Remote Plasma Maintenance in Low-Pressure Discharges with an External Magnetic Field

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1 Journal of Modrn Physics, 01,, Publishd Onlin Octobr 01 ( Rmot Plasma Maintnanc in Low-Prssur Dischargs with an Extrnal Magntic Fild Stiliyan Lishv 1, Antonia Shivarova 1, Khristo Tarnv 1 Faculty of Physics, Sofia Univrsity, Sofia, Bulgaria Dpartmnt of Applid Physics, Tchnical Univrsity-Sofia, Sofia, Bulgaria ashiva@phys.uni-sofia.bg Rcivd August 18, 01; rvisd Sptmbr 16, 01; accptd Sptmbr 4, 01 ABSTRACT Th spatial structur of rmot plasma rgions in rf dischargs is analyzd basd on a D modl of fr-fall rgim discharg maintnanc. Sinc th study is dirctd towards dscription of th magntic filtr rgion in th tandm plasma sourcs of ngativ hydrogn ions, hydrogn dischargs ar considrd, with a wak magntic fild locatd outsid th rgion of th rf powr dposition. With th formation of diffrnt rgions in th discharg th rf powr dposition rgion, th rgion with lctron magntization, th transition btwn thm and th rgion bhind th filtr th rsults display suprimposd ffcts of nonlocal discharg maintnanc without and with a magntic fild. Slight dcras of th lctron tmpratur accompanid with strong drop of th lctron dnsity is th pur ffct of th plasma xpansion in rgions without xtrnal magntic fild. Strong drop of th lctron tmpratur accompanid with formation of a maximum of th lctron dnsity in th filtr rgion is th pur ffct of th plasma xpansion through a magntic fild. Basd on th rsults for th spatial distribution of th lctron dnsity and tmpratur obtaind with shifting th position of th magntic filtr, optimization of th sourc rgarding high yild of volum-producd ngativ ions is discussd. Kywords: Rmot Plasma Maintnanc; Tandm Plasma Sourcs; Magntic Filtr; Hydrogn Dischargs; Fr-Fall Rgim 1. Introduction Th construction of th rf sourcs for plasma procssing tchnology [1-] has brought to th for th nonlocality of th discharg bhavior and th mchanisms of th rmot plasma maintnanc. Concrning hydrogn dischargs, th rf sourc of ngativ hydrogn ion bams [4] dvlopd for th nutral-bam-inction plasma hating in th intrnational tokamak ITER is a particular cas of such typ of a discharg. Sinc th sourc is a twochambr on with rf powr dposition to th first chambr and plasma xpansion in th scond biggr siz chambr, ffcts of nonlocality, i.. th fluxs (chargdparticl and lctron-nrgy fluxs), govrn its opration [5]. Morovr, with its dsign of a tandm sourc with a magntic filtr locatd in th scond chambr, th plasma xpanding from th first chambr passs through a rgion with a magntic fild. In a way, th dscription of th sourc opration provids a possibility for studying combind ffcts of nonlocal discharg bhavior both without and with an xtrnal magntic fild, as it is don hr. Spatial sparation, by a magntic filtr for lctron cooling, of two rgions in th discharg with high- and low-nrgtic lctrons (rspctivly, with high and low lctron tmpratur) is in th basis of th ida for th tandm sourc [6] dvlopd, starting in th 80 s of th last cntury, initially for dc (filamnt) sourcs of ngativ hydrogn ions. Th ida stms from a conclusion that such a configuration of th sourc nsurs optimum conditions for th two-stp raction H Hν, H ν H H for volum production of th ngativ ions ( H ) via dissociativ attachmnt of lc- ν trons to highly vibrationally xcitd molculs H vibrational xcitation of th molculs in th rgion with a high lctron tmpratur and ngativ ion production in th rgion with a low lctron tmpratur. Th opration of th magntic filtr as an lctron coolr has bn usually strssd on as a rsult from th sourc modling [7-15], involving transport procsss acting in a combination with collisions. Emphasizing th rol of th transport procsss dscribd within th fluid plasma thory, th 1D-, D- and D-modls in [16] provid dtaild dscription of th filtr opration showing both lowring of th lctron tmpratur and formation of a maximum of th lctron dnsity in th filtr rgion. Rducd by th magntic fild thrmal conductivity, i.. supprssd nonlocality in th lctron hating, acting : Copyright 01 SciRs.

