1Le~e1n J. *Rafi2£e m$ka1
`‘Department of 9% :35
`New Maxi-:9
`.
`L35 C¥’U’i'f€S,
`
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`. ..
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` edited
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`»
`»
`:3?!
`Chemicai and Laser Sezfiences. ‘Diwsion
`ms Mamas Nat1is3n*a,¥ ‘Laimratrjr-v
`L03 Names, New Maxim
`
`MARCEL DEKKER, INC.
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`New York" and Base!
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`Library of Congress iiiafaljgzfgi:1g4i§14}§1}3iit;ati<2n. Data. .,
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`cizexnifzal. afi£3,bi01¢gica1 ap.’91icaii0nsAf e»di.ted
`Lase;~it:;Iu.<:e-ti §1asm-as ::
`by Leezi
`R§1:§3}zie:31s}(i, ’33avi:1 Ag. iiremers.
`V
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`
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`V?1}fg:;mg. 2.1
`$1..-Cre
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`-94%)
`,:V§f‘j;g}1’“§3;€:~:x$;reriasets.
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`This baak is printad on miiiafrea ;p:e2;:«e,:'r'_.
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`Copyrigh‘-t © 1989; MARC.BL.DEKI{ER. me. An Rights Reserved
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`Neiiher this book no: any part: may ha repmduz:ed Q1‘ transnaitted in any form
`in by my means, eiectmnirz er mechanintai, in::Iuc¥i=ng plmtucopying, microfilming,
`and recording, or by any jnfexmation storage and retrieval systexn, without per
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`MARCEL .DEK}{.B'R, INC‘
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`

`
`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
`
`’
`
`Canteniss
`
`3,3
`
`Intmduxetion to X—ray Diagnostics
`References
`fl
`9
`
`4 i;;;s’e'§r;S1:st.aine£1 P18511135
`Dennis R. Keefer
`
`‘
`
`4.1
`4.2
`4,3:
`4.4
`4.5
`
`I’ntr0z3.ucii0n
`Princigzicz; cf Qper2iti{2’n.
`Ar-u”z’1ytic,aI MQéie}.s
`Bxperimen.t:a1 Studies
`App1,i<;ati£3n.s of the LaS—€:r~SL:.s{a£ixl1ed Plasma»
`Rcferances
`.
`b_
`
`5
`
`i’nér~t.iz’:liy Confined. Fasimt
`Robert L. Mcflmry a_n_§..3nh::
`
`’S<)'u.res
`
`5.1
`5.2
`
`51,5
`
`5.5?
`5.8
`
`.
`
`V
`
`Isiistaricai Overview
`LasVer~*Fusi0n Szzaiing Laws
`Cor-anal Physics
`X~ray‘Gen€:’1"éitiG:i by L:ase'r~1?rad':3ced Plasmas
`1.as€:r—'Driven Abiatixiij
`i%Iydri:3:3y:za:x11:ic:Stabfiity»gfg&E:I§‘£i3*¢1y D1"7"i’Sii.€’:.I1_.:
`lz’°mc§.iaii,::sn U‘n’.iformi£yR&q_u§1:é:1§3.aI}.15
`Impiosiim Experiments
`Rflffiffifiéfifi
`
`‘
`
`-
`
`‘
`
`.
`
`b
`
`6 Laser-Bases!iS’;e.n1i<:un.:311;:£ar’filiariitziiixiil
`
`Iaseph ‘R. ’Wachte’r
`
`5.1 Aspects of Semicandtwtor Fabrication
`(3.2
`App1.i<:at.i0ns ef Lasers in-the Sem_ifc0nidu.ct0r I.ndu$t1'y
`6.3
`Research Areas T
`T
`_
`6.4 Outlook
`Refarences
`
`‘
`
`7 ; S-pectmchemical Anaiysis Using Laser ?1asma.Exéit.at:ia11
`L-eon J. Radziamski and David A. Cremers
`
`Review
`7.1
`-Methods. and Properties of Analysis Using Laser 1"-fiasmas
`7.2
`Analysis of Gases
`7.3
`7.4 Analysis of Bulk Liquids
`7.5 Analysix of.Particle.s
`7.6 Anaiysisbf Solids
`7.7 Advances in Instrunmxitzition
`
`133;.
`161
`
`169
`
`169
`1.'??.
`1182
`189
`19:6
`293
`
`2&7
`
`20?
`2.-:11
`21?
`224
`227
`239
`243
`251
`2&0
`
`269
`
`269
`276
`233
`290
`291
`
`295
`
`295
`296
`302
`306
`309
`313
`318
`
`

`
`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'tar:{s
`
`153.4
`
`Las¢::r—Pu}.svad Powésr Sxvitching
`Refierances
`
`Index‘
`
`%
`
`-
`
`‘V
`
`424
`432
`
`437
`
`
`
`

`
`
`
`
`
`Fiasmeae
`
`iiemis FL. ifieeiet
`Center for Laser.g1§pp§£3£3.‘¥3¥2?3=5
`ifiziversitgr .ef'Iffiérszze.-me‘ 2_S§)z2z3xf? I%zszitz:!e
`'3’i:Z§::}z:2:“:é:z, Teiarzessee
`
`4.1 INTROBHCTION
`
`
`Plasmas created by the .rac:i.i,3z§i£1Iie..fr£?:1‘£1;ft1s*3 -¢jr,=.=e£i.§a$.€1‘. Imams ’£’?~€‘é!‘€% "first »t'3'bv
`served. with the ativent‘ ef “Egiani ' I
`tzciheiéi, rainy’ lasers by Maker
`et ai. -(1963). TI1ese"pIa£m§s £92?’
