraNec=ECe 3 i H. : thecruxofthematter isthie: nowthepeakcurrent inthe discharge isnolonger limited bythe gap and external inductances. L,theinductance ofthemetql plates cofnecting Cytotheelectrodes, canbemade much smaller thay Lgay. Typical numbers might be: b= 4wh ' Ce4mF \ex!20kV Tyr [GVoe=YOKA. ‘Thus,thedischarge ourrenttoainversion aremorethandoubled. ic ‘These peak currents demonstrate apoint, butareprobably not actually realized since thevarious losses, including the excitations ofthevarious mblecular states, havebeenneglected. Theyappear, ofcourse, asimevarying resistances. ' ‘ ‘' , i 5 1 ' ‘ | { ‘ { 7 - : - 6 | Section 2:optimizing pressure . : Inequation I-15it.wasshowthat . INVERSION =<psRF) : .SNE) Given gparticular laser geometry andadischarge circuit, J andB/pare‘predetermined, aghasbeen shown, aslong as Veupply2VacWhenpis20htheinversion islow,Aspincreases, Eincreases soasitokeepE/pconstant, RyandW_ remainfited,andthe,invereton growslinearly withp.When preaches acertain value, B=Vao/a cannolonger increase duetothevoltageLinitation, E/pdropsandR,falleofffairly steeply (see Figure II-4) agelectron temperature falls. The productofpwithRg,atanctionwhichincreases aspincreases, iswhatproduces amaximm itiversion andanoptimum pressure. With Vgupply around 30kVands=3 cm,the optimm pressure is foundtobe20torr. | 1 1 | 1 ‘ : i | { ae : ‘L t Section 3:optimizing nitrogen laserdesign 1 Themore power supply voltagé available, themore power output that canbeobtained from thelaser because (1)electrode séparation canbemade large forlarge volume, and (2)overvolting will behigh. ‘ t Practically, apowersupply orsomereasonable voltage ischosen, perhaps with consideration 40thebreakdown voltage ofavailable highvoltage,lowinductance eapacitors, ‘andthentheoptimization begins. Frameconomic considerations, themaximum sizeofCy)+Cy isalso determined. Thequestions are: (1)Howshould theelectrodes ‘beconnected +oCo?(2)How should thecapacitance bedistributed ‘between CyandCy?(3)What should betheelectrode dimensions, shape, andseparation? ' (1)Tokeepinductance low,the&capacitors shouldbeascloseto the discharge tube asispossible; they should bearranged along thelength ofthetube andshould beconnected continuously to theelectrodes viacopper sheets. Aninductance calculation will bedone later. : (2)Chéosing theratio of04/Cgisaplayoff between peakcurrent and overvoltage and isbest determined experimentally, asis theoptimm pressure, Inour laser, apatio of6/0, =4wan foundtooptimize power. / (3)Thecurrentdensityinthedhecherge atanypointis(see-} i fl ‘ - ' 3. Figure II-2) given by , J= = (7) wxt andthetotal inversion peromofelectrode separation is controlled tyIwhich, ashagbeenshown, isdetermined by external parameters. Thus,changing ‘thewiathandlength ofthe elettrodes does not change the amount ofinverted population. The separation should beaslarge ascan beovervolted effectively vythe power supply, since the total inverted volume ispropor— tional toseparation s.Practially, however, theseparation ischosen sothat the laser beam can bécollimated byavailable lenses to thedesired beamshape.Even‘though thetotalinversion is unaffected tythelength oftheelectrodes, their length is important because ofsaturation effects. Theelectrodes should bemade long enough sothat formost ofthetr length thenitrogen population