2 ST. LISHEV ET AL togthr with diamagntic drifts is shown to caus th drop of th lctron tmpratur in th filtr rgion and th formation of a groov thr. Diffusion and thrmal diffusion acting togthr appar to b rsponsibl for th formation of th maximum of th lctron dnsity in th filtr rgion, slightly shiftd from th sourc axis du to an E B-drift. Th main trnds in this pattrn of th filtr opration hav bn rcntly confirmd by both modling basd on PIC and fluid-plasma-modl simulations [17,18] and xprimnts [19,0] on th lctrongativity and th concntration of th ngativ hydrogn ions. Th lattr shows that th spatial distribution of th lctron dnsity and tmpratur, and of th plasma potntial, stmming from th nonlocal discharg bhavior dtrmins th conditions for an ffctiv production of th ions. This initiats th thortical analysis prsntd hr on th changs in th spatial distribution of th plasma paramtrs with changing th position of th magntic filtr. Th spatial structur of rmot plasmas sustaind without and with an xtrnal magntic fild is discussd in th study. Hydrogn dischargs in a fr-fall rgim ar considrd within a D fluid-plasma modl rgarding dscription of th magntic filtr rgion in th rf tandm plasma sourcs. Th rsults outlin th ffcts of nonlocality in dischargs with a localizd rf powr dposition and plasma xpansion into a rgion with an xtrnal magntic fild. Th transition btwn th powr-dposition and magntic-filtr rgions as wll as th rgion bhind th filtr displays th ffcts of plasma xpansion without magntic fild: slight dcras of th lctron tmpratur accompanid with strong drop of th lctron dnsity. Strong drop of th lctron tmpratur and formation of a maximum of th lctron dnsity in th filtr rgion ar th charactristics of th plasma xpansion through a magntic fild. Th rsults obtaind for th distribution of th lctron dnsity and tmpratur ar discussd rgarding optimization of th sourc with rspct to high yild of volum-producd ngativ ions.. Basis of th Modl Th modl prsntd hr is an xtnsion of th D modl from [16] towards dscription of th fr-fall rgim maintnanc of hydrogn dischargs in an xtrnal magntic fild. Th configuration of th discharg vssl is schmatically shown in Figur 1. Th rf powr dposition applid for th discharg production is localizd (Figur 1), with a half of a supr-gaussian profil in th z- dirction: m 1 z P z P xp w w0 p (1) whr P is its maximum at w0 z 0 and p scals its width. Th magntic fild th fild of th magntic filtr is also localizd, positiond bhind th rgion of th rf powr dposition. Dirctd along th y-axis, th fild is homognous in th x-dirction, with a Gaussian profil in th z-dirction cntrd at z z 0 : z z 0 Bz B0 xp () B whr B0 B z z0 and B scals its width. In th prsntation of th rsults in th nxt sction, th position z 0 has bn varid. Th rsults givn furthr on ar for th distribution of th plasma paramtrs in th (x-z)-plan (Figur 1), i.. prpndicularly to th filtr fild. Th spcis in th discharg ar lctrons, th thr typs of positiv ions ( H, H and H ) and hydrogn atoms (H) and molculs H. Th rat cofficints of th lmntary procsss ar calculatd with a Maxwllian vlocity distribution assumd for th lctrons. Th magntic fild is wak, so th lctrons ar magntizd and th ions ar lft unmagntizd. Th gas prssur is low and th discharg maintnanc is in th fr-fall rgim. Th lattr is spcifid by accounting for th nonlinar inrtia trm and for th inlastic collisions for particl production in th momntum quations of th positiv ions. Th lmntary procsss for production and dstruction of chargd particls and hydrogn atoms ar listd in Tabl 1; th rfrncs for th corrsponding rat cofficints ar also givn in th tabl. Th quations dscribing th lctron componnt ar th continuity quation and th lctron nrgy balanc quation: n n Γ () t t nt t J P P Γ E w coll dc whr n, T and Edc ar, rspctivly, th lctron dnsity and tmpratur (in nrgy units) and th dc fild formd in th discharg E dc ; is th lmntary charg. Th x- and z-componnts n Γ b n D n D T T xz, xz, xz, xz, T b n μd n μd d zx, d zx, T d n T T zx, of th lctron flux Γ account for lctron mobility, diffusion and thrmal diffusion across th magntic fild (4) (5) Copyright 01 SciRs.