`gas‘ brezakziown at
`
`..
`the .fo-case of a lens and were
`J fine tii::ration =91‘ £he"I’a.S6r
`.
`puise. Plasmas were aim @¥:;~:serve=s:1m.-arm onethe .st:.rfas:ées 0f mat-eriéils ix»
`r2adiate—d by ’h=ig1a+;1:0wer pulseszi or »:<::e:ntinu;:ms Iaeers anti '.t}.<";§ 13zf>iE3j§fig?3.t6iI1t:O
`-the inc.iden't "beam at .s’:.zh-se:ii:::
`1s3;;fper“
`_1;:veIz;‘x<;_£i§ies.
`flze. advent of
`
`:c.m;t:inuejns, high-pémver £2-arban
`‘£11,’:
`eeame.§ess;i'b§e tic sustain
`a plasma in a s'te»ady—state é:en£iitie;n..:2..»,*1r tee feeies of .a.1as:er"bea:n_, 3.13% the
`first. experimental abservatieix -Of‘ a “e.Qnt1'n13o1:3’*Qpti£:=a1 :i.is::ha::#;ge” was re-
`_parted by Generaitw. ex; .a1.. (37%). This eentinucms, }asee-sustained vpiasma
`(L8?) is mften referred to as 2: eeniixzumzs apticai eiisehayge ((20113) and it.
`has a number of zmiqne pmperties» £1.13: make it an "lixrtsaresiing ca:nd.ida*te far
`a variety of appiications.
`,
`The laser-su.stained plasma shares many eharaeteristics with ‘ether gas
`discharges, as expiained in detail by Raizer (19813) in his I:-omprehensive. re»
`view, but it is sustained through .at3s0rpt’ioI1 of ‘power from an optica1’beam
`by the p.r(3.cess.0f inverse brems’strah1ung.— Since the eptical frequency of the
`sxxsmining beam is greater than the plasma‘-frequency, t}1’ebeamis 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»
`efrequency electrical fields (n1ic.rowave and electrodeless discharges) that
`operate at frequencies below the plasma frequency and sustain the plasxna
`thmugh absorption within 21 thin "layer near theplasma surface. This funda-
`mentzxl difference in the power ab.sor_pti0n mechanism makes it possible to
`
`
`
`"i 89
`
`

`
`170
`
`V
`
`Keefer
`
`gcnc’;cz£e smgagclysstatcogllasznas, _h_a_vin:g .maxi2fnu*m temperatures of 1{¥,{}O0Ii or
`xnoroifx a small coining rgoar inc»-foexzs of a lens», far away from any co‘I1ifi>i3i.11g_
`str'nc£.m*c. A photo of.a.p'las1na. sustained. by ;a laser beam focused xvith a Ions
`is shown fin Fig.
`,- T»,
`{K} W Gaussian beam from :21. carbon dioxicic
`laser won in '
`bi’
`focal lmgth lens into 2 :atm nfi flowing an
`V "
`
`gen.
`4.. ( .).;s§io*;vs schen§,.aiicall.y how the: plasma forms within :l1c:fjo£;al'
`region,
`
`.
`
`e been ‘produced in a variety of
`' ‘boa t:ii,o,>':idc> lasers .op€-;rai;ing at
`
`'
`
`’
`
`
`
`{:3.‘§%3}, Wells "e1;a'1.. A{198'3).,,and..=CZrons»iand’
`-t the
`:::an be opeziateéd sn’f<:’£:'aS.S«
`dz“
`operaxei ca flowing
`J
`
`envisonmcnt have been ’caI,ied ‘5plasm:.énr-ons” in the Soviet literature, anfi
`the lasar--.snst.a’ined ;)§:. is often rcfermd to as an ‘*opti.cnl plasmatrong’-”
`
`
`
`
`
`’
`
`tho./sn.si:aini:ng boom, and
`of”t““e pin" ‘ma.
`cwida» range of ézondi-tion3»1;s~
`i.§:i§i§?£;.i‘€3
`..
`lions of 135%: gjowcr, flow, and optica1:configur;a~
`
`
`
`
`
`{*3
`
`
`
`
`’ pi.-
`potao:t.:aI -3'
`hogan and inn» power can. be. beamcci rem.o_tely, it has.
`Gp£':‘;.r[at’,: in par
`been p::opnscti .t}‘1.a1: the
`=co1;z‘ld be us-ed for high specificaimpnlsn. Space’
`propxilsioni. A nunib-or of papers: '22aw: -d.e‘a1"tw.ith this 8p‘p1i£:~ati0n_,. and it was
`the subjoct of 8. reviexv by Glufrib anilklrier (1984). Thompsor; et a1. (19%)
`described oxporimcnis in Whikh "laser energy was converted into. el.eotri»$a}'
`‘energy using a -laser~.susitained argonxp}as3:£1a. Crcmers at :11. (’l9_8_5) have
`suggested tho
`as a source for sp-octrocllexnical analysis and given .s1omo
`experimental rcsulas. Cross and Cremexfs (1986) have s11stai11od plasmas in
`the throat of a small n»o.zz'le to produce atomic oxygen having a directed
`‘velocity of’sovcm1—.k.1n/sec for the laboratory study of surface interactions at
`energies and particle fluxes similar‘ to those experienced by satellites in’ low
`garth orbit. Other applications are sugges-ted by analogy to other plasma
`devices including light sources, plasma‘ chemistry, and materials processing.
