edited
`Lean J. R:afi2ie§msAE<i”
`‘Department 9-? 1% 51:35;
`TNQW Maxim state %
`A
`
`L35 Crates,
`isfiexzas
`
`.
`>
`:3?!
`
`
`C‘hemicai and Laser S<:ier1;:es.‘[3i'v%sion
`L03 Mamas Nat’ia3Ana,¥ ‘L3i3t3'Fa‘tt3rv~
`L03 Atamos, New Maxim
`
`
`
`MARCEL DEKKER, INC.
`
`New York" and Base!
`
`i
`i
`
`%
`
`ASML 1017
` ASML1017
`
`

`
`
`
`
`
`Li%::ra.ry of CongressEafalggagix;g4i§141§n}3iit;ati(2n. Data .,
`
`;:‘§z§isi¢;a:1'i;, cixexnigzal, and hioicgical appficaii0ns.f e..c2ite-:3
`Lasexmiusze-ti V,;;1asm-as ::
`by Lewis
`Réxxiziemski, ’33a’x«’id 23;. iiremers.
`>>
`
`>
`‘
`
`.1." Rhdziexnski, Leon 1., ’ §9;'z3.s'3§
`
`’:‘;3awer.iasers.. ’
`
`0'13?
`
`This baak is prizwzd on sreiiiafree ip’:e2;:«e:r.
`
`Qopyrigh’-t © 1939; 1*:iARC.BL.DEKI{.ER. me. A1: Rights Reserved
`
`Neiiher this book no: any part may b,a_rep‘mdw:ed Q1‘ transnaitted in any form
`in by any means, eiexxtronizi or mechanicai, including plmtucopying, microfilming,
`and recording, or by any .inforrnation storage and retrieval sys-fem, without per
`mission in writing from the publisher.
`
`MARCEL .DEK}{.B'R, INC‘
`
`270.Madisim Avenue, Nexv York, New York 10016‘
`
`Current printing (last c¥i.gif):
`109876543321
`
`PRINTED IN THE UP41I’I’ED STATES OF AMERICA
`
`ii
`ii
`
`

`
`Céntents
`
`
`
`iii
`-xi‘
`
`36
`
`6]?
`
`6.Ԥ
`
`'33
`
`72
`
`7,5
`7’?
`
`88
`
`§2
`
`93
`
`:95
`
`99.
`
`I00
`
`101
`
`101
`
`105 M
`
`105
`
`110
`
`
`
`
`
`3 {ntro»duc£ion to Laser Piasma. Diagnostics
`H _ Allan A. Hans; and Hector A. Baldis
`
`?»1
`3.2
`
`Introduction
`
`Introduction to Optical Diagnostics
`
`ix
`
`fLaser-Infl11c=efl.. ’Br-eaiyfkzwzzz Au U‘§1sdat£:.
`
`;I§;;t;a:iu»c't:i;1n
`of Eicctrons
`.
`Eiemran €§'r{::§v£E1 in -.Ga$e»s
`Lasér~I:a;&.u::.:w;'z.',Eneraizzgmwxtx mi Solids am Liqzms
`.. {fim::»aiu.s:i:iz3g 'Rem_ar_i<s
` R:a:fm’*en:¢:.e:s
`
`{!(1€1iI}‘g.1§'f .P?us£—Br=eakti.ox&In Phenomena
`abexf
`Ki)-Qt
`
`Z’5:it.f<3»§i¥;:<:3;iiz:s:1
`Ciifizsatpifin 0f 21 ’P’mpagating flasma
`Absmrptian {Zhafanteristics Bf Hcatsni Gases
`Figattgrgs cf 1?fi:opagati.n_g Plasmas
`$3312.-~I}i1X1.Ensi0n.a} L:aser~S'u';3po1'1.ti:€3 ’CB1‘£fl3’H$1i0n Waves
`C3I.1e~Di.m.ensi0naI ’La.se:r~Suppcarted Detonzxtican Wave
`*One»13irj11.ans.ira’na} Laser~Suppin“te-d Radiation "Wave
`j:’i.‘ransi¥t'it3'r1 Regicms
`Radiai Ex;§arz.si:3‘n
`Thezfmal. Co;up1i.ng.
`523.3. Other Factors‘
`S’umn1a;fy
`References‘
`
`»
`
`»
`
`

`
`
`
`
`
`x
`
`0
`
`Canteniss
`
`3.3
`
`Intmduxetion to X—.r.ay Diagnostics
`Raferencas
`_
`p
`
`4
`
`i;;;s’e'§r;S1:st.aine£1 Piasixtas
`Dennis R. Keefer
`
`0
`
`4.1
`
`4.2
`4,3
`4.4
`4.5
`
`I’ntr0a3.ucii0n
`
`Princix‘-33133 of Qper2iti{2‘n.
`2—’;>ma’1yt'ic.a1 MQ£3e}.s
`Experimen.t:a1 Sfndies
`Ap;31,icati£3n.s of the Lase.r~S1:.s£a;ix:ed Plasma.
`Rcfcrances
`V
`b_
`
`‘
`
`-
`
`5
`
`i’nér~t.iz’§liy Confined. Fasimt
`Robert L. Ivicflmry am. Jana’
`
`’SO3;III‘es
`
`.
`
`’
`
`133;.
`161
`
`169
`
`169
`
`1.'??.
`1182
`189
`I95
`203
`
`207
`
`20?
`2.-:11
`217
`224
`227
`239
`243
`251
`2&0
`
`269
`
`269
`276
`233
`290
`291
`
`295
`
`295
`
`296
`302
`306
`309
`313
`318
`
`5.1
`5.2
`
`51,5
`
`5.5?
`5.8
`
`V
`
`.
`
`Ifiistaricai Overview
`Las0er~*Fusior: Scaiing Laws
`Car-anal Fhysics
`X~ray ‘Genexatiau by L;ase'r»Fmdx3ceci Plasmas
`1.33::-:—'Driven Abiatixziij
`§%i}ydr:3:1y:za:x11:ic:Stabfiity»;::§15xE;vI&i’i;i?s*<i*;1y* I3:-iv‘s:n.:
`.1I‘m::iiaii,::sI1 U‘n:i»£ozmi:y }'§§::q::i1:t:§z:<:.a’_z}.t;5f’
`Impiositm Experiments
`Rafemnces
`
`A
`
`6
`
`El..mei?—Base£1:8’;2.n°1ici3n.i111£:££1rfiibriimiifiix
`
`Iaseph "R. ’Wachte’r
`
`5.1 Aspects of Scmicandtwtor Fabrication
`(3.2
`App1fi<:ati0ns-of Lasers in-£113 Semifconductor I.ndu$t1'y‘
`6.3
`Research Areas 0
`0
`_
`6.4 Outlook
`Refarences
`
`‘
`
`7 0 S-pectmchemical Anaiysis Using Laser ?1asma.Exéit.at:im1
`L-eon J. Radziamski and David A. Cremers
`
`7.1
`
`Review
`
`-Methods. and Pmpezties of Analysis Using Laser 3?1asrnas
`7.2
`Analysis of Gases
`7.3
`7.4 Analysis of Bulk Liquids
`7.5 Analysis of.Particle.s
`7.6
`A11a1ysis‘ofSo11"ds
`7.7 Advances in Instrumentation
`
`