issaturated. Increasing length further willnotincrease power output (forafixed d#ive current). Howefer, iftheCy coupling circuit isextended alongwiththelasertube,thetotal drive inductance ‘shalved ejchtimethetubelength isdoubled, s0there issome benefit inpeak current, Most researchers, however, seem toagree that with asigle plane-mirror system, anslectrode lengthof1misaboutaslongasisuseful. Inthesiggle spark gapscheme ofFigure 2jallthecurrent met ultimately pasethrough thespark gapahdincreasing tubelength beyond 1mmerelyraises,primary,Gifouitinductance witharesultant deterioration inaV/at.Inatmultiple gapschemewhere : | ! : . .' ‘ 9 ‘ } everything isextensive along the tube, power output for long tubes i islinearly proportional toHength. The operational cost is anincreased demandonpowersupplyourrenttochargeallthe capacitors. : ' Section 4: the question ofdischarge uniformity’ i: 1 That auniform discharge is,‘first ofall, desireable oanbe easily demonstrated. For simplicity, assume that the discharge "sparke" inNequally spaced{channels along theelectrodes as shown inFigure 4. The total gain ofall the channels is ‘ ' : Pique 4. determined bythe total current Iwhich, ashas been remarked about 5times, isfixed. Ifthetotal gain isG,,then thegain ofeach channel is1+G,/n. Asn->4 thebeam passes through each differentially thin chahmel with unity amplification. Ifoneoftheendcliannels generates spontaneous noise Poff, thepower output ofthetube is { |mn = \+@)- Ra=B(\= Poutisthusasonotontcatiyincreasingfunctionofnandhasq Hl\ . .! ‘ ' 10 ‘ ; \ alimiting value of : i @’: Ru(mae) =he. ; . This limiting value iseffectively reached when . G,{ m= 10S, ' For auniformly discharging laser tube that saturates at10kW from 10niofnoise, Gis ! LnPa®=2,3\04(4)=is=23\oq (1%)=, PB “4(i=)=. ' ‘ . Anaforeffective utilisation ofthis gain, there should beat ledst 150 channels. Ifthe discharge only sparke at5of6places, thegain, instead ofbeing 1)°,isonly ot ios. is~ SsPast,(+BYxio. , This loss ingain isanothér{reason whyovervolting thedischarge isimportant {besides thethotthet overvolting provides ahigh 1 electron temperature). When the electrodes are highly overvolted, BofVag=B+Vgcislarge,thechannel-initiating avalanches i form very quickly. Thefaster thechannels areformed, thecloser together they‘canbeforthe!following veason. Whenonechannel isformed, ittends to short'the electrodes and the local potential :1 i. { : .i n ’ falls. ‘This potential drop propagates asapulse dow the electrodes atsomething resembling the speed oflight, sono new channels can beformed where this pulse has passed by(see Figure 5). Thus, i#f the channels all start forming insome i t ae ie Gro~sec Fas. 'en [i 4msee ' time @,they canoccur as‘close together as i KH=c#, Overyolting hastheeffect ofdrastically reducing @.When the electrodes are overvolted by500%, @,the time for a channel tobegin forming after the first channel has formed, iadowntoafewpicosecondd, soxisontheorder ofmm,andthe gain ofthe laser isvery high since n,'the number ofchannels into which the total current isdivided, isvery large. 