`The physical procossns that detcrminc the uniq_ue characteristics of the
`LSP will be. discussed in Sec. 4.2, and the the.ore'tical analyses that have been
`used to describe the»LSP will be addressed in Sec. 4.3. Exper.imental results
`obtained will be presentod in Sec. 4.4 and compared with the t’heoretical
`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 FRIPICIPLES Q33" -{)1’ER!s.Ti{3N
`
`Plasmas that are c.:'e.ai=e~d 01* sustained by iasers can be g=enerated_i_n a variety
`uf forms, depending?-@n’tI1b 1:113:-aic:£»f;;;§s’£i::s cf the laser and optical ge£3me~
`
`try used ta genzrata the;
`' zg21«’§:n€jifg§I”pn§3é»d. iassrs can igxmcrata plasma
`breakdawn .dira£:tiy wi_t}é'i_1: 21 gas {1}.at,r&snIi$ ii} ;a transient axpanding gsiasma‘
`similar to .2111 expiasienq
`Imzgai ’§a§.fi.r intensities £11331} Iongsr puke iimes,
`.p}33mg5 may *:bg"gn»§{;‘a;g.aba»; .g.gj-W '_ .su1"fa§:»a3: nid than ;3r§paga:fi’.ifita the 5113»
`
`
`a:'aini_x:1g baaxzn at».super3ox:§’é Va}
`itiss as:
`~ r—s::s1£;iI;e£3 dets:3n.a3;i@;1 (LSD)
`wave or :snbsen,ic valocitias as”'ia},a§$é
`, aiizesd ébmbnstifin {LSO} xvave.
`
`These tramient piasmas have ‘beef: £3i${n}.s33d by Eaizer {I-980) and wi 11 net
`
`be treateéi here,» If :*;h_Ie: iiagsefiis’
`K 9312-.
`’
`’
`,
`-é_'r.a:£1,:1v.:i tfzté; £3}'f§?E§:i53}
`.}ge02i:t%try, flaw, a:14;i.’y‘mas:1rf¢:az:sa
`..ra§2,..»
`3» geaiiiyvéiazs I.;S.-P
`
`
`
`fie c<3n’tii:mt1usi3* 'm3intaix2.;eri.at’ ajwéaz‘
`11:33‘: ’thaj_ was of the ’bea.1n. The
`inifensity that is aXfE£i1a}3§§}iff{}fi1 a"¢t3x1t§tzuous;Iass’r -is insufficiem to cause
`braakdtnwn in tha gas, h1€¥‘£V€:%If::I‘, and an .auxiIim'_y‘ 3£m:rce musi be used. to ini-
`tiate thepiasma. A sketch {if 2*: sieady-s'£at‘r;.1a.se.r~=sus’tai'ne.d plasma is shown
`in Fig. 4.’i£(§). T116._p1as'ma:m.ay'ba»stz.s:ai::ied
`Ia azmfining c11’a;’:11b§rt%3
`ccmtérsl the ‘flow and. prrcssixre 01‘ in -apex}. air wt ~21 large, chamber where the
`t_1ow‘i_.S idem-rm-i.ned by th:=::rm.ai:I. buzayancyz.
`V
`,
`in 131311)}? ways, t11::1asar~s’u:siain;eti. gléisrna is si’zzxi_}.ar ta direct current or
`iawfzaqtzancy -eie<:;r:}s:I¢3;3*3
`anii £I1.i£i£i:3xv;im;g.di1§£11a:°gxi:s’t§§.at are {apex-
`ated in similar .gj;ase.s an
`at ;::ma;:e:s. Ifiitfiwever, this LS1’ will g€=n6.r‘~
`,
`any has .m£m~: ’c:{iiftj‘1_§3=’€¢:x%:f: 311.9%
`a°??,€‘e;fi§‘§§gh6Y:max§.15i1‘!;1m.téifipfiratfire th.a:1.n-t}mr
`»§:.£3ntin1.20u.s am s:{:§m*.caf; aixdi
`biz: :$u:~§'¥a:i11’€::é§ in 3 staady state well away from.
`containing boundaries. A .f3.z:n.d'an1ei£ii:a$ v:1iiffir’enCe:in'tha way in which en-
`-ergy is ahsorbeé by the plasma is 2‘:3$§:s9:3$i§3I.€:* £03: £12636-. 1}i?£3i.£}I}6» charactaristics
`-of the LSP.
`-
`
`4.2.1 Easic Physicai Frncesses
`
`In a £Ii1"B£‘:t current (dc) arc or in an in::¥uAct:§’ve}y cgauphzd p1asma‘(.ZCI’), en-
`ergy is 'ab.ss:>rbed thr0ug11 ohmic .heating produced by. the 10w~fr::quency or’
`direct currents flowing in the plasma. The eiecirical conductivity of an ideal
`plasma is. given by (Shka’mfsky at al., 1966)
`
`J
`
`neg
`== ---
`
`1/~—~iw
`
`in (z22+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 'fie1d,Au the effective collisicm
`frequency for electrons, andi thesquarc root of »»1. In the do arc (w 2 0),
`the currents are’ transmitted through the plasma bcztween electrodes and
`
`

`
`Lasebfiustalned Plasmas
`
`'
`
`-.