`
`X3
`
`321
`
`323
`
`32?
`
`327
`
`3.27
`
`331.3
`
`335
`
`341
`
`344
`
`345
`
`34’?
`
`347
`
`35!}
`
`353
`
`363
`
`365
`
`.369
`
`372 %
`376
`
`376
`
`385
`
`385
`
`386
`
`413
`
`§¥¥§€‘fl¥$
`
`'Pmgm::a.sis
`Referencas
`
`
`
`’un‘t}a'n2enia¥;fi:)f 2%u.1;1:2’1y$is of Sniitis b;y Las-e1?—i’t‘oduc»ed
`3.:-15:13:13
`
`fang W. Kim
`
`=C§ia:pt:e'r C!:rganiza'tion
`.I’:2:ri:1»:iueti0n
`’?ihe:m.m£:nalagy :’ai:' .1335: Heatring of Condense..d~Phase
`Targets.»
`
`’t%iy.a:.Spe-etrizaszapy
`lhiteiisi y Zxicasnrements and Bi'e.menia1..Ana3ysis
`.Sz2m.ma1ry
`Refe:r::.nc=es
`
`’
`
`Laser V-:«;ipu1'i.zaEtin11 far §.S 2t.’mp!_e Inirothxctian in Atolni-cimxd
`ems $pm.:.trasc;apy
`aseph 3.l’I.€d.§3G13,, 133:5: Mitchell, and Nic'ho1a.:~: Negjar
`
`.:£'3t2nv§:n.fi1:in,3i Stiiirl »San1;3'ie’Intr-oii‘ucti0n fax A't:3mic
`8pect,ras»eapy
`£;asa.r.13gi3Iai§‘i3n. raf’S:::fi’<':i Sampies
`'L:a.ser.A131a'tisn far =Smr11r;%3i?» Iixtriacinctica in Atcmie
`S';2ectr:3.s.m;>py
`iigizztixrzz Marits af ’f;.as-at Abiatian for Sample Intmduction
`in Atomic 8’p€:.:ftxcs<:opy
`-
`Laser »SQ1Z1T{}¥3.»S’f{}I‘ ’Mass Spectrometry
`Appiicatians of Laser ’M;icmp'r»o¥3e
`Appl.ieatiQ.ns of Laser De:s»or_pti0n and Postionizatien
`.=Con::1usia:n
`
`References
`
`
`
`Czxrreni New Applications of Laser Plasmas
`Allan A. Bauer, David W. Forsfund, Colin J. Mcléinstrie,
`Justin S; Wark, Philip J. Hargis, Jr., Roy A. Hamil, and Joseph
`M. Kindel
`
`10.1
`
`Introduction
`
`18.2 Applications of Lassr~P‘1asma~Ge.nerated Xqays and
`Particles
`10.3 Las::r~P1’asma Acceleratioxm of Particles
`
`

`
`xii
`
`_
`
`b
`
`.
`
`=£3;:m'teri{.s
`
`1114 Lasem-Puistad Power Sxvitching
`Refierances
`
`Index‘
`
`%
`
`-
`
`1»
`
`£324
`432
`
`437
`
`
`
`

`
`
`
`
`
`magmas
`
`{mania FL. itieeist
`Cfimter for ,£££h5':er.g§}9pff£:a¥3%2rz5
`Zkzimrisigz .9f'It?é::;2é.-mag »:,_SjIg:«;w:: Izzszime
`'Yi£Z§::}za:é:’a, Tennessee
`
`4.1 INTROBUCTION
`
`-first »t”3'1b»
`Plasmas created by the .ra¢:.imian%..fram ;£as:m:i .:ass::: beams
`served. with the ativcnt‘ {sf “giant pnlsa’ Q tzcifaeiéii, ruby» iasers by Maker
`
`
`at at (1963). Thase’ -plasmas £92-’:’
`1221;‘ gas‘ ’b.re:akdown at
`t'h—n3.f0-6118 of 3 lens and warn
`iha tii3:r£;tiot:’i0f £ha'I’a.Ser
`..
`:3 L
`_
`..
`;;::1155<:L. Plasmas were aim a¥:~:s:€*;1*%sr:i7£.£:2
`.-am: onA£116»st:.rfa£ies vi Ina:-erials :ir~
`radiate-d by ’h=ig’1a-gpzjwer pulseszi or »:<:a:ntinu;:ms iassmrs zansti ttis 11.i.”iE3j§fig 8.t6 into
`
`-the inc.i£3an't ‘beam at .s’::§3¥:mni::
`’Vsz;:;1’;33r”’
`1;:’vt;iIz3;;£i;ies.
`{I33 advent of
`:c.m_1t:inuojus, high-pmver £2-arbszin
`‘die
`_ 3,,’
`h§§éa1ite.b§?£3S§;ifi,§E tic sustain
`a plasma in a s'taa‘(iy—stat£;z €’i€3}1.ii3iti£1n.,i1..»,*if
`i'¥§Jf§ fiwizzs of a.1as§:r"b¢am, 3.12% the
`first. experimcntai abservatirzziz -63? a “cgxntx-muons’=opti::=a1 {3.iS{2}mIl'.;g%'” was re-
`_p0rted‘ by Generaitw. at .211. {1§7fi). This aontinucms, }aser-sustained vpiasma
`(L8?) is taften referred to as a coniizzuws aptical ::§i.sc,1f‘:.a.rge ((23113) and it»
`has a numbar of zmicgne praparties»t11?at make it an ”int::,restir:g c.a‘nd.idat’e. far
`a variety of appiications.
`,
`The laser-su.staim:d plasma shares many charaateristics with mixer gas
`discharges, as explained in detail by Raizcr (1989) in his coxnprehensivre. re-
`view, but it is sustained through .abs0rpt’ion cf power from an optical beam
`by the p.r(3.cess.0f inverse bremsstrah1ung.. Since the optical frequency of the
`sustaining beam is greater than the plasma‘-frequency, t}1’e‘beamis capable of
`propagating, well into the interior ofthe. plasmawhere. it is absorbed at high
`intensity near the focus. This is in contrast to plasmas sustained by high»
`Vfrequency elezctrical .fi.e1ds (n1i£:mwa~/e and electrodeleiss discharges) that
`operate at frequencies below the plasma frequency and sustain the plasma
`through absorption within 21 thin "layer near theplasma surface. This funda-
`’menta.l difference in the power absorption mechanism makes it possible to
`
`
`
`"i 89
`
`

