EFFECT OF PLASMA-WALL RECOMBINATION AND TURBULENT RESISTIVITY ON THE CONDUCTIVITY IN HALL THRUSTERS

Transcription

1 EFFEC OF PLASMA-WALL RECOMBINAION AND URBULEN RESISIVIY ON E CONDUCIVIY IN ALL RUSERS A.A. Ivaov, A.A. Ivaov Jr ad M. Bacal Laborator d Physqu t cholog ds Plasmas, Ecol Polytchqu, UMR 7648 du CNRS, 98 Palasau, Frac Prmat adrss : RRC Kurchatov Isttut, Kurchatov Squar, 38 Moscow, Russa Abstract hs papr dals wth th oprato of all plasma thrustrs ad th trasvrsal to th magtc fld currt such systms. h problms of th trasvrs coductvty ad rlatd procsss ar tratd th framwork of th wll-kow Morozov s modl, th dffrc s th addto of th mchasm of plasma rcombato o th walls of th thrustr ad furthr volum ozato of th utrals cratd at th walls. h dstrbuto fuctos of th utrals ad scodary lctros gratd by ozato ar foud, as wll as th xprsso for th trasvrs currt. h obtad rsult cotas a addtoal corrctg factor compard to th covtoal Morozov s quato for ths currt ad prmts a bttr quattatv agrmt of th thortcal xprsso ad xprmtal rsults. W also stmat th mportac of th grato of th trasvrs currt du to turbult rsstac arsg bcaus of th strog all currt th thrustr. Our stmats show that ths phomo ca play a mportat rol. I. Itroducto h ar-wall coductvty was proposd by Morozov 968 [] to xpla th coductvty of collsolss plasma across th magtc fld all thrustrs. I th sam work Morozov has otd that th coductvty could b xplad by th prsc of os plasma, howvr h ddcatd th ma attto to th ar-wall coductvty (.w.c.) arsg from lctro-wall collsos. h problm s mor gral, sc t ca rfr to all th plasma systms wth sulatg walls trasvrs to th magtc fld ad wth appld lctrc fld paralll to th wall. As a rul both th plasma dsty ad th utral dsty ths systms ar low ough for th lctro ma fr path to b much largr tha th tr-wall dstac. hus ths plasmas ca b cosdrd as collsolss. Assumg lctro-wall collsos, Morozov has dvlopd a w approach for calculatg th ar-wall lctro currt []. hs mthod cossts makg us of tgrals of moto for lctros collsolss approxmato. hus havg foud th spac-tm voluto law of th lctro vlocty dstrbuto fucto, th boudary codtos for ths fucto wr usd, amly th lctro vlocty dstrbuto fucto at th wall was chos as maxwlla, wth a crta tmpratur. Morozov [] assumd that th tmpratur of th mttd lctros s dffrt from that of th plasma lctros. Comparso wth xprmt brought about th d of choosg dffrt shaps of th tal lctro vlocty dstrbuto fucto [], ad of cosdrg th scodary lctro msso from th sulatg wall [3]. W propos to cosdr two addtoal mchasms th framwork of th orgal modl. Dspt of th xprmtal vrfcato of th.w.c. modl [4], accordg to Morozov th problm of ar-wall coductvty ad rlatd procsss rmas th ma task to hac th thrustr ffccy ad sur logr lftm ad low lvl of os [5]. h frst addtoal mchasm w ar gog to cosdr th prst work s rcombatoozato th ar-wall plasma rgo ad ts fluc o th lctro currt all thrustrs. hs procsss wr usd, partcular, to stmat th o currt systms wth a vry strog magtc fld, so that both th os ad lctros wr magtzd [6,7]. h scod mchasm of grato of th trasvrs to th magtc fld currt s th turbult rsstvty [8,9] that w wll dscuss Sc. IV. Lt us frst study th utralzato procsss. W wll us th approach dvlopd by Morozov [], addg th lctro-o wall rcombato ad volum ozato of utrals mttd from th wall. A mportat qusto s th ucrtaty cocrg th rgy of th utral atoms lavg th wall. Lt us dscuss mor dtal th o-wall tracto. Svral procsss ar possbl, dpdg o th rgy ad mass of th cdt os, as wll as wall matral ad surfac stat. So w d to kow th