`
`A 173
`
`the size of the plasma is determined by the ‘size and spacing of the electrode
`and the c-anfi.ning bcmndaries.
`In the ICP, the curlrants are ir1ducsdli’ni»a
`the plasma fmm alternating»cu:1*entsfi<:swirxgin.a Sur1‘£3:undi.ng .so1enoifial
`c;c;~ii.. The are is sag;
`ixmgl xyibthin a container that determines the plasma
`dian1etei', 'wheI£:as fine Ian
`of the "plasma
`determined by tl:16length Qf
`H
`the sbiemid.
`'IT,1€:‘-.3333? apergtes at. frequencies will belflw the Vplasma frequemzy
`
`9
`
`-~--'-—--
`
`_»
`
`1.1}?
`
`=2
`
`W»
`
`4
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`.
`
`7
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`
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`b
`< >
`~4.,2’
`
`w31e1'e..¢g i.s%’ti;t: yiérmittiviity af fi?ae»spaae:.. In this frequemzy range, the 636:6’-
`3:rQmag‘ne1ie.’fiélL:i flags illffii prajpagaie as :a wan: within the pilzwma, ml: is
`.a:;u%3n;i:ate§i. aj.s{"ar.1’: ¢va.ne$i:;enti'wave (Holt and Hask-all, 1965) aver dis-taznces
`cit‘ the arckr -af-ihta ;skfi;2’:'.1 iiepth ’
`’
`»
`
`
`
`(4-3}
`
`is 1l_:h_e spa-ail: of Iiivght.» ’}fhu.s, thaplasma is su.s~tai.ne::il by azwgrgy-333*
`-where:
`serbed within a..small.}a;,:.é:r near its autar surface. that praduccs‘ a r‘at.hm‘:flalt
`temperature ’p=’rj{:5fi§3;fi
`.thep'lasm.a and limits the maximum tzmgaera.
`
`txxrsgas that ¢ai:Be¢btaines3.,
`V
`-
`The fr{§q";,1§§n(;y gf {E15, gptixzal fields .-(28 T}~Iz for the 1&6 gm car'b*c>n.. diam»
`ide lager) us:c£1.far‘iht:
`is greater than the plasma frequency, and the1's~
`fora’ fl1e»i'nGi’d’en't’ laser. imam nan -propagate well into the irnterim‘ before
`it is siibgnifissaniiy »ali:>’$-Qtbed 't}11~”£}’3:Igfh the _pr0c:ess Of .invarse ‘nremsstrah1u13,g
`(Shkatofsky at 211., 1966)‘ Sim:-e the f0cusi'ng of the law: beam praducsd
`by a lens or ‘mi.t.mr is e»ss.e'ntially presemed as the» "beam propagates jinta the
`plasma, very largeafielzfi. strengths may beproduced within the plasma near
`the beam focus. 1?; is fl38S:B large field strengths that lead tq p-eak tcinperay
`tures in the LSP that are genarally greater than those obtained with either‘
`dc arcs or tl.1eICP and make it possible to sustain a small Volume of plasmla
`[near the focus, Wei"! away from any confining walls.
`Inverse bramsst.2'ahlung~ is a process in which the plasma electrons ab~
`sorts photons from the laser beam during inelastic collisions with ions, new
`trals, and othsr elasztrons. The collisions betwew electrons and ions are
`"the _dominant process for the LSP and the absorption coefficient is given by
`(Shkamfsky et al., 1966)
`
`‘Y
`
`W 1rc'3n.S0G 1~—e'”“’”‘T
`(La) ”“;&:r
`(
`Fzw/kT
`
`>
`
`V
`(MI)
`
`

`
`am
`
`’
`
`,§<.e»efer
`
`where ii is Planckfs constam ciivided by 271', k B0i:am.a:§.:1’s c»£3n»3-£31113 81153;?
`"the. tem§m.r.aiure of§:hee1::c:rons. The facmr G is the Gaunt factor and the
`fiactor 3235 ‘isgiven by
`
`
`as M 16.n.+nZ2 9&3
`
`3
`
`‘
`
`1/2
`
`
`
`35:? _.
`
`I
`
`I
`
`(4.5)
`’
`
`
`
`
`
`£acmr¥.is. a.
`T when 2.’ is the ionic cha:rge and :24. the ion -dezxsixy. ‘Th:
`mecfiaazmjaii carractioxz to the -::.1as.si.c.ai theary,-_’ami a:z;iensi¥ve z:£*xhies
`
`
`11’-ewabeen given by Karzais and Latter (1961),. 13:3:
`'11;s1;x3.£. case xvi:
`(ha phstoin energy i:s’much1assthan aha
`"
`»
`.
`g.
`
`
`bmzzketmzi term in
`(4.4) is zmarily .in<3e-psi: ..
`m=efii:eiant;'is essennaiiy »pr:3gmrti:ma2 -in the, ségnam :3? i
`size ca’? am-.*::,$‘1'+* wmf ggepand an sevciai
`_:g;;e;ao.n1et:y;, 1aser*pcs’wer«, and ai}sQrp.ti»0‘n cnefifieiant.