3 1618 ST. LISHEV ET AL. (rspctivly, th first thr trms in th right-hand sid of (5)), for E B-drift (th fourth trm) and for diamagntic drifts du to dnsity and tmpratur gradints (th last two trms). Th corrsponding cofficints ar b 1 b, T D D D 1, b Dd b and d T D d D ; hr b m D T m and ar th mobility and diffusion coffici- nts along th magntic fild, B m is th lctron gyrofrquncy (with m bing th lctron mass) and a m is th frquncy of lastic collisions with atoms and molculs. Th lctron production and losss ar via th procsss numbrd by 1, 5 and 6 in Tabl 1. Th x- and z-componnts 5 J x, z Tμ, d x z, T TΓ z x x, z (6) of th lctron nrgy flux J includ th conductiv (th first two trms in th right hand sid) and convctiv (th last trm) fluxs. Th corrsponding componnts of th thrmal conductivity tnsor ar 1 and d with 5nD. Th lctron nrgy losss in collisions Pcoll accountd for ar th sam as in [16,4]: atom xcitation and ionization, dissociation, ionization, xcitation of vibrational and singlt stats of th molculs and lastic collisions of lctrons with atoms and molculs. Th last trm in th right-hand sid of (4) accounts for lctron nrgy losss for maintnanc of th dc fild in th discharg. Th quations dscribing th ion plasma componnts ar th continuity quations and th momntum quations n n t (7) t Γ Edc m v v v of th thr typs of positiv ions ( = 1,,, rspctivly, for th H -, H - and H -ions), th lattr writtn in a stationary form. Hr n, v and m ar th corrsponding dnsitis, vlocitis and masss and ( n t ) is th ion production and losss in inlastic collisions, as spcifid by th procsss in Tabl 1. Sinc a fr-fall rgim of discharg maintnanc is considrd th nonlinar inrtia trms in th momntum quations of th ions (th trms in th lft-hand sid of (8)) ar takn into account as dominating ovr th diffusion. Also, du to th rduction of th lastic collision frquncy at low gas prssur, th inlastic collisions for (8) Tabl 1. Procsss involvd in th chargd particl balanc and th balanc of th hydrogn atoms. Raction numbr Procss 1 1 HX Σg H v 1 H X Σ g H1s H1s H vh H1s Rfrnc [1] [1] 4 H H H H [] 5 H 1s H 6 H HHH [1] [1] 7 H H H [1] 8 HH H [] t ) ar includd in (8) via th no- ion production ( n tation i ad [1] m n l l l 1 i n t which combins both lastic collisions with atoms and molculs (rspctivly, l 1, ), with rducd masss l and frquncis l, and inlastic collisions (th scond trm in th right-hand sid of (9)) for production of th ions. Th inrtia trm spcifying low gas-prssur dischargs, rspctivly, fr-fall rgim discharg maintnanc, shows vidnc in th wall shath [5] whr th dc potntial drops strongly. In gnral, th inrtia trm plays th rol of a rtarding forc that limits th strong incras of th vlocity in th wall shath. Sinc in th wall shath th dc lctric fild is almost prpndicular to th corrsponding wall, th paralll to that wall componnt of th ion vlocity can b nglctd ([5] whr it is shown that this dos not influnc th accuracy of th solution) and, thus, (8) can b writtn as: x m x x x x (9) (10a) z m z z. (10b) z z Furthr on th collisionlss-cas nrgy-consrvation law of th ions 1 m, x z m (11) can b usd for dtrmination of th spatial drivativs of th vlocity componnts ( x x and x x ) in (10); m is th maximum valu of th potntial. This prmits raching in an xplicit form solutions for th ion vlocity componnts. Copyright 01 SciRs.