2 prdomat procsss for th tracto of X + os ad boro trd walls for th rgs of th cdt partcls th rag 3-5 V. hr ar umrous paprs dvotd to th tractos of th obl gas os wth mtal surfacs. h gral cocluso s that th os ar compltly utralzd, oly about.% of os ar rflctd o-utralzd []. As for th lctro jcto du to o bombardmt, t s also vry low aroud.5 lctros pr o []. Actually, w ar dalg wth sulatg walls, so th prvous data ca oly b usd as a vry rough stmat. owvr, v for th sulatg surfacs th utralzato s clos to % []. Sputtrg ca also play a mportat rol plasma-wall tractos startg from th rgs of th ordr of ~ V. owvr, accordg to th xprmt ad umrcal smulatos [], th sputtrg for X + os for ths rgs s glgbl t rprsts about or 3% of th cdt o flux for th rgy 5 V. So, summarzg all th stmats ad obsrvatos mtod abov, o ca coclud that th ma procss ths rgy rag s th utralzato of th cdt xo os ad thr subsqut rflcto (probably aftr th adsorpto by th wall). Aothr mportat qusto s th tmpratur, or, mor prcsly, rgy dstrbuto of th atoms cratd durg utralzato of th cdt os. W dd ot fd th rqurd data for X atoms. owvr, w ca hav a da of a possbl rgy dstrbuto from som spculatos ad, possbly, from umrous paprs cocrg th tracto of hydrog atoms wth th walls [3,4]. Sc th X atoms ar havr tha B or N (mass rato s about.), th drct rflcto of th cdt os s rlatvly small, othr words w hav som tracto of th cdt os ad th wall matral,.. thrmalzato, th rgy of th httg projctls s maly trasfrrd to th atoms of th wall. As for th tracto of hydrog wth th C walls (th sam mass rato ~.), th rgy of th rflctd atoms s about. of thr cdt rgy [3,4]. I othr words, th rgy of th rflctd utrals s sstally lowr tha thr tal cdt rgy, th xcss s dpostd to th wall. Lt us assum that plasma movs alog th magtc fld ls to th wall ad rprsts a collsolss flud havg a ma vlocty qual approxmatly to th o acoustc vlocty. As a mattr of fact w ar dalg wth th xpaso of plasma to vacuum, sc th plasma dsappars at th wall du to stat rcombato. hs procss taks plac o th scal comparabl to Dby lgth, whch s much lss tha th ozato lgth, λ : λ = V () σv whr s th plasma dsty, σ V s th rat coffct for ozato, V s th thrmal vlocty of th utrals lavg th wall. Lt us stmat th ozato lgth for th typcal paramtrs of all thrustrs 3 usg Xo as workg gas: cm 7 3, σv cm s, for lctro tmpratur th rag from to 5 V. (a) If th utral tmpratur s low (clos to th wall tmpratur,. V) th ozato lgth 3 λ s a fw mm. For th sam plasma paramtrs th Coulomb collso lgth s largr by a factor. hus th ozato lgth s comparabl wth th chal wdth, lctro-o collsos bg glgbl. At last, lt us stmat th lctro-utral collso lgth. Assumg a uppr lmt for th utral dsty of 4 3 cm, w obta for th lctro-utral collso lgth svral ts of cm, ad oly for utral 5 3 dsty cm, w would obta ths lgth comparabl to th chal wdth. hs stmats show that th shortst lgth s th ozato lgth, ad t should b cosdrd furthr dscusso. Of cours th Dby lgth, whch s of th ordr of cm s much smallr tha th ozato lgth. Smlar stmats of th ozato lgth wr mad by Bugrova t al [5], but thy compar ths lgth to th logtudal sz of ozato ad acclrato layrs, whch ar shortr tha th chal lgth. hy rqur that th ozato lgth should b lowr tha th logtudal sz of th ozato ad acclrato layrs. Not that th chal lgth s to 3 tms largr tha th chal wdth. It mas that th cssary codto for th thrustr oprato, accordg to Bugrova t al [5], corrspods to th rqurmt that th ozato lgth s lss or comparabl to th chal wdth.