`
`’
`
`-
`
`170
`
`V
`
`Keefer
`
`g¢:n;:;m£€~ 5’£ea;c1y4sta:<;;}iasII3§s,lzaving .maxi2fm,1m temperatures sf 1f3;{}GOIi at
`1nt3rt:»iix a .s1ma§I vaiume near mg»-f0¢1:’s.af%a was», far away frets: any cc:I.iif1i3i_ng_
`str'ncmrc. A photo of.a.p1as:na. sustained by ;a ‘iaser beam focused with a lens
`3 shown in Fig.
`‘
`"
`’
`;.}
`V
`:
`J
`laser was
`%
`gen. Fig; 4.:i( .).:$§iea;vs schem,
`mgimx.
`”€2o‘:z'timze1;:s
`
`
`
`
`3
`
`e been ’pr{}{i11ce{i in a vaxfety sf
`
`13:23}: :ii_oxida}aaa'rs .£:>}3e’raiif{3’g at
`,
`,
`"
`. 2': 25 W ta saverai kmwatfts, ’£saI..r:3::;t
`_.
`£1”.
`a. 1:1: mmati, (3
`air‘ é:.>.r.1a.rge. »»chamb:ers’with_.
`. Vgravidafi. by :2-x=a*t‘u:::-ai seoxrsmctina, §:2u't- mz:5nt' axe
`’ " £3 7$i:‘»?s1;l.; b’{:3;9%3}, Weéiie max, A{198'?),, and. =C.f.rz3s2s»ia11d’
`
`
`
`__
`
`1733. within tha.«sn.stainin’_g beam, and
`§:~f”t""e
`iwidrg. range cf é;,{{£)I1di'ii€3’I’I.,3*i18~
`:.:2:2:;.
`1 »
`La.
`£3 .<*-.:;:m;1‘£_::::;za;4:i£>.a::s af 1356: »;:i<;w=,sz*, fiaw, and optical :ca12figur;2z~
`
`
`
`‘
`
`.a-gxnail, is-elated vélume
`‘iii? ausiaixia ;§:1§i$.I£:a
`._
`, agzd,»
`pa:r%ax21re$..has siiggested a xmxnher af
`axis §Qr'§h%E:»1a3£3I~suS§t;»':1ifiE:d plasma. Sings the LS? can.
`,§r£3;jr:*G:gz:n and iha» paws: <: aI1.b£. beameci remately, it has.
`ep»e1rat'e in pa’:
`been prioprszseci. 1113;}: the
`=co1;z‘k*i be us-ed .fer high specifimimpnlse. space
`propx:3.sion:. A numb-er bf gaajgersi '223%: -d:e‘a1”tw.ith this ap‘p1i£~ati0n_,. and it was
`the Subjgct of a :e?iaxv ‘by Giuiiib an:1’K.rier (1984). Thompson et a1. (19?8)
`described axperimcnis in Whi,Gh "Laser energy was converted into. €:1..et:trit;a}'
`energy using a -}as’er~.susiained argcmyp}as3:s1a. Cremers at 211. v(’19f85) have
`suggested that
`as a source for Sp-actrochemicai analysis and given sicime
`experimental resulas. Cress and Cremexis (1986) have s11stai11ed plasmas in
`the threat of £11 .s1.naI1 11»c3.zz"it: ta produce atczmic oxygen having a directed
`‘vefocity of’sevcra1—.k.m/sec for this laboratory study of surface interactions at
`energies and particle fluxes similar‘ to those experienced by satellites in’1ow~
`garth srbit. Other applications are sugges-ted by analogy to other plasma
`devices including light ssurces, piasma‘ chemistry, and materials processing.
`The physical procassas that determine the unique characteristics of the
`LSP will be. discussed in Sec. 4.2, and the the.ore'tica1 analyses that have been
`used to describe the»LSP will be addressed in Sec. 4.3. Expe1iimental results
`obtained will be presentsd in Sec. 4.4 and compared with the t’heoretic.a1
`predictions. Sec. 4.5 will consider some possible applications.
`
`
`
`

`
`La~3?er—$us1ain‘e-£1 Piasmas
`
`‘
`
`1?‘?
`
`(1?)
`
`(3) Phattigfaph of a plasma sustained by a 600 W carbon dioxide laser?
`Figure 4.1
`bgam focused vmh a 191mm fecal length lens. (I2) Schematic mprelsentatien sh0w~
`ing how the pkzsma forms within. the focal volume.
`'
`
`