4 ST. LISHEV ET AL z x m m m x x m z z (1a) (1b) ndd for complting th ion fluxs Γ in (7). In a way, th two rtarding forcs th inrtia trm and th momntum losss in collisions ar combind dfining ffctiv mobilitis spcifid for ach dirction. Th Poisson quation n n, (1) 0 1 th balanc of th hydrogn atoms Na N divda Na t t and th xprssion for th gas prssur g a m a (14) p T N N (15) complt th initial st of quations. In (1)-(15), 0 is th vacuum prmittivity, T g is th gas tmpratur, is th Boltzmann constant, N and a Nm ar th dnsitis of th hydrogn atoms and molculs and Da is th diffusion cofficint of th hydrogn atoms dtrmind according to [6]. Lik in [16], th boundary conditions ar for th fluxs at th walls (th fluxs of th chargd particls and th lctron nrgy flux) and for a zro potntial of th dc lctric fild (du to th mtal walls of th discharg vssl).. Rsults and Discussions Th rsults discussd hr ar for th axial (z) variation at th discharg axis (x = 0) of th plasma paramtrs obtaind from th D-modl dscription prsntd in th prvious sction. Th siz of th modling domain is Lz 0 cm and L x 10 cm (Figur 1). Both th position z0 of th cntr of th magntic filtr and th gas prssur has bn varid, rspctivly, in th rangs z0 10 = (10 0) cm and p.5 mtorr. Th magntic fild in its maximum is B0 50 G with B = 1.58 cm and m = ; th xtnsion in th z-dirction of th powr dposition is givn by th valu of p 4.7 cm. Th total applid powr is 100 W. Th valu of th gas prssur assumd is 00 K..1. Discharg Structur and Its Changs with Varying th Position of th Magntic Fild Figurs and prsnt th rsults for th lctron tm- Figur 1. Configuration of th plasma volum and illustration of th z-variation of th filtr fild and of th rf powr input. Figur. Changs in th axial variation (at x = 0) of th lctron tmpratur and dnsity with varying th position z 0 of th maximum of th magntic fild; p = 4 mtorr. pratur T and dnsity n for and varying. p 4mTorr z 0 Copyright 01 SciRs.

5 160 ST. LISHEV ET AL. Figur. Comparison of th axial variation (at x = 0) of th lctron tmpratur and dnsity for diffrnt valus of z 0, as markd on th figur; p = 4 mtorr. With th xtnsion of th powr dposition rgion of about z P 5cm and of th magntic filtr rgion of about zb 4cm, shifting th position z 0 of th maximum of th magntic fild btwn 10 cm and 0 cm displays ffcts of plasma xpansion from th powr dposition rgion into rgions without and with an xtrnal magntic fild. Th axial profils of th plasma paramtrs (Figurs and ) obtaind for z 0 15 cm show th complt pattrn of conscutivly ordrd rgions in th discharg: plasma xpansion from th powr dposition rgion first in a rgion without a magntic fild followd by plasma xpansion through th magntic fild and nding with xpansion again in a rgion without a magntic fild. Thus, th nonlocality govrning th opration of th discharg via th lctron-nrgy and chargd-particl fluxs from th powr dposition rgion is th factor dtrmining th axial variations of th lctron dnsity and tmpratur. In th rf powr dposition rgion th lctron tmpratur stays almost constant and th lctron dnsity slightly dcrass. Th drastic changs in th axial profils of T and n ar within th full width zb 4cm of th magntic filtr: strong drop of, i.. an ffct of lctron T cooling by th magntic fild, and formation of a maximum of n in th rgion of th lctron magntization. Th physical pattrn which stays bhind th changs in th spatial distribution of th plasma paramtrs in th filtr rgion has bn dscribd in dtails in [16]. As a summary it is, as follows. Th strong drop of T in th filtr rgion is du to rducd by th magntic fild nonlocality of th lctron hating. With th localizd rf powr applid, th plasma xistnc outsid th rgion of its dposition is du to th lctron nrgy flux (and chargd particl fluxs) from this rgion. Th supprssion by th filtr fild of th cofficint of thrmal conductivity, rducs th lctron nrgy flux J and causs th drop of T. Figur 4 shows th axial variation of th contributions of th diffrnt trms in th stationary form of th lctron nrgy balanc (4): Th powr input in th magntic filtr rgion via J (in particular, via th conductiv flux) is in a balanc with th lctron nrgy losss in collisions (mainly inlastic collisions); th contributions of th lastic collisions as wll as th nrgy transfr btwn th lctrons and th dc lctric fild (th last trm in (4)) ar ngligibl. Th formation of a minimum of th lctron tmpratur in th filtr rgion (Figurs and ) stms mainly from th thrmal (conductiv) flux associatd with diamagntic drifts (Figur 5). According to th scond trm in (6), th axial (z-) dcras of T lads to a thrmal flux in th x-dirction (Figur 5) which is rlatd to a diamagntic drift. This causs an incras of T in th x-dirction. Consquntly, th lattr dtrmins a thrmal flux rlatd again to a diamagntic drift, howvr, now in th z-dirction, that rsults into lctron hating bhind th filtr and, thus, into formation of a groov in th filtr rgion. In addition, th diamagntic drift in th lctron flux ((5) and Figur 5), also contribut through th convctiv flux (th last trm in (6)) Figur 4. Axial variation (at x = 0) of th contributions to th lctron nrgy balanc: P w (xtrnal powr dposition), J and P = P + P (lctron nrgy losss in div coll l.coll. inl.coll. collisions prsntd sparatly for lastic P and inlastic collisions); z =10cm, p =4mTorr. P i 0 Copyright 01 SciRs.