3 A op qusto s th ar-wall utral dsty. I stady stat th plasma flux to th wall ad th rtur flux of utrals from th wall should b qual. hs allows us to obta th uppr stmat for th arwall utral dsty : V = c, = () s r W s th wall tmpratur, s th lctro tmpratur, c s s th o acoustc vlocty, M s th o mass. hs stmat gvs th wll-kow rsult that th utral dsty s approxmatly o ordr of magtud largr tha th plasma dsty. (b) If th utral tmpratur s hgh (comparabl to th rgy of ozato) th ozato lgth accordg to Eq.() s crasd by approxmatly a factor of ad xcds th chal wdth. Actually, as soo as th ozato lgth xcds th chal wdth th plasma dsty wll go dow bcaus th ozato procss s hdrd. h fast utrals aftr multpl collsos wth th walls acqur th wall tmpratur, th ozato lgth wll go dow ad th cas of low utral atom tmpratur wll b attad. h purpos of ths papr s to calculat th lctro trasvrs currt gratd by th volum ozato of utrals producd du to plasma-wall rcombato procss ad to mak a stmat of th fluc of turbult rsstvty o ths currt. W II. Nutral atoms dstrbuto fucto. Lt us troduc a coordat systm tradtoally usd plasma thrustrs, amly axs x s drctd alog th magtc fld,.. across th chal, wth ts org at th xtral wall, th axs z s alog th appld lctrc fld,.. alog th chal (s Fg. ). Sc th scal of th procsss udr cosdrato s much smallr tha th radus of th thrustr, w hav chos th Cartsa coordat systm. W wll cosdr th problm of ozato of th utral flux from th wall by th volum plasma. h plasma lctros hav a rgy of - 3 tms th ozato pottal so thy ca oz th utrals. h scodary lctros formd by ozato hav a rgy of svral V [6]. h formato of th scodary lctros ad os s rlatd to th dsty of utral atoms at th pot whr ozato occurs. Sc thr ar o collsos th utrals mov from th wall alog a straght l, utl th momt of thr ozato. h quato dscrbg th voluto of th utral umbr s as follows: dn dt = N σv = ν N (3) whr ν s th ozato frqucy dpdg o th lctro dstrbuto fucto ad th ozato cross scto, N s th umbr of utrals. Sc th vlocty of th utrals rmas costat utl th ozato momt w obta for th stady stat cas o-dmsoal approxmato th followg: dn V N σv dx = (4) c th ozato lgth s gv by th quato: V V λ = ~ (5) σv V σ σ sc th vlocty of th utral partcls s much lss that th lctro thrmal vlocty V. Our stmats Sc. I show that th ozato occurs at rathr short dstacs (lss tha th chal wdth). O th othr B z E y x gas trac B plasma th chal Fg.. Schmatc dagram of th plasma thrustr, coordat systm. 3

4 had th utral ad plasma dsts ar suffctly small ordr to glct th fluc of collsos alog th utral partcl trajctors. Lt us cosdr ow th stady stat utral dstrbuto fucto corrspodg to th statoary utral flux from th wall. h th ktc quato for th dstrbuto fucto f t f + V = ν f (6) r o ca omt th tm drvatv ad fd th soluto, whch bcoms maxwlla at th wall : f V = ν f (7) r h soluto of ths grally spakg 3D quato ca b foud two ways. h frst o s basd o th hypothss that th ozato lgth s small compard to th charactrstc dmsos of th wall. c th dstrbuto fucto dpds oly o th coordat x prpdcular to th wall. h Eq. (7) bcoms o-dmsoal: ad ts soluto s: r N V f x = ν f x 3/ x M M f ~xp( ν ) xp( ( Vx + Vy + Vz) ) Vx π s th tmpratur of th utrals, whch s clos to th tmpratur of th wall. h scod approach cossts cosdrg th moto of th utrals alog th charactrstcs arbtrary drctos. h utral partcl dos ot loos thr momtum or rgy, ad th probablty of ts xstc o th gv trajctory dcrass xpotally wth tm. hrfor o ca cosdr a arbtrary pot P locatd at th dstac x from th surfac ad fd th dstrbuto fucto at ths pot (s Fg. ). h partcls arrv to ths pot alog straght ls,.g. from pots A ad B of th wall. h dstrbuto fucto alog ths ls dcrass xpotally, thrfor for a gv absolut valu of th utral vlocty obta: V w 3/ x M M ν V x + y + z cosθ V π ( ) f ( P) ~ xp( ) xp( V V V ) Idd th path of th partcl s cos xθ ad ts vlocty s V. O th othr had sc V cosθ = V, w com to th sam rsult as that of Eq. (9). x Now w kow th dstrbuto fucto of th utrals. I th followg scto, w wll fd th dstrbuto fucto of th lctros producd by ozato. wall os A V O x P x cos rcombato B (8) (9) utrals Fg.. Schmatc rprstato of calculato of utral dsty pot P. III. h dstrbuto fucto of lctros Vlasov quato for lctros has th stadard form: f f f + V E+ V = t r m c V () 4