`
`“£72
`
`Keefer
`
`4.2 FRINCIPLES Q33" -{)}r3’ER!s.Ti{}N
`
`Plasmas that are c.re.at=e»d 01* sustained by lasers flan be g=enerated_i_n a variety
`uf forms, depending?-@n"tl1b £1132-avc:£§;:ls’£ic;s cf the laser and optical ge£3me~
`
`try used in generate ilaetm;
`' zgl1«’§:n£%jf_g§I»’p13l3é:'c3. lassrs can igxmcrata plasma
`breakdawn .dim.£:tiy :wi_ilé'i_13 a gas i1;.a:,r&suI£si.n zatransiclnt axganilinggélasma‘
`similar to 1:111 explesiong
`Image? §a§.fi.r intensities anal longs: pulfie times,
`plasmas may l2e}in.iti:att3iia’£ 5:3
`.$uff_3€'€=3
`1311 {I133 ;3rujpaga:fi’.ifita the sus»
`a:'aini_x:1g baaxzn €{i».S!i§}t3f3{31?§;{§ val
`itiss as:
`~
`fr-~s::s3;£;izr;x<:s.t3 dets:ma3;i<::n (LSD)
`wave or :snl3sen,ic valo{:itias 3373» lgfigé
`nee: ébrfabnstifin
`WEW6.
`These tramient plasmas have beer:
`slid by Eaiizzer {I-980) and will not
`
`be tmateél here,» If :*;h_Ie: liagsafiis’
`l
`~ef1‘.a:£1,:1v.:l t§13;::*;zrtiiia}’
`:w:z;:-
`
`lggeomatry, flaw, a114;l,’;§ar&asi1rf¢s’a:;,e:
`__
`.rz’_:§3«,..»
`3» aa%:ly»»:§;%a:s
`may
`’
`
`
`52 centij;fi1t1nsl§;'m3§fi£aixi§§».at’3333:3331”
`11.§ia‘1"El:2a:_ was cf the 'bea.m. The
`inifensity that is axzailalziliz iffimiz abfiiliitiixuoiiallasfir -is inwfficieni to cause
`maakdtnwn in tha gas, hosvgvér, and an .auXiIiéa:‘y sflmrce must be used to ini-
`tiate theplasma. A sketch {if 5: sieaiiy-s'£at‘r;.1a.sa.r~sus’tai'ncd 13121311121 is shown
`in Fig. 4.’i£(§). T113_plas'ma:m.ay'l3a»stz.sf£ai;:ie£3
`Ia emnfining cllaiilbfir £6
`ccmtérel the flow and prrcssixre 01‘ in -apex}. air wt £1 larg-e, chamber whcrc the
`t_1ow§_.:’; determ-i.ne_d by t.3‘:1$rm.:e;.I l.:'3u»z;3_yancy;.
`V
`,.
`In znany ways, the laser-su5iain;.e:l. glasma is similar is direct curran: gr
`lqwfzaqtzancy -elec;r:f>€I§.l;3*3
`anii f..t1.i£i£i:3xv;i2€s;g.dilsc11m°gxi:s’tl§.at am €3p~e.r-
`.
`aired in similar .g1;ase-s an
`£11" préfis-:%13;£€=S.
`Iiiifiwevicr, $116 11.3? 'W§}.1. gene:-
`any has .m{':re czsiir:-1’ act: 313.6 mzaga lxiiigher ;maxi.mu.m teznperature El1.an.n'tl1:=:r
`»§:£3ntin1.20u.s am s::i'm*.ce§ aizdi
`biz: :$u:=;'§a:i11’€::é§ in :22 steady state well away from.
`coniaining boundaries. A fin:§.£3afi18f£iir35}L v:1iffflr’enca:in'the way in which en-
`-ergy is absorbed by the plasma is r23.&§1r9:3éil3l.€:* £0.11 ‘£31633-. xxiizique» charactizristics
`-of the LSP.
`-
`
`
`
`‘
`
`4.2.1 Easic Physical Erncesses
`
`In a Cl}l?:E5£‘.‘€ current (dc) arc or in an inéluctlvely coupled plasma ‘(.ICI’), en-
`ergy is 'ab.ss:>rbecl througl1 ohmic .heati.ng pracluizzed by. the l0w~fr::quency or’
`direct currents flowing in the plasma. The elacirieal conductivity of an ideal
`plasma is. given by ~(Shkamfsl<y at al., 1966)
`
`J
`
`neg
`= M
`
`1/~—~iw
`
`in (z22~l~w3)
`
`4.1
`
`(
`
`)
`
`where it is this electron’ density, 8 the electronic charge, m the electron mass,
`to the radian frequency of the applied electric field, 1/ the affective collision
`frequency for electrons, andi thesquare root of M1. In the do are (as 2 0),
`the currents are’ transmitted through the plasma bcztween electrodes and
`
`

`
`Lasebfiustatned Plasmas
`
`'
`
`-.
`
`A 173
`
`the size of the plasma is determined by the ‘size and spacing of the electrode
`and the L;-o.nfi.::ix1:g boundaries.
`In the 143?, the currents are i.nduee€i.iI1iG
`the plasma from aliernrfiing cu:rent:3. flowing in a surrounding .so1enoifia1
`
`<:;c2ii.. The are is sag;
`inmgi
`' "thin a container that determines the plasma
`dian1€:tor,
`'whe.I£:as fine Ion
`of the "plasma
`determined by t}:1e}ength of
`"
`the soiemid.
`TI*.1€:*.,I'{33P operates 33. frgquencies well below the Vpiasma frequency
`
`p
`
`.........
`
`_»
`
`1.1}?
`
`::..—~
`
`WP
`
`4
`
`.
`
`7
`
`
`
`9
`p
`< >
`~4.,Z
`
`whe1'o..¢9 i$?"fi'.1fi}§£?2Ii}1§£ii‘52ii}* of fi?ae~$pa<:e:.. In this frequomiy range, the 6}€:£!~
`tromag‘na1io.’fiaIjtifioeésinaflzrofpagate. gss a ‘wave. xviihii: the pI1.a9ma,b11i“is
`.a,u;¢n;:_ate;i, agan ¢”a.ne$h;enti»wave (Holt and Hask-an, 1965) over dis-tagnces
`
`£43}
`
`is V£E1,e‘Sp:e'afl: O‘f?ii/ght:" ’Ehu.s, thapiasma is su.s~tai.ne::iI by azxoxgy-333»
`-where.»
`sorbexi within a_.sma§1..ia;,:.e.r near its outer surfacs that produces‘ a rathm':fiat
`temperature pirofiitsg w“'“
`thgpioasma and limits the maximum tzmgaera.
`t11r£%.i::$ that ¢ai:"Beobtaines3.,
`V
`-
`The frt%.€;"u§ncy of {ho goptitzai fields (23 'I‘_Hz for the 18:6 gm ca;r'b*on_. diox»
`ida Zasor) nsgcdfior-tho
`is greater than the plasma frequency, and the2'a~
`fore the .i'nGi’d’en'£ iasor. imam nan -propagate well into the interior bsfora
`it is s:i,g£xifi<3anf‘i}},y »a}3s-otbtzd’ ’t}1r£:¥.:g.h the process of .invarse ‘nrem.sstra121u11g
`(Shkatofsky at 211., 1966)‘ Sine-e the focusing‘ of the law: beam producsd
`by 21 ions or ‘m5.I’.I‘.{)'IT is ess.c-ntiaily preservod as tho "beam propagates into the
`plasma, very 1arge..fie}z:i. strengths may beproduced within the piasma near
`the beam focus. 1?; is £12853 iargc field strengths that lead to p-oak tcinperay
`tures in the LS1’ that are goneiraily greater than those obtained with either
`dc arcs or the EC? and make it possible to sustain a small Voiilme of plasmoa
`onear the focus, ‘W611 away from any confining walls.
`Inverse bramsst.z'ahIung— is a process in which the plasma electrons ab~
`sorb photons from the laser beam during inelastic collisions with ions, non»
`trals, and othsr elmztrons. The collisions betwew electrons and ions are
`'t}:1o_d0r‘ninantproceSS for the LSP and the absorption coefficient is given by
`(Shkarofsky et al., 1966)
`
`W
`
`“‘
`
`re‘ 3n.S0G 1~—e"”“’”‘T
`o -.
`
`(La) kr (
`
`Fzw/kT
`
`>
`
`V
`1.4.
`
`0 )
`
`