`sf. the-..1aser 'b::ain as it propagatas witmn the
`
`.
`
`Jar:
`
`«~+--~~aI
`
`%
`
`
`
`- where s is ‘the: distance alnng the Eocai ¢i_im<;zic::1 e:’f5_;3:*:::;3 agatigm.
`abagrgzy
`.
`:i;§ce;-» it
`ma-..s .
`tizankngth ifs: ix 3; .+*;iam.ii1’ant».§ength aegis f>c:N.}'.*:s‘.*..
`‘inf: £§'ist;anc’:je.-0335:: whigch th£3’p~{3wé£.,iS absc1x*bav:i fwm {?he’bai:am., Far 'tfiI1is‘r:§c23;a
`
`:59-n,»t"fi.¢ dimension Qftha fiigimampasaiizre ;’aTbsaib§.2z;‘
`2:2:
`n
`piiaatxza
`alcmg the: laser beam wfli he of the cider’ tai t}1:¢;»a¥3sar§:ztz»c:n ia_.:1gi33_.
`’iti':~:.ihe absorption 1em‘g.1:h that determines ‘tli1e91z=i:ngt}1§c2f
`’ ‘e.»;3}a2si21a.zz1::31:;g fize V
`Exam iixigs, :1. is the @1336; beam éiameter ;tha‘t. daie’:x:ii.aea piasma >dian:;g.-
`’I*£1e’;s1:zs::aa expixnds :9 ii}! ma begin eozre. .wh:¢re it
`gaze. is «*.~1?3$*Grb
`pawar, "then rapidiy c}s::z;re=a:ses in ’ten:peratur»e. m:tsi.:§rs the imam ti1rtm1_gTh
`thermai canciuction. and radiativs kiss .machan.isms..
`The pnsition‘ 9f the
`‘relative to the foca} paint is £:1‘i'tic.ai in ::ietermin~
`ing its structure andfiie range of para.mcters far which it ‘(-1313 be .maiI'itaine€I.
`when the plasma is initiated near thg beam foam, it pmpagatea intro. tha
`sustaining beam and seeks a stable. _position. The pasition c:fst.ai3iiitywiI1 be
`1ocated‘where the imam intensity is just stxjffisiant t11at.tha‘absai*be»ci power
`will baiance thalosses due to convection, thermal c<)n:3ucti{m, and the;rm.a1
`radiation. A _number of factors combine to determine this pcssition of sta-
`bilityjncluding the transverse pmfi1eTof’the incident beam, t.hefoca1.leng-th
`and aberrations of the focusing lens or mirror, the plasma bpressura, 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 := al
`
`V
`
`(4.7)
`
`

`
`La.ser~$usia’inet:: Plasmas‘
`
`3?5
`
`where I is the I0z:.aIim1_dia1_v.:e: cf tbs: laser beam. Smce I depends an -the
`transv-ersi: profile 0ft}’1e'incitiBn‘t beam a’s.’-weii as iha focai Zength and abe’r~
`rationis of the lens, these -charazzterisiics wiii .:infiLuen<:-a £i1e’I.t:2ca’3:i0n within
`the focal rsagiion at
`:’:hewn1inim1:;£n.su3t3i.ni:t;g i’n.tan.sity is Icicatzzd. F01‘
`exfdmpie, far a small f{12umb,er'i"n;$,. the.'i:1£€nsit3¥ éecreasea rapidly with im
`
`cmasing dist.a3:ixce fmztzn..1hia»’fz3cus*.’an€i»the piasma will ,s’tabi.1i.ze.:’:1c:ar the focus.
`‘Fm -a larger Tfinumber system.,ih3i':»_i.:3£$¥1S3iy’iifififfiitfifis168$ rapidiy and the
`plasma win ;stabi1i2e .ai.2r::p<3s§’tia:z £332»
`.
`war ml. .. fie fo;=eu‘§. I::“<3a=e:¥., for
`
`
`
`
`gxgsfiicieniiy fic:’rxg:=”fo.<,:.a?.1.1:::?;;g1£h,$-; :a:x;ci is
`11’
`p=awer3 §z1;as;:nas..}::ave ‘been ob«
`s:
`served to ;::ropaga,:a
`.
`.. R fiiiafg. :1ii§3£}) as “’I.a:s¢r«s;;ppqzted com-
`bustion wavefi’ .a,£. .s:x3:3s<3x‘:i.£::; “aicz
`Tha zimaiiexzi ;~r;;>.a.t.i,,2::.1 5
`,
`’Ia5tf0ns bemaeen. firm up 1:223? §?%:&::m:2;i'
`the gas, am! the fl0w:£.hr*cm:" '
`’
`the -tcmpe::’jatu;.-“e and fims:
`s,t«aij’_
`from the las-er beam. with the -pa
`
`” smatis »§;,§’1tE*..;1;t§;t§n:t:§§1:i53s:_3.L".;é3?!’t{1,:tt3'i.n£€.rx§~
`-
`,3. z_t.'£g.$a"-,-,.£.‘
`€:p’1‘s?3is.sIé1i*:i:=r:;f
`-wiigiin
`piasma,
`
`
`
`
`
`
`.
`
`gzi
`
`.x..a<,'3
`imh .
`
`. me .
`Mast mi xhaeariy exp. ..