5 It s kow that th dstrbuto fucto rmas costat o th charactrstcs, whch ar dfd by th quato of moto of lctros. Sc w hav costat appld lctrc ad magtc flds, th soluto of ths quato s th moto wth costat vlocty E c 5 alog th y axs ad cyclotro rotato aroud magtc forc l. As for th lctro moto alog th magtc fld, t s also occurrg wth costat vlocty alog th x axs. c Vz = V s( ωt+ α) E Vy = V cos( ωt+ α) + c () Vx = V Lt us stablsh th rlato btw th thr costats Eqs. () ad th dstrbuto fucto at th wall. At th momt t = (corrspodg to th ozato momt) th lctro has th vlocts V, V, E V z. O th othr had w obta from Eq. () that ths vlocts ar qual to V, V cosα c V sα rspctvly. I othr words, Vx = V = Vx Vy = V cos( t ) c E ( Vy c E )cos( t) Vz s( t) c E ω + α + = ω ω + () Vz = V s( ) ( E ωt+ α = Vy c )s( ωt) + Vzcos( ωt) x y +, I th systm of quatos () th vlocty compots dpdg o tm ar xprssd trms of th tal vlocty of th lctro producd by ozato. W assum for smplcty that th tal lctro dstrbuto fucto s maxwlla, wth a crta tmpratur. As for th rat of ~ ~ W lctro grato, t s proportoal to th rat of dcras of th utral dsty. Lt us calculat mor prcsly th rat of th lctro grato. I ordr to dtrm th cssary factors, lt us mak us of th fact that ths factors ar dfd by th product of th probablts that a utral wll arrv to th pot x ad th probablty of ozato of ths utral a trval dx. h frst probablty s x ad th scod o s xp( ν ) Vx dx dx ν σ V λ = V. It should b potd out that th factor x trg ozato rat s avragd ovr all th plasma lctros rsposbl for th ozato of th utrals. So t dos ot dpd o vlocts of wly bor lctros. hus, usg th dstrbuto fucto for th utrals (9), th rqurd lctro dstrbuto fucto has th followg form th vcty of th pot x : 3/ x M MV dx 3 xp( ν ) xp( ) ν V Vx π Vx df = d ( ) 3/ m mv xp( ) d π V (3) o obta th cotrbuto to th lctro currt dj z from th layr of thckss dx, locatd ar th pot x, w hav to multply df by ad V z gv by ().h tgrato ovr z ad y compots of utrals ad wly bor lctros s trval ad gvs us 3 / x x z ν ν π x x M dv MV x E dj = dx xp( ) c V V

6 ( ) x / mv dvx ( ωt) m s xp( ) π (4) Sc th lctro s movg alog th magtc fld wth a costat vlocty Eqs. () ca b rplacd by t x x =. Lt us ot that x x Vx V x, th tm th systm of s of th ordr of th Larmor lctro radus, othr words much smallr tha th ozato lgth, sc th tm t s masurd lctro tgral. hus w hav / E M dvx MVx x z ν ν π V x Vx dj = c dx xp( ) / m ( ) x x mv x s xp( ) dvx ω π Vx dj ovr x ad multply by π R o obta th total currt t s cssary to tgrat chal radus. (5) / L E M dvx MVx x z π ν ν π V x Vx z ω for, R s th ma I = R c dx xp( ) / ( ) L m mv x x x xp( ) s dvx dx ω π (6) V x ρ x λ L, othr words, th fact that th Usg th sam approxmatos as Morozov [],.., L currt flows oly th ar-wall ara, w obta 4 π E Iz R c m ω (7) IV. urbult rsstvty currt. Aothr mchasm that could grat som currt trasvrs to th magtc fld s ay sort of procss that crats a ffctv collso frqucy ν ff. Idd, th quato of moto for a lctro ths cas s h soluto of ths quato s = ( E+ [ v,]) ν ff mv. c [ Eh, ] c ν = ν + + ω h =. / ω ff ff νff ω c v E, (8) 6