`
`374
`
`’
`
`,ij<.e»efer
`
`where E is Planck’s constant divided by zar, k B0i:am.a:§.:1’s c»£3*n»St23Iil?a 8137
`-the t£:mp€’:.r.alure ofl:hee1e.c:rons. T113 factor G‘ is the Gmmt faster and the
`Easter 3:59 isgiveu by
`
`
`A. 3
`3
`15;.
`.22
`
`. L‘
`.
`.
`.3133 "~'-’—" *“** nflfin
`3 H1203’
`.47n°.g
`
`112
`
`I
`3kT_.j
`
`.
`
`‘
`
`I
`
`(4-5).
`’
`
`»
`
`-.
`mg "‘iw imam.
`’-
`32.32:’ i
`;i§’gi-v“c.m» by ear’: law
`
`£acmr,.is. a
`T where Z is the ionic cha:rge and 3,, the ion -dezxsilzy. ‘The
`mecfiaaniclail currectioxi tea the -::.1as.si.c.al theary,-_’amil aztiensiire ”!.:£i’xhies
`
`have} been given "by Karzais and Latter
`Fdr f
`‘
`"
`"
`’ ” " ’
`the phgtofn energy is ’mm.:.h lass than than
`’
`bmzzketalzi term in
`(4.4) is zmarily .in<3e.;§e:1 \.
`.
`cIc:=efiieient:"ls ess.enl;ial2y»pmpz3r:i:mai "t=G”l:ha.$§;1;2a£::. :3.
`size ef the
`will Clepefld an several féctflfis
`_2g;:;a:a.n:et:y;, 1aser»:pcs:ver, and a}}s£2rp.ti»c3’:x cnefifieiant.
`szaf. the-..1aser ‘imam as it prupagrates v2i:thin the
`
`_
`
`
`
`.
`
`“~=«' -val’
`
`‘
`
`..
`
`(.4-E6)
`
`F.EE3‘: abaargzl
`’
`~ where s is tha distance alnng the local :i.i.rex;:.ian £§i’5_;3:’:iii3
`.
`tinnifiength Life: is a daminantlength scaia fc:r’t}'.1s‘3.
`,,
`. 288 it :c§.e=;:rl-:‘*;r’. ma-..s .
`"H133 r:§'is_t;anc=e.-oyggr xvhigah tE:’a’p~{3w€;£,iS absGx*beé¥ frgm {?h:e’bai:am., F&r'tFhis’r:§caa
`2:
`:59-n,»t"1%m dimension Qftha»§ii’gii~:a3It1;}a£aI£iifa ;é2£¥2s:>3éb§i:z_.‘
`"<2:
`piiaatxza
`
`alcmg tha laser beam will he of the cider’ taf ;h:¢;»a¥3sar;):t:»c:n itzzzgiiz. ésiihaiigh
`it is {he absorption 3.Emg1:h that determines ‘tlilailangtii ief-tha»;3}asma»a1:an;g the 7
`Exam fixigs, :1. is the laser beam »cI.iarmeter amt. diziezmiizxes ti-1:2: galasma ’§fi33.I§§?e¢'
`tar; ’I”i1e’;31£1s:11a expands to fill the. begin £:i3.11”eI .ui§:'1.”ti:r:e it
`able fie «21?3$*c«fl3
`pawar, than rapicliy ciaszzmazscs in tenzperazure. m:tsi.:§::: tihes: lsaam ti1rau1_gTh
`thermal <:a.n::1uction.a.nd radiativs lass .machan.isms..
`The pnsition‘ 9f the
`relative to the facal paint is tiriiicai in deiermirb
`ing its sitruciure andilie range cf para.mcters far which it ‘cat; The .maintaine€1.
`Whan the plasma is initiatad near the beam foam, it pmpagataa into. the
`sustaining beam and seeks a stable. _position. The pasitidn nf stability will be
`.locat»e»d‘wher:: the imam intensity is ‘just sujffizziimt t11at.1:.ha ‘a’bsm“ba»x;l power
`will balance tlxalosses due to convection, thermal ccynfiuctinn, and.therm.a1
`radiation. A _number of factors cmnbine to determine this pcssiilcm of sta-
`bilitylncluding the transverse pmfile of the incident beam, t.hefoca1.leng-tl1
`and aberrations of‘ the focusing lens or mirror, the plasma bprassura, and the
`incident flow velocity (Keefer at 211., 1986; Walla at 211., 1987).
`The power per unit volume that is absorbedby the plasma is given by
`
`
`
`P == crl
`
`V
`
`(4.7)
`
`