6 ST. LISHEV ET AL. 161 Figur 5. Arrow plot prsntation of th lctron flux and of th lctron nrgy flux in th (x-z)-plan; z0 10 cm, p 4 mtorr. to th incras of T bhind th filtr and, thus, to th formation of th final distribution of th lctron tmpratur. Th apparanc of th maximum of n in th filtr rgion is du to diffusion and thrmal diffusion acting togthr: du to th axial drop of T th thrmal diffusion gains in importanc forming a forward thrmal-diffusion flux. On th othr hand, th diffusion flux is lowrd, du to th magntic fild. This rsults into an accumulation of lctrons in th filtr rgion and a formation of th maximum of n thr. Sinc only axial profils at x = 0 ar prsntd in Figur th shift du to th E B-drift of th maximum of n in th x-dirction shown in [16], is not discussd hr. Th axial variation of T within th full width zb of th magntic filtr rgion includs its drop, th formation of its minimum and its slight incras furthr on (Figur ). Compard to th structur of th T -profil, th structuring of th n - profil consists of mor dtails. Th incras of n in th filtr rgion lads to formation of a minimum in front of th filtr. Th formation of th main maximum of n in th filtr rgion is prcdd by slight maximum and minimum. Th strong drop of n aftr its maximum also starts within th filtr rgion. Th minimum of T and th maximum of n, bing slightly shiftd from th cntr of th filtr, ar at th sam position. With a magntic filtr locatd in th vicinity of z0 15 cm, two rgions of plasma xpansion without magntic fild show vidnc in th axial profils of n and T (Figurs and ). Ths ar th transition btwn th rgions of th powr dposition and th magntic filtr and th rgion bhind th filtr. Th pur ffcts of plasma xpansion without magntic fild ar: 1) a vry slight dcras of th lctron tmpratur rlatd to high nonlocality of th lctron hating du to th high valu of th thrmal conductivity cofficint without magntic fild (Figurs and ), and ) strong dcras of th lctron dnsity (Figurs and ). With a position of th magntic filtr clos to z = 10 0 cm, th plasma xpansion from th rgion of th rf powr dposition is dirctly into th magntic fild, i.. plasma xpansion without magntic fild shows vidnc only bhind th filtr. In this cas th drop of th lctron tmpratur in th magntic fild rgion starts from its valu in th powr dposition rgion. For a position of th magntic filtr approaching z0 0 cm, th pattrn of plasma xpansion without magntic fild (slight dcras of T and strong drop of n ) covrs almost compltly th total volum of th discharg. Shifting th position of th filtr fild away from th powr dposition rgion dos not influnc th axial gradint of T (Figur ). Howvr, th maximum of n in th filtr rgion bcoms lowr (Figur ), sinc th incras of n in th filtr rgion starts from a lowr valu of n. Th lattr is du to th largr xtnsion of th rgion of plasma xpansion outsid th powr dposition in front of th filtr and, rspctivly, to th strongr drop of n thr. Th structuring of th axial profils of th lctron tmpratur and dnsity in th filtr rgion as wll as thir complt bhavior, including th rgion of plasma xpansion bfor th filtr (xpansion outsid th powr dposition rgion) shown in Figurs and agrs qualitativly vry wll with th xprimntal rsults from prob diagnostics in [19,0]. Not only th minimum of T and th maximum of n in th filtr rgion hav bn xprimntally obsrvd. Th ntir bhavior of th profils, including thir changs with shifting th position of th magntic filtr, follows th trnds outlind in Figur : 1) lowr T bhind th filtr and highr maximum of n in th filtr rgion whn th filtr is locatd clos to th powr dposition rgion; ) th sam gradints of T in th filtr rgion for diffrnt positions of th filtr; ) a minimum of n prcding its maximum in th filtr rgion; and 4) th sam position of th minimum of T and of th maximum of n in th filtr Copyright 01 SciRs.