7 So, dpdg o th ffctv collso frqucy ν ff w wll hav a crta small compot of th all currt th drcto paralll to th lctrc fld: v E ν c ff z, ν ff ω ω. owvr th frqucy of collsos of lctros wth varous partcls s vry small, othr words w ar dalg wth collsolss plasma. So ν s just som ffctv frqucy that appars, for xampl, ff bcaus of th turbult rsstac all plasmas. Lt us stmat th cotrbuto of ths rsstvty to th crato of th currt trasvrs to magtc fld. Lt us study som mor dtal th mchasm of ths stablty. h flow of lctros rotatg crossd magtc ad lctrc fld wth th vlocty u= ce/ ca grat a o acoustc stablty f th vlocty of th lctros s largr tha th o acoustc vlocty [8,9]. c s < u< hs stablty, tur, grats a group of hot os, whch causs th rducto of th growth rat ad th stablty stops. It lmts th vlocty of th lctro flow to a valu fror to ce / ad ths way w hav a ffctv turbult rsstac, ad hc th collso frqucy ν ff. h gral quato of th balac for th stablty s [8,9] = ω pw a d v kv kv v u ω ω W k d =, ν k ff W = ω p, M a = α, α = 5.36 m W /4, (9) r W s th rgy dsty of os plasma, ; th frst trm corrspods to th xctato of th wavs by th lctro flow wth th vlocty u, th scod o to Ladau dampg, th thrd o to th rducto of th stablty du to hot os ad th last trm rprsts o-lar Ladau dampg. From th quato (9) w ca s that two stablty mods ar possbl: quaslar mod f th last trm s glgabl (ad u αcs ) ad o-lar mod wh u αcs ad th olar trm plays a mportat rol. W ca stmat th ffctv collso frqucy ν ff from quaslar mod approxmato. h lctro rotato vlocty ths cas s lmtd by (cf. q. (8)) ad E u= αcs = c ν + ω ν ff ff ce = ω. u 7

8 o calculat th vlocty of th lctros u w d to us th complt balac quato (9). Ulk c u ad for th hydrog th last olar trm s mportat xo. So barg md that / s / ω kc, w rwrt th q. (9) as follows: stablty ~ s For th small valus of th rato / vlocty alog th magtc fld s ce u cs cs ω = α v v u ω u. () p ω ω w ca put th last trm u αcs p E ve = αcs c α c s So th trasvrs currt cotrbuto du to th turbult rsstac s / ad th avrag lctro () E It πrl αcs c α c s Lt us ow compar th two currts classc Morozov xprsso ad th turbult currt: / () I I t E πl αcs c α c E v c ω W ca stmat th maxmum valu of th squar root: / max / s (3) E c ν ω ω = 5.36 αc ω ω v ω M ω 3/4 ff max γ st u p m p s Ad aftr that th q. (3) ca b rwrtt as I I t max 3/4 m ω p πl αcs5.36 M ω m π 5.36 E v c M ω 3 For most of th all thrustr systms ~ cm, ~V, B~Gs, L~cm ad th rato (4) s about.. hs stmat s obtad th codtos of quaslar approxmato ad wak turbulc. For hghr valus of lctrc fld th obtad rato ca b sstally crasd. So, w ca s that th currts ar comparabl, so ths mchasm ca b also addd to xpla th dffrc btw th orgal Morozov s rsult ad xprmt. 3/4 ω v p L (4) 8