`chamimm £51": in §2pi~;n»air, ’sI¥31ef$»t: »
`by the effects mi therma} buoy
`iifefi, i::2%‘giI¢3z1:.5,i3fi33£K.azer anti
`the fpr—’€é$?;t1¥?e and mat po*’s%r»'.
`’
`~ "
`vatieaiy of gas-es (Eisn-
`,.
`pres.sc.re w11.er:a»it»was ’pnsEsib}e':<3. ,
`
`Thfise. ~3x;:%erimn.nts.
`.
`eraiav et »ai., 1'9?2:; ’K<3z1¢;;‘v 4% at,» 1495
`f¥31P”§3£>3fih};aserAp6sver anti
`indicated] that iherf: were ’np;‘;:>’er anti ’i£:tx=¥£'-—E1‘
`.
`.
`pressure at which the LS? szmzsici be an:-ai:aineéi;.
`Generalov et 31.. (1972) suggested that the upyer iimit. fax: p-mare’: was a re-
`suit of forming’ the LS? .v¢:ith a horizontal beam. In this bgeemetry, thermal
`buoyancy ‘induces a flaw transxzers-e to the =0.;f:¥;::it;ai axis. Tim intiuced fimv
`<:.an*ies. the plasma up and mat of the beam-w31ve3::.h.igimr‘ Easier mpmver causas
`the plasma ta stabiiize‘ farther from the focus. They ware u‘nab1ayt0 estab-
`Iishan ’upp-en." pews: limit when the exper.iment was caperated with the: beam '
`pmpagating vverti.ca11y upward. Koziflv 62.31. (1974) deys¥c3 pe.d a radiative
`model fer the LS? and explained the upper power limit on the basis that
`the plasma must stabilize class: emimgfh to-the’f0ca1‘p0int_ that the geonueb
`V ric increase of laser bean -intensity geing. inta the ‘plasma was greater than
`the loss of intensity due to absorpfion. They speculated that the faihxre of
`Generaiov at al. (1972) to observe this limit in a vertical beam was riue 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 Apxfsssure and lasar power that will support
`
`
`
`’
`
`

`
`‘W6
`
`Keefer
`
`Fflastxnas gust-a.i.ned in the frat: jet issuing from 21 1102213 have
`a szabie
`been studied by Gerasinzenko at 31. (198.3) who I’t1E<’:1'.5UI'€d
`the discharge
`atzciqtanbgtzs for the existenzzn nf a szea€ijg~st=ate
`ants’ havn been zzoncixicted in czmfined -tubes
`mi'nat+a:s;‘t,.
`fibw? (’Wei}.e 6: 211.,
`1!; W35 I
`,:fo’unri ¥:h.a£:=i:n additinn. in bpnwer and prassnrn, both the flow and nptibcai ge-
`’ "
`"
`b
`'
`I””:diI’1fl3'.1€n'(:-3 on the <:haract1:ris£icsV of £113
`
`- «*3 inc intnnsi .3: is jns? s“z;:’fii’:cié
`nmns»s..at1nna?fyeéxtnpoxntmglie
`_
`-
`.
`»
`_.
`.
`
`
`asma béc
`at inc ‘five? a$sc:§rb:;9:=c1"no::§ -‘t.
`’5_b_eam, gzvcn byfi
`4.?),"is balanced-’
`A
`in
`the: wnvectzsvn, cnncfuc-give,» .and radiation ’Ica:ss-es.
`.Smc»e:, in gemerai, "the
`t"
`_
`the 13:33:12,. the plasma. will a.cijust..§n 3529., 3; I
`'Qn3t.3£x'ra'£i:9n eif
`and. =z:-nér”
`
`
`
`»
`
`._
`
`._
`
`Ia ;a3.i£>I1. in thc ’g§IaS‘r’n%a. n¢¢.nr$ bath.
`-
`ans, resniting in ling ’radiat,inn and absnr
`:13}. nfizn
`2; r.
`
`tinn, :>aI§fi:f»I.>:&&.t."fi:D’-tlnfi and: fffifififffifi transnzians that I‘-éfiifli in mnizin-uuzn ‘ta.
`”
`a:jbsn3fptinn.. Qve.
`{iIza.:2pt’_i<:aIéi_y thinpnrtion at‘ the s_p>3=ct1‘.nm-,thi
`
`nu xvii?
`has sizrnngiy ;1b_$i:fbeii by the piasnia er sn:‘rm;2ns;iing :::3t3’ie;r
`mgicms anti wii} simpiy esc;ap»c frnm the plasma. Other {Martians cf the spec~
`mam will bn stricngiy absarbed, 1‘es'uking in a trzmspnrt of energy within that:
`plasma. In the Gginiisaiiy thick1'i1n’iI:,_ this resu1‘ts;in a diffusive energy transf
`p-or: that is simiiar tn thermal cnnnuczion, but may be significantly larger.
`Dataiied ca1Acui.ati0:ns. of the LS? (Ieng and Keefer, 1986) indicate that this
`radiative tr.ansp01*: is a szionxinant factor in the determination cf the struc-
`ture and p0si.t.io.n of the LSP. In particular, it is the radiative transport that
`’ determinns the tnemperature gradient in the upstream .fmnt of thcplasma,
`thereby determining the positinn in the beam for which convection Iesses
`are balanced by -absorption.