`
`Laservfiusiaineti Plasmas‘
`
`3?5
`
`where I is the Iona} irradiaznce of the Eases: beam. Smce I depends an -the
`transv-ersa profile 0f the "incident beam a’s.’-weii as ‘the focal ¥ength and aber~
`’ra'zicn.s of the lens, these -chamczterisiics wiii .:infl.uenc-a £i1e’I.t:2ca’3:i0n within
`
`the focal region at
`the».
`inimm:n.sus1:ai.ni:t;gi’n.tan.sity is Icicamd. F01‘
`exampie, far a small. ffxznmbfir» "’n;$,_ the.'i:1£cnsit3¥ decreasfis rapicily with im
`cra.asi.n_g .dist.a.nce ftam..1hh?:*facus;2m€i»the p_1a‘sm.a»w.i11.s’:abi.1iza:ncar the focus.
`‘For -a}ar-ger.ffI111In.¥j)er system., ii1;sji':»..i.:3'e.=r1S?ity’ Ciecrzafias 168?: rapidiy and the
`p1asmawii’I.;stabi.1i2e.ai.2r:p0s§tia:z fzxi.
`awa: Em. ..
`neué. I::“<3a=e.-(1., for
`.s':_31ficienfly 1cmg*fo;;a’:I .1cr;;g1£h§ :a::;.?1} 1
`s:
`p=a‘v}'er3 §z1;as;:nas..h:avie’be=en 0b~
`-
`’
`’
`”
`'
`’
`vgfifiififg. 1193i?) as “’I.a:s¢r:zs;;ppo}*ted cam-
`
`
`
`
`,
`b
`’
`Tha. zimaiiaexzi ;~r;;>.a.t.i.,2::.1 :
`’Ia5ti:'tsns bemseen.i1rm apiiizzsaigésgzmg, 9.
`
`”
`
`'
`
`sizitaiis »3§.§’14E*.e.t*€$1?I2:i:§1fi1;“.:s:_17'¥._3r§It.1I1%:'i.nierx::~
`’
`’
`-
`.3.
`z..1:xg»$a=.-_,.»§. aprcssufenf
`’ "
`witiziin ’£h.¢%:¢ ;::«Ias:ma.,
`
`
`
`a $t:éib.I¢ -;:‘iax::::a
`a.n:i.;fi{aw .fbf._r.
`Mast céf xhaearzy 61:33 me.
`chambers tn": in §;p&n»aiEr,’xY§E1efi%»t11’ "£1.
`by the effects at‘ therma} bmzy-
`‘
`
`the ipr.essar:e .3215 inset powar»-.
`.
`.
`pressure w11.er’a»i:was l1‘:::iS.si3:5.1~&*:«’§:i3
`- Thfise. -axperimnnts
`.
`.
`eraiav et .ai., 1'9’Z2;; ’K<3z1¢;;=v 4% a‘{.., 1494:
`f¥31r”33£>3fih}.aser.p0sver anti
`Enézficatcdf, that filers wars np;‘;:>’er anti ’ix::t*».=’iv£'-—E1‘
`.
`.
`pressure at which the LS? =£:i3i:i.'i€i be snataineéi.
`Generalov et 31.. (1972) suggested that the upper iimit. for p-owe’: was a re-
`suit of forming’ the LS? .v¢ithA a horizontal beam. In this ,geemet:ry, thermal
`buoyancy ‘induces a flaw transxzers-e to the =0.;f:¥;i§:ai axis. The imiuced flow
`czarries the plasma up anti nut czf the Beam 'W31Efl.h.§g§}fiI“ Easier npmvez“ causas
`the plasma :0 stabiiize‘ farther from the focus. They were unabla to estab-
`Iishan ’upp-er pews: jimit when 1115 expaximmgt was aperatcd with {ha beam '
`pmpagating verti.ca11yV upward. Koziflv et_;a'1. (1974) d6ye¥c3pe.d a [radiative
`model for the LS? and explained the agape: power limit on the basis that
`the plasma must stabilize class: enangh to-the’f0ca1‘p0int. that the geonueb
`V ric increase of laser beam -intensity geing. inta the ‘plasma was greater than
`the loss of intensity clue to absorpfi-on. They speculated that the faihxre of
`Generaiov at al. (1972) to observe this limit in a vertical beam ‘was due to
`rapid extinction and reignition of the plasma.
`It is clear from the experiments of Generalov at al. (1972) that flow can
`have a large effect on the range of Aprcssure and "laser power that will support
`
`and zharmal razziiaticm; ’.Fhc pas.
`at which the piasma stabiiiz ’ :§§x2e: 1.
`
`

`
`‘W6
`
`Keefer
`
`
`
`Fiastxnas sust-a.i.nsd in tho frat: jot issuing from a nozzio have
`a szabio
`boon studied by Gerasimenko at 31. (198.3) who n1aa'.sured the discharge
`’%;s*f&3e%?i‘3 nnincigy alozxyg {ha bean: andxannges for the existenizn of a $toa€iy~st=ate'
`
`d;‘is's»;:h
`..Rn;:::nn1.%i§»
`y
`nonts’ havn been oozxcixxctnd in confined tubes
`
`:.vha1%e’=»£.0i1:ced nnnyactinn :1 :ni'nat€-ni nu: flow (‘Wane oz 211.,
`:£9{87_). 1:; was
`.:f0’unr?: ihaifi-n addition. in power and §}f$S.Si1f-£3, both the flow and nptiycai ge-
`OYII.
`in ”
`' gvg-:2:pi”GfBfindinflnen'c:-3 on the cfharactmisiicsyof tho =
`
`
`
`
`tho L-SP <:s:;:;.:icif2_:»’c=;, susta.i-nan are ya}
`y
`_y
`._
`o~:nIy:.;Eor the gmriicziiar.-experimental’ gjeomntrynsed to obtain ithkem.
`
`
`
`when tho pins
`inn ‘ iasma -
`
`
`
`
`
`
`thnft itiho ’3=1e-2* absorbed fmm £235. tzeoam, given byis balanced-’
`‘fine: convective; con§’uc'§i9<7.o, .a‘nd irafiiation Ioiss-es. -Sincies, in generai, "the ‘in,
`
`
`' _ T, the B33122, the p1asma.wi11 a.<:ijust.._;i‘z"2 size, snap»
`
`
`
`
`
`
`2!; rBs:1x‘F:...nf‘E3onn3i4h:o:nn:i iransitinns,» rosniting in lino ’rar}ia£,ion am: absnr
`tion, =and..frno;~?§:onn£i amzi fies-afrose téran:si‘tions’that resin}: in .m'ntin'unzn vraciz
`a’iiQn»-afifi: ahsoafpt
`Qve; §I1e.op£_ioaI§_y thinportion of the spectrum, ‘chi
`ran.1.am>.n xvii? : stmngiy ;i?::$i:rbaii by the plasma or sn:‘ronnr3ing nifinm.
`regions and wii} sinxpiy osc;ap»c from the plasma. (Ether Iportions of the spec» b
`mam will
`sirongiy absorbed, 1‘e2:'uking in a transport of energy within the :
`plasma. In the oniiizaiiy ii1ick1'imiI:,_this resu1‘ts;in a diffusive energy trans“
`p-Cart that is similar to thermal coimtiuction, but may be significantly larger.
`Detailed cn1Acui.ations. of the LS? (long and Keefer, 1986) indicate that this
`radiative trzmsporz is a szionxinant factor in the determination of the stmo
`turn and position of the LSP. In particular, it is the radiative transport that
`’ determines the t7ompe'ratur,e gmdiont in the upstream .fr.ont of thoplasma,
`thereby determining the position in the beam for which convection losses
`are balanced by -absorption.
`The position of stability for the LSP also depends on the plasma px'os~
`sure, The absorption coefiicientis a strong function of plasma density, as
`soon from Eq. .(4.4).. If the pressure is inczroasocl and the absorption ooe:ffi«
`cient increases, than the plasma can absorb more power from the beam and
`will move away from the focus to a lower intensity region in the beam. At the
`
`
`
`