1 ' ‘ ' ' i t |i Ot ,12 | Section5:laser tube description | ‘ A ' t Anitrogen laser\which vas constructed for the purpose ofpumping : ‘organic dyes, -had thefollowihg characteristics: ' The electrodes were 45omlong, ofpolished semicylindrical brass tubing, diameter 2.5om,smoothed ends, separation 3om. | ‘The discharge vircuit supplied 30KVDC at5ma. The spark gap used . \ wasanEG&G'GP-14 capable ofhandling 100kA.Capacitor ‘banks were made from Spfague 2500 pF30kVunite, All wiring consisted of . copper sheet, 30omwide(seeFigure 6),Thedischarge circuit ‘ a‘ o: 1 Figtnn 6. ' isshown inFigure 7. , 4M byt ba ba. ‘ 1 F Fig2 ‘2owF| Suk by by ds 1 Nitrogen gaswesflowed atayerslowratethrough thetube; optimum pressure was 22torr.| Thevoltage ondlaser pulse abeshown in|Figure 8.Thelaser pulse issome10nseclongandoocuis some50neeoafter thedischarge d © (a) voltage across discharge tube. Vert: 10kV/om Base: 50nsec/om ; pote 12 (b) laser pulse. Vert: un- cal ibrated. Base: 50nsec/om : aS COS Fiquen ®. a —— - - ‘ 13, : ‘| ‘ H voltage begins tofall, which isconsistent with inductance caloulations forL(tocone H Energetics: the power supply iscapable ofsupplying 150 watts of i powér, “The energy required tocharge the primary capacitors C,is om Wa=@v*=asjouten, i Thus, the maximum pulse rate isabout 8pps. The energy stored in ©,is,ofcourse, only9J;theenergy perlaser pulse, asmeasured byacalorimeter, was .50¢5 pJ, for awall-to ~laser-pulse efficiency of3X1075, Theaverage power during thelaser pulse H is e W 1.5\-3 W/ w= Wa SES =Sokw, i fo,-4 . i At8pps, the average laser power output isabout 4ali, Misc:Theelectrodes wereeachmountedonthreeboltsinsidea 3"0D, plastic tube. The end, windows were 3"Corning No. 7740 pyrex glass plates with alosp of.3dbper window at3371 A.The sparkgapwastriggered byan’EGSGTR-153 pulsetransformer driven byatransistorized phlser (schematic inappendix). f 1 1 | 1 . j i i 1 1 an ‘ ua ~ 1 :| Sectiom 6:inductance cAclulations | i 1 The inductances shown inFigure 7are not entirely trivial to calculate; ‘anattempt will belmade here tocalculate L;.Since theelectrodes were connected’to thecurrent carrying sheets by three bolts, thesheets werenotasaffective astheymight have been inreducing inductance. Theinductance fromCpintothe discharge canbemodelled asthree rings omnected inparallel asshown inFigure 9.Using another ofGrover's formulas® , ©W(t)=re.[dnSe-5| (v)‘ andusing a=5om,b=1om,|wefindthattheinductance ofeach ~(EP CoFF Frq4 ‘ I ring is192 nH, sothat the three rings inparallel give 64nH, suggesting that theL's inPig. 7areabout 30nHeach. Theother induetanoes showainPig.7areprobably alsoofthesameorderof magnitude. i| Anewlasertubeisprosentiy| beingconstructed withtheintention ofreducing thecritical currpnt—Limiting inductance L3.The electrodes for the new tube are 1mlong, and the current sheets and electrodes are all formed; from the same piece ofmetal as 1 .} 1 ' i shown inFig. 10.Thesecondary capacitors Cyaremounted soclose that they actually touch theplastic gastube. TheL3inductance canbe 1 ee, iow aVec=aw Fquae10. Bonrt— modélled asashort-circuited tranmission line. According to Bleaney #Bleaney3, theinductive reactance ofashort, short circuited transmission line‘ to. Xu=2tdC254) } Sinceweareonatimescalevttensofnsec,typical)isseveral meters andQisafewomsowecansaytan(x)*xtoget t Ay=2rd Qo »! o = Ree 3 or LG)=Llow’)BoC. (:2);30 For#parallel plate transiission line, Z,is 1 R= B77 >) | { } 7 1 : 16 Thug, thetotal inductgnce of’thesecondary discharge circuit is, he= = - 14 GN) Vas G4) ' i whete lengths are inom. Putting innumbers asshown inFig. 