`A
`The positinn of stability far the LSP also dapends on the plasma px'es~
`sure, The absorption coefiicientis a strong function of plasma density, as ‘
`seen from Eq. (4.4).. If the prnssure is i'nc:re:ased and the abs01'pti(3n <:Qeffi«
`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 3??
`
`5211114‘: 'tin1e,, ihc'pia:m1a:1ength aiong the .beam »c1ccr-eases beziaus-e {if the de:~
`:;1f£:as’e in absargatinzx }s:}gti1., 13111 the d.imnet=e.r i.n<:re:ases ta fit} the _Im"»gar :¢:.m;s’s
`$e<;ti<}.n sf zhva beam, Thus, far the s.ama1ase.r b-3-am ma-é.itica::, a .’higher-
`
`px‘essur»e:
`wii} stziiiiiiiize
`a, Quint farther away fmm the ma: gixaint arzci
`have 3 :’s'm'a}1a:r.»}angth~'1o~d1ame1e’r ratio ’th.a.rz 3 I-mvm*aprassu.rc
`.
`Incidazzi iasezf p{)we3:, as wail as tihc f/munher and ab:srra¥i£3n.s cf the fa
`£:_.:uSi1}g 9133363,,» will also _i’;_*:.fiu.enc»e the §:%£38i.£§£3’r2. at xvzhich the
`$t:ab.i§ize;s
`3316 .2I::.sa‘n’3., Fmm {me 'f0mg::}i’3:1g <3ii5<:us.si£3i}., it is cigar {hat as the?)-e.a.:r1
`puxvar .is1nc:’f<’:.,a.:;’e£1, the piasma will mauve up t11ehean1 away ifrbm the fixzai
`gtsrslizztg. T1215 distsance 1.hatit'mi3ves.'is nistsrmineé by ‘the .f!n.um'b=e£ (ratiiz mi
`., fig
`._
`.
`‘
`,
`
`
`'
`
`83%
`atzit cizifiasma 'p=0-aition (Kmfmf et :aL, 1986.}. In partgicluiéir, Wfh:!Ei1‘i
`2:11:33": E3e=a'm fmm a22.n.nst;.ai2ie1a¢ser <3:3i:.§}}at£)f:fi}£ii1$=€§ii 133:3 sghericai Ivans,
`it. réithices an am’nn’iar’pmfQc,us region. befbre reachirzg»’€h€
`
`, fif:¢£:ilp{§int',
`
`_ the
`» s::'1*3s;é:rvat:iA£).:1.s :E§is€:11.$se:.1 abave, it is £‘3.£i31“ that’ £heb:;:$£>sii.i£:i1x sf
`1 m; .131.
`{ha piasma relaiive in -the focai paint has a: pmftmnd effzézéi 133:: ‘:i§1£3’}§1§1;8II1a
`eristics:. Atthe zzpjpar iimits gf ».at3§:«.i¥i2y gfitsr bath }.ass;':r-*pa:;wer'ian~:1»
`.;;;%1..::xra::i:
`a}f§§’=i%€£r's ;hat the pi.eizsma hecizmes ?L1xrist;a"b'}.e ssxhan ii: graves, 1:c:»:::
`
`
`pm
`far‘ffeTm fi.1é: £063}. peirzt. This may 1236 due, to £116 afai-:1, as prQpQs6di.3yf’Kt§25i£3v
`at Vail. s(3§9?££}, ihmas ‘iihepiasma .mavas sufiicifently ’f.ar’awa5r
`113.,
`iha V1”..-iiite (sf in.c’mase of the beam .ime:1siiy in ihza fiiiraciiiqh. af‘ egzyopagiaticign
`’ aims smazisr. S’irzc.e tam tampareitura s::%:£ '=t}1:€f
`;2§.a;s.m,a .m3.3,st 5 ”
`a1a§,a;i,a {he
`
`
`i1eam>prppiag,ate-s into the npst:’eam edge Qfitixietpj-’Iasmai_ .:ifiien§i§§?‘i0f~£_I1e
`baaxn ’.n:'msi: 3515:: increase. At same paint, ii1e;dms’ra.as’e. -of f}1t’3 hli‘sE3.II1 in;wns.iiy
`due-ti: »a.i}si3rpti0n is greater than the incrieeases due: in f0c%::.s§:1g, SC! the piasnza
`Eséeomeéa unstable and extingui-s'hcs. Recent <:.a1cn}atit3ns by Sféng. gm :1, Keefm:
`(198’?a’},i1mv§:ve:r, iniiicatez that there may ex.ist1.oca! 're:gi»:s.;1s. =withi2: t}:1e’LS-EP
`»vhera.t}1e’b-mm .in1;ens:ity c}m;rAe.as-es ‘as it penetraisas the plasma.
`. Accmsidarabie degree of ecmtrol of the structurs am: position Bf ihe:’LS?
`can be gained through both optical geometry and flow, in Vaddiiian tc) Iasar
`p-zxwcr zmrzi. ’prcssure. Utilization of these aciditicmal parameters nmake-.5 it
`possible: to successfuliy op»c:ra'£e the LSP ever a wider range Of exptzriniemtal
`ccnesiiiiims, enabling 21 wider range of potantial appiications.