`
`
`
`§;,=a»s.er-'S'usta’¥ne»d Ptasmas
`
`' 1??
`
`‘ ”
`
`'
`
`831.1%» ‘$1116. the zpiazmxa iength aizmg the .beam »ck:cr-e.a-ses bmcaus-e zaf the fle:~«
`£;1f§;as’e in absarptimx isrxgtix, 13111 the d.imnet=e.r i.n»<:re:ases ta ii}! the .larger :c.m;s’s
`$e<;ti<}.n sf zhva beam, Thus, far the same laser beam stars:-niititizis, a .’higfhar-
`
`px‘essuir»e
`wii} stziiiiiiiize
`a, Quint farther away fmm the ma: gixaint arzci
`have 3 :’s'maI1a:r..}angt11~'1o~C%1arnc1er ratio ’th.a.rz 3 I-0xvm*~:prassu.rc
`.
`,i11cide21iiase’r p{)we3f., as wail as tihc f/number and absrra¥i£3n.s cf the fa
`gusixlg Qpties,» will also .ir’:.fix.z.enc»e the ;3;3si,£iz3n. at which the
`St:;zt3i}izes
`iihe .2bsa’m., Fisam {me '=‘,£o:as;g::{i’:1g <3ii5£:us.£i€31}., it is cierax fhat as the?)-e.a.m
`pom: is increassziv, the piasma=wiIf1 mmze up t11eb£:an1 ixway ifrbm the fixzai
`T115 distance that it mtzzxzes. is zistermizzegi by ‘the .f!n.umb:&r (iiagiiiit {Bf
`
`3.2 in tiiéhe: 33€:a::I2.d;i’¢ti11$'£e2f:i’n£:i}£i€1:1t’§3:1flmfii-Iztzsizfzg
`”
`”
`.
`nee tihe rata»0fch.a11ge»»’inimami?ntei1sfi’£§’
`.
`_-
`mi
`
`:22 air’: in’£:was£:.in ffnumbe.-r; Lens ai:err:a§:ions:.ean-.ais::>..§1ars,%a
`81333 {:1
`Va _e£:.é‘t {§3}.p¥asma p=o-aition (Kaefmf et :aL, 198$}. In part;ic11k::r, Wfh;E11'i an an-~
`231333": Ema-:2; gfrrsxia: a’n.n.nst;abie1a¢ser <>:2+i:.i,£}21t:>:r:’E;:}s:::z»a:se;::i 133:3 sghericai I.e;:z.s.,
`'it..pr£3d13-ces an am’nn’iar’pmfQc,us region. befbre reaching» {ha ff}:-15:11 p?:i:si.I1}:;,b and
`_ £112:
`’
`t_§i1i;‘; ragian'n1.ay’1:23su.§i:im1’i’t0 »sz3.st.a;iz1 an azgnuiar" 2131.3;
`
` m: {ha z:»'bs;é:rvat:iAn.:1.s :c§iswu.ss::d. abcve, it is cigarti1.at’£heg;$%:>sit»i£§n Gf
`{ha plasma relaiive in -the focai paint has a: prafwndeffzészéi’<1:2-”ii1¢’:p}:asma
`=;:istics.. Aifile upper limits Qf:at3%t*.i¥i2y :f::sr bath i1.as::r—: -pa:;»ver< ml»
`,;:ha.:f;s:::te
`
`923
`V
`a}i§§’=i§€£r's
`that {ha pi£ixsn1.a:ii:ecbmes xx:ist;a“b'}.e sixhan ii; ixnavasma
`£ar‘fm1’m;
`fi>»<:;;¥. paint. This may be dm: to tits :1’.at-:..i, as prQposed»byf’Kt§2fi:3v
`at Vail. :(3§¥?£§}, ihatas ‘iihapiasma .mavas sufficiently f_ar’awa3r
`iii:-£:u;s:.,
`iha ,i?i§{t§§ 933 in.crga;se cf the beam .in£ensiiy in ihsa aiiracéticzh. af‘ -agzrczpagiafiain
`’ aims s:i1a.}I6r. Sines the. tampareitura s::%:£ '=t}1:<i’ ;2§.a::m’:,a .m3.J,$t 5 "
`ease.-tax:-itxe
`
`beam grgipiagates into the uy:t:’aarzi ecfige itixietpj-’Iasmai_ .:ixfi:énsi:3?‘ii:tf~zfI1e
`baammnst 3715:: increase. At some paint, §i1e:dac’ra.as’eA-of i}za.’b»aam iI1.;’czé;f1s.iiy
`due-ti} »a’.i}si3rpti0n is greater than the incrieeasa due: ‘E0 f0c%::.s§:1g, SC! the piasnza
`Essécemeéa unstable and extingui-s'hcs. Recent <:.a1c:,.z}atit3ns by Sféng. gm :1, Keefm:
`(:9a?a}, hmvaver, indicate: that there may exist 1.0031 're:gi£3-213. =withi2: t}:1e’LS-EP
`whom .£}1e’b-mm .intans:ity dm;re.as-es ‘as it penetraies the plasma.
`. Accmsidarabie ciegree of £10I1t1'O10f the structure and position Bf ihezlgfi?
`can be gained through both optical geometry and flow, in Vaddifian tc) Iasar
`p-zxwcr zzmzi. ’pressure. Utilization of these aciditicanal parameters nmake-.5 ‘it,
`p’0ssib1i~: to successfuliy opczrate the LSP ever a wider range 0f exprsrinfremtal
`conesiiiierzs, enabling 21 wider range of potezntial appiications.
`
`’
`
`‘
`
`
`
`13.2.2.
`
`?1asn1a Characteristics
`
`Laser~sus.tained plasmas have been operated in 21 variety of molecular and
`rare gases at pressures from 1 to more than 200 atm. The resulting plasmas
`have characteristics that are similar to are plasmas operated at similar p1‘f3.S-
`
`