10, weget L=1.8 nll, avast improvement over the former design, . singe noweach L;isonly .9nHasopposed to30nl,This 30-fold reduction ofinductance could, according toequation (5),increase current andlaser-output byafactor of5or6to 300 kW. . ' : : Thecharacteristic impedance tethetransmission lineusedhere 4 isabout 12, For anexample ofanitrogen laser driven by amohlowerimpedance line(%=41.2)seeGelleretal.4 1 ' 1 1 ( . : i 5 } " we , { or a ; Digestionete)rigghnn- Sails weeneenyeTele oTee ; | if a . i LN! 92~--- =---- ==r hoesenerrere aN i. eos Spores tpelt WiTh } DE 949 oo.. sewed EEE ae eT eT tote)necA|ALAM) OR awider? io. HSS LTH) r= “|a PPee Pali t= onSSE . AlatSAR See TEBd .Arron, S Ao, whE [EE : HLL 444.4. AUHEE= ry Sed=F - igh.ids wd Zt ; : “wp PES UT add Spee cLGERBER SiR Eq8 ee or ‘ me ill= / f ; . i= | / ode,; |=i gow -ok : hi= i . ~ f = 4 sed =— a -FgPuydatBearerLengDiseeshes atheosioualeasireaahofthem,Theout ae anylevelsa’,w,z,ywhoeeheichtsabovethegroundstatearenotknownareindicatedbybrokenlines. ..‘helibrokenorioneswndlgienailingatheiheadientecnoicon Umit,The : Ly hoe heavy horizontal arrows desjeaated Prgiveeepositions ofobserved predisciation limits, v cf.MBSERESSSA7OPENSUlSrereromcing otilacsthehighermembersoftheRyedbegseietene cet ate uvebeesopie annuvethes=vorlonal inves observed .1BitesteeheeGeiniceTanakaaadfalamioe(407),AnenloiogRydbergseries ee (Hopfield (331) andTakamine, SugasudTanaka (6602)] hasbeenobserved veryclosetoHopfeld’snye iron is“TheopersaaofthissereGroby#24")aentshows. oe et : | . boon | oa er oe ,TRANSMISSION CHARACTERISTICS . } ou OFQUARTZ ANDVARIOUS GLASSES ©ois0x0»!Bot,per: eee Se REVI TV LNLAWESEEES EA lidesss|) ACENSISsli netiYHness)1ase Ah ECU da TTT CUE ANIAN) UEC ell poreNeaCT |AAA ba AS |ET Ae. ACS 7OZONE}GERMIDALTi megane Worclerah—Angivons a . ein 1 i 13 References for Part II: li,g. Heard, Nature, Nov 16, 1963; p667. Inthig oneparagraph report inthe London journal, Mr. Heard, then ofEnergy Systems Inc, ‘Palo Alto, describes hisnew UVnitrogen laser which puts out’ anastounding 10watts of‘peak power. 2y.a, Leonard, ‘AVCO/Bverett Regearch Repprt #252, July 1966, p53.. Leonard's work isalso descrited inAppl. Phys. Letters, 7,pp4-8 (1965),andinotherAVCOreparta. 37,Liewellyn—Jones, Zonizatiod endBreakdown inGases (London: Methuen, 1957),.p 29. The equations used inthie peper also appear inanother Methuen monograph bythe same author entitled Phe @low Discharge. H i 43,5, Thomson, Conduction ofEleétricity through Gases (Canbridge: University Press, 1906) ; 53.8. Townsend: ! : ‘Theory ofIonization inGasés byCollisions (London: Constable, 1910)Electricity inGases (Oxford: Clarenden Press, 1915) Motions ofElectrons inGasge(Oxford: Clarenden Press, 1925) 6 : Frisdrich Louis Carl Heinrich ‘Paschen isalso responsible for the Paschen-Bach effect. : Ty.Wolff,Wied.Ann,XHXVITI, ,1889,p222.(Wied.Ann.wastheAnnalen derPhysik undChemie; nowjust Annalen derPhysik) H i .1 t i i i { i i ae ror References for Part III: , . . 1 jl F.W. Grover, "Inductance Caloulations: Working Formulas and Tables" (Dover, New York, 1962), p.35+ 2 ' Grover, loc oit, p.143. p.1, Bleaney andB.Bleaney, “Electricity andMognetiom", 2nded, (Oxford, Clarénden Press, 1965), pe309. } 4 M,Geller, DE, Altman, andfA, DeTemple, Appl. Optios, vol. 7, pp2232f (1968). : 1 i . f ! , : ‘ ‘ } : i i 1 ! ::