`
`13.2.2
`
`?1asn1a Characteristics
`
`Laser~sustaim=:d 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-
`
`

`
`‘W8
`
`'
`
`-Keefer
`
`sures, but the peak tenaporaturcs in the LS? am usually somewhat higher
`than "those for the comparable am. Ratiianon from the plasxna can be 3 Sig-»~
`nificant fractio’n of the total power ,inpI12, a:n.~:.i .r21r3.iaiion '.tI’anspor‘!: plays a-
`major role in n‘etenn;inin_ ’*’§;l1e structure of the plasma. Continuum -absorp—
`tion processes are ofpaitifizfilar,1’3n“:po1*tanco in these plasmas since thopower
`to sustain the plasma is aiasorbnil -throngh, those. mo-chanisms,
`The» .con.tin1mm ansornzion pxnaess=inyn1ves both bo'on.d~fsrne trans.itio_n.s
`(p}1»oto’ioni;zation) and fi'.oo~.f£‘on transitions (invnrao l:n‘nmsst.fahlnng) in
`’which photonjs are absorbnd. from tl1o»l.a.sorlf3eam. This .free—-iron; transitions
`involve nlectron colfisions with Zions, ’otl3er éeloctrons, and Inoutral particles"
`(ShIl;aIi3f$l£y $1 .31.,
`3;’S*i5?6};;; £3r.i:e:2n, ’19fi.4}..
`:éiomi'nan:t absorption process
`
`for than is fi3."1fDiIi_g}i ;:n'lllfa_ion.§ ihoiwnen
`.
`..
`.113 3-nciions, and the a_b3o:p~
`-don cooificient for ibis procosa: is» given by
`For the usual Case in
`the 'LSP.‘, kw «ea: 3:? and {lie absnrpiion in app1‘oximatoly'nrngsortional to the
`sq’na’r=:: of tin: la$.er- xvavolnngtjlgl
`to
`Strong.-xvavelnngill cinpencienco,
`all of .t.h6. rwnrteé. e7i_Pe:i.n:nn'tn1 :%iz:s'nil.£:s.for’1n.e LS,P”hav'e» been obtained us«
`ing tho 1-9.6 gm w.avol::ngth carbon ciiflxiado laser; Sim: the length scale
`for the plasnza is of the order of the absorption .lenj'gtIh;, tho length of -the
`bplasma and .1113 power mqnlrod to ’s*us'to1“:n it iwonld be nxpezztccl éo increase
`dr.a:nun.icany fnr'shnrtfer an-’veln:ngth_ lasers £;‘ur:rentIy, -thé. only other lasers:
`flizit are ’fil<;t=:ly eanciidatns to sustain nnzmn-anus gzlzxsnxasv-aria» the hyfirognn
`or :ien.‘£eri‘um.fiuo.rid.e ah::zrxical¥ase1ts,ti1’at opnrato at waval.eng:Lhs of 3’ -to
`4 ;.&m..
`l
`'
`'
`.
`Tlznrnzal radiationyis iniilie of this :n2ns..tI.i:n§or’tan’1 c'ha;~;acterisiics of the
`LSF. Thermal -md_.i.a1:io1n l'o3t.ffo1i1.‘£li¢’;3Ia§§'ii13 can ai:co‘nnt for nearly all
`the ;;=ow::1' absoribed by tine ';'3la,s.;na whnn tlzo flow through the plasma is
`small anti. will account for :a s.ign.ifioant f:aoiio'n of absorbed pews: even
`when the convective. losses are large. The thermal :rad.iation. consists of
`continumn radiation resulting from _rec0x1il3ination (free-bound transitions)
`and bramsstrahln’ng (iron-fr-an tr-anlsitionfl) as wall as lino radiation (bo1..1nci-
`bound transitions). Calculaxinn of this racfiatiozi is straightforwar-d, al~
`though rather tctiioos, when the plasma is in local thermodynamic equi~
`librimm (LTE) (Grimm, 1964).
`‘Local tlzernloclynamic equilibriutm is as-~
`tablished when the electron collisional rate. procosses dominate the pro-
`cesses of radiative decay and recombinafion. When LTE is e~st.ab.lishod
`in the plasma, the density -in specific quantum states is the same as a sys~
`tom in complete thermal -equilibrium having the same total density, tam»
`perature, ancl chomicalv.c_omp~o3ition.
`It should be emphasized that this
`does not imply that the radiation is similar to a blackbody at the plasma
`temperature. In general, the spectrum of the radiation from the plasma
`will have a complex structura 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, as
`
`1:}:Ii3;:;=d
`is} i3'*::£.’si'i1 {he cxp*e'rime:ntai tempe3:aiures~.shz3wiz_
`in Figs. 43-2, 4.4, and 4:;Z(}..is =:icss,rii:s~:.<;i
`Ci-etaii in »Sec.. 4.4.2). Ti1:is.’§igu.se
`shciws "an. is:ciiis:m:»pic:t cf ziie» ts:i:::§:«s:rst::sms ’fi3¢£1$i3’i‘cd is .an.LS?sz:sa:a jéti
`in 2,5 aim bi =’ gun. ‘by .3 mtiscn ’c1iv;3x-ids Iasier »c§;er*a£’ing at a wiaveieizgfix
`i’i3..i6 gm. ’.1?i1e’,;5iass:ia ‘iezigifh. ass diameter, as cistcrminsti by tag ::s;.5ssK
`"is-otiiasrm, are 311 aiiii émtn, rfispcctivcly. biota the stung i:~em’peratxsre:: gm<ii-
`ants that cxisii