`
`177:8
`
`-
`
`-Keefer
`
`am usually somewhat highs:
`sures, {mt the pcak tenupcraturcs in the
`than these for the ccmparable arc, Ra:¥iati=on "item the plasma can be a Sig-
`nificant 'fI‘aCiiO’I1 of the total pzawar ,iz?:pI.1.t, and .rar3.iaii0n transp.r;:2r!: plays 2.-
`majcr tale in t:‘ctctminin_ the structure‘ of thc plasma. Co1::tinuu.rn —abscr-p—
`tion processes are cf13attici3lar,1’mp0.ttatzce in these ;plasm.as since thcpower
`to wstain the plasma is aiascrbati -tlzrctzglz these. me.-chanisms,
`The» .caniin1mm ahccttzztizm putiizccss iinyclvcs both l:}{)'i3I1fi.~fi‘€f3 trans.ition.s
`('p}:»0tci£>nizatii}n) anti ft'.6c».f£'cc transifticns (invcrsc bt‘fimsst.f’ahluéng) in
`wlzich phm:tmjs are absorbcd. fmm the»»l.a4scr’l::eam. Thu .fr<w-ices. transitions
`iI1?t:tlv6=»‘:flectron ccllisicms with 56:13, Gthfif éclcctrcns, and .’ncutr:al particles’
`{siziiaamfslfty c: .31., 3;’9‘§S-;;; £3:r.i‘c:m, ’19fi4}..
`i39mi'nan:t abscrption process
`
`for than is fiiiffliligli cc?ll§3_ion.§ ihctwcteti
`.
`..
`;xft.s 3-m3”icns, ,ar1d*t,hc a_b%m:p~
`-tiozt cccfiicicnt far this ptcccsa: is» given by Eq.
`For the usual Case in
`the 'LSP, kw ~.»:<:::k:'1’~and the ~a'?bs£33.fpii<:;I1’ is; appraximatcly‘ garcgtortianal to the
`sq’na’r=t-: of the la$.er- tvavclcxzgtjlgl
`ta
`’$irs3z:g,'xvavelcr;=gtIl ticpcncicrtcc,
`.311. cf _t.h’c_ rwcrtcci. e?£P€£i;ma.n'.t£2l
`{ES'i3Il.-.€Ii»if£}i" 111.8. LSP"h,:aw'c» beer; cbtaincd us«
`ing thc 1-9.6 gm w.avcle,;ngfl1 carbmn Ciiflxidc laser; Si-ace the length scale
`far the plasma is of 1:he—:*::.rdcr»cf the abserptian .lcnjg¥;Ih;, thc» length cf ‘the
`bplasma and .1113 pm;-er mqttired ti) ’s*us'ta1”:It it iworxld be cxpcctecl in increase
`dramatically .fm'shx:3’rter aaiia’vel;c:1*:gth_ lascrs Ctyggrcntly, -tfité. cnly other lasers:
`-zliztt are manly canciidams ta sustaizt £;{it1I?i122'{1§i}11§‘1 gzlajsxztast-arc» the itysilrcgczi
`€11‘ denicri'um.fluc.riid.c chcmical lasers mat cpcratc at wavclettgtjhs cf 3’ to
`4 ;.&m..
`'
`'
`'
`.
`Tltcrttzal r,a>di:a>fi!>01Et>..iS iizaiiilie cf thfit ::1}I£:st.’.i;2:;§c:’ta:z’1 c'ha:;acterisiics of the
`LSF. Thermal -rad_.i.a1:ion jO3t.ffG1'3Il.’ih3}313$'ifi3 can ai_:c0’nnt fer nearfzy all
`that ;;=t3wc1' abimribcd by the 'f3l’a,s.Ii”1a what} £115:- flow througlz the plasma is
`small anti. will account for :a s.igx.1ilicant fmciie'n of absorbed pews: even
`whcn thc ccnvcctlvc lcsscs are large. Thjc thermal rradiation. consists of
`continuum radiation resulting from _reccx1il3i1*;ati0n (free-bound transitions)
`and bramsstrahlnng (fffifi-’fI‘-fifi tr-ansitionfl) as well as line radiation (:bC}1.,1I1(3*
`buund transititms). Calculatitzn of this radi.atit::n is straightfcrward, ab
`though rather tctiieus, when the plasma is in local thermodynamic equ£~
`librimm (LTE) (Gricm, 1964).
`‘Local tltcrmcaclynamic equilibrium is es»
`tablishcd when the clcctmn colclisional rate proccsscs dominate the pro-
`cesses of radiative decay and recombination. When LTE is c~st.ab.lishcd
`in the plasma, the density -in specific quantum states is the same as a sys~
`team in complete thermal -equilibrium having the same total density, tern»
`peraturc, ancl chcmicalv.c_ompc3iti0:1.
`It should be emphasized that this
`does not imply that the radiation is similar ta a blackbody at the plasma
`temperature. In general, that: spectrum of the Iadiaticm from the plasma
`will have a complex structurc consisting of the superposition of relatively
`narrow spectral lines and a continuum having a complex. spectral struc-
`ture.
`‘
`
`

`
`s.ss
`S55
`
`§ ,
`
`Laser~8ustairie-ti Piasmas
`
`"179
`
`
`
`.
`
`_
`
`The sbscrptifiszn: c-ociii cient in this plasma‘ depends on the waveicngtli, and
`far thc u'i:r.svi.t31ci."portiQn cf the spccuum bslciw the wavelength iii thc rcso»
`nanceiimss ('£}.‘ai1.Siti
`:13 in 'ivii1g the grmimi state), the r.ac:iia2_ie.n is stmrzgiy
`
`abscirhxcd by tiiii pia ’
`_
`the cca1cr.su.:muxicii.ng gas. This rcsniis in a
`szrazijg raciiativss 'ira,:is{3Qrt”'mecha’nis’m that is imgiartszii in :ietcm1.i.iiin_g the:
`st:mc.:ii:i::'e ifithe pias’ma.. Qitsn, 'rz;d;iative tr-anspcri. for stIQng1y.ai3££3ri}in_g
`gases is :zn€i<ia:iic::i as :21 -ziiffusivc ensrgy trans-port simiiar to thc.nna1..candue~
`izion.
`£i1¢’.s£m:iIgiy itinizecixjsgicns -a:f"the piasma, the r.adiativc ir;anspcrt_.:is.
`many iimcs iarger tiiraiz the ’i=i:_tr.insie ihsrmsii ccnciucticn and is flit? dc?-i1i=i2a3::’t
`}2;sat~trans£c:r
`Thiis -is cspccisiiy iii:-V3 in the ugsirsam tcgisii cf
`~X¥h{i}‘ii:
`’e*t;e~;:1:p:»3;rii£=2ir[a graiiient is ilaidgc, zmd .ra£i.ia£it:).x_1 tfansfifiift
`fisiiit
`izozisisf
`i*2z:5»’1g3ssasis cf»-the insiident "flaw.
`titéiaiigsrssssssisrigth regiicm s'i3mr.c the rcssnsncc transii;i;:>n.s, fi%is..ab~
`,,
`scsrptiizm of'ii1e.,razii.at’infi by tiic piasma anti t'he surrmznciifng gas is much.
`smafilerr. "I113 =ai2scr;:'iii3n 1.ezzg1;i2. for this is-diatidn is Qfitiszi large -xsiizriz
`éi
`
`{scams <:i1<a'rac:s'risi:it;:e::ii.msn;sia;ix1s of the splasma, and 'fI711}fih»f3f’ii1fl,f3§?t1fEi..1{§2i
`es; 963.
`tsgiczi .Q:f:t;i1e.:spcctru’i:2, {he piasma may be cnnsicisrcci cap
`/ziciaiiy thingaIitiif'ti;ezpias:1121.is in L'.i‘}?., than the €:.sc:aping:;’:a3;iiatiOn eanfbc
`’us's-xi is characterize the tempcraturc within the LS? {£{e=e:£ss at 31,, 1?§86;
`
`987).
`
`
`sass §’??i‘§f1:_iI.‘1
`iii-E: piasz‘-as is far fmm sniicrm,