9 V. Dscusso. I Sc. I w hav mad th stmats of maxmum utral dsty th vcty of th wall (s Eq.()). Substtutg ths xprsso to Eq. (7) w arrv to th followg xprsso of th trasvrs currt: hs xprsso has a addtoal factor I z ce = π R m π ω N / N (5) compard to th rsult []. h coffct has appard bcaus th lctros aftr th ozato of utrals mov all th drctos, whl th orgal Morozov s modl thy ar mttd from th wall oly to a half-spac. Lt us stmat ths factor. Sc s th tmpratur of th lctros producd by ozato ad s of th ordr of plasma lctro tmpratur, ad th tmpratur of th utrals N s of th ordr of wall tmpratur W, as w dscussd Sc. I, ths factor s of th ordr of. Lt us compar th obtad rsults wth xprmt. If th.w.c. modl s vald th currts dffrt sz thrustrs should b proportoal to th ma radus of th chal for th sam plasma codtos. Ufortuatly systmatc masurmts ar uavalabl ad comparso of dffrt thrustrs at th sam plasma paramtrs caot b ffctd. hrfor w ca lmt ourslvs to comparg th thoroughly studd thrustrs, such as SP-5 [7] ad SP- [8]. For SP-5 w hav th dscharg 3 currt of A, D= 5mm, plasma dsty cm, th lctro tmpratur to V, th avrag lctrc fld V/cm, th magtc fld 3 Gauss [7]. Accordg to th.w.c. modl [4] th calculatd currt s a fw tths of Ampr,.. o ordr of magtud lss tha masurd. Smlar stmats for SP- show that th calculato also udrstmats th currt by a factor of t. Sc th rsults obtad ths papr gv a rqurd corrctv factor of t to th stadard.w.c. rsults, o ca cosdr that th ma faturs of th all thrustr wr corrctly dscrbd by th orgal mthod. akg to accout th plasma rcombato at th wall followd by volum ozato allows attag a bttr quattatv agrmt. A scod cocluso followg from ths work s th mportac of usg of a havy gas as th workg flud. Sc th ozato lgth s vrsly proportoal to th squar root of th o mass, for lght gass th ozato lgth ca xcd th chal wdth ( 5mm ). h ozato pottal of ths gass s also hghr tha havy gass, thus prohbtg th oprato of thrustrs wth xstg dsg ths gass. Aothr mportat mchasm of th currt grato s th turbult rsstac arsg bcaus of th stablty gratd by th all lctro flow th chal. W hav stmatd th mportac of ths phomo ad mad som calculatos th smpl cas of a wak turbulc. h rsults show that ths mchasm should b tak to accout whl cosdrg th phoma takg plac th chal of a all thrustr. It s a volum procss of th currt grato, ulk th othr wall rlatd mchasms mtod abov. Ackowldgmt. hs work was carrd out wth Groupmt d Rchrch CNRS/CNES/SNECMA/ONERA N 3. W gratfully ackowldg th lghtg dscussos wth E. Bhrsch ad E. Parls. 9

10 Rfrcs [] Morozov A I 968 Joural of Appld Mathmatcs ad chcal Physcs (Zh. Prkl. Mat. kh. Fz., russa) 3 p 9 [] Morozov A I ad Shub A P 99 Sov. J. Plasma Phys. 6 p 7 [3] Morozov A I 99 Sov. J. Plasma Phys. 7 p 393 [4] Bugrova A I, Morozov A I ad archvkov V K 985 Zhural hchsko Fzk 55 p 7 ( russa) [5] Morozov A I 995 4th Itratoal Elctrc Propulso Cofrc, Moscow, Russa, Sptmbr 9-3, Papr IEPC [6] Ivaov A A, Lma V G 978 Sov. J. Pl. Phys. 4 p 374 [7] Ivaov A A, mchko N N 99 Sov. J. Pl. Phys. 6 p 863 [8] Sagdv R.Z., Vksht G.A., Psma ZhEP., p. 97 (97) [9] Galv A.A., Sagdv R.Z., Foudatos of Plasma Physcs ( russ), Moscou, Ergoatomzdat, 984, p. 4-3 [] Rdhad P.A., obso J.P., Korls E.V., h physcal bass of ultrahgh vacuum, Chapma ad all Ltd,, Nw Fttr La, Lodo, 968. p [] Prvat commucatos wth E. Parls, dc.. [] Elovkov S.S., Zkova E.Yu., Mosuov A.S., Smov A.A., Shkarba I.I., Yurasova V.E., Izvstya Akadm Nauk,, 66, p ( russa). [3] Bhrsch R., Eckst W. Physcs of plasma-wall tractos cotrolld fuso, Ed. By Post D.E. ad Bhrsch R., NAO ASI Srs, Srs B: Physcs Vol. 3, Plum Prss, Nw York ad Lodo, 986, p [4] Eckst W., Brsak J.P., Appl. Phys., 985, A38, p [5] Bugrova A I, Km V, Maslkov N A ad Morozov A I 99 AIDAA/AIAA/DGLR/JSASS, d Itr. Elctrc Propulso Cofrc, Octobr 4-7, Varggo, Italy, Papr IEPC [6] Iokut M 97 Rvws of Modr Physcs, 43 p 97 [7] Gurr G, Mchaut C, Bacal M, Vsslovzorov A N ad Pogorlov A A 998 Rv. Sc. Istrum. 6 p 84 [8] Gasco N hss of th Uvrsty of Provc (Ax-Marsll I) «Etud d propulsurs plasmqus à fft all pour systèms spataux»