7 16 ST. LISHEV ET AL. rgion. As it has bn alrady mntiond, th magntic filtr is a ky componnt in th dsign of th sourcs of ngativ hydrogn ions dvlopd for fusion applications. Th rol of th filtr to cool th lctrons, ncssary for local production of th ngativ ions by lctron impact with vibrationally xcitd molculs, has bn usually strssd on. Howvr, th rsults in Figurs and show that th structuring of th axial profil of th plasma dnsity can b also mployd in th optimization of th sourc. Sinc fficint local production of ngativ ions rquirs not only low T but also comparativly high n, conditions for maximum ngativ ion production should b lookd for by choosing a propr position of th magntic filtr with rspct to th powr dposition rgion and th xtraction rgion. Th axial profil of th dnsitis of th positiv ions (Figur 6 whr th dnsitis of th molcular H and H ions ar givn) show th sam structur as that of th lctron-dnsity profils: strong dcras du to plasma xpansion outsid th powr dposition rgion and formation of a maximum in th filtr rgion, followd by strong drop aftr th filtr. Th structuring in th axial profil of th dnsity of th H -ions is bttr pronouncd. Th valu of th maximum of thir dnsity in th filtr rgion is vn highr than that in th powr dposition rgion. Th changs in th axial profils with varying th position of th filtr fild ar also th sam as of th lctrons. Sinc th lctron dnsity is comparativly low, th concntration of th atomic H ions, not shown hr, is lowr than that of th molcular ions (about 5 tims lowr). In gnral, th axial profils of th ions show that th plasma quasi-nutrality in th diffrnt rgions of th discharg is nsurd by intrplay btwn th concntrations of th thr typs of positiv ions... Influnc of th Gas Prssur Figur 7 shows rsults for th influnc of th gas prssur variation on th axial discharg structur for a givn position of th magntic filtr z0 10 cm. Th rsults for th lctron tmpratur (Figur 7) and dnsity (Figur 7) in th powr dposition rgion show th basic trnds of th changs in th gas discharg bhavior with varying gas prssur: highr lctron tmpratur and lowr lctron dnsity for lowr gas prssur du to th incrasd chargd particl losss via thir fluxs towards th walls. Furthr on, in th filtr rgion, this trnd is kpt: th highst T and th lowst n ar for th lowst valu p 4mTorr of th gas prssur. Figur 6. Th sam as in Figur but for th dnsitis of th and - ions. H H Figur 7. Comparison of th axial variation (at x =0of th lctron tmpratur and dnsity for diffrnt valus of th gas prssur p, as markd on th figur; = 10 cm. z 0 Copyright 01 SciRs.

8 ST. LISHEV ET AL. 16 Only at th vry nd of th discharg, in th wall shath at th back wall, du to th largr gradints of n for highr gas prssur, th lctron dnsity drops fastr whn th gas prssur is highr. Th mor pronouncd structuring in th n z-profil for highr prssur is rlatd to th rduction with th prssur incras of th diffusion cofficint outsid th filtr rgion. Th gradint of T in th filtr rgion dcrass with th gas prssur incras. Th positions of th minimum of T and of th maximum of n in th filtr rgion slightly dpnd on th gas prssur. Th lowst valu of T in th filtr rgion and bhind it and th highst valu of n in th filtr ar for th highst valu of th gas prssur. Th axial profils of th dnsitis of th positiv ions follow th trnds of th axial profils of th lctron dnsity (Figur 7). In th ntir gas prssur rang studid hr, th concntrations of th molcular ions ar highr than that of th atomic ions. Also in th ntir prssur rang th structuring of th dnsity profil of th H -ions is bttr pronouncd and th maximum of thir concntration in th filtr rgion xcds th dnsity valu in th powr dposition rgion... Axial Profils of th Potntial of th dc Elctric Fild in th Discharg Figur 8 shows th axial profils of th potntial of th dc lctric fild for diffrnt positions z 0 of th cntr of th filtr fild for p 4mTorr whras th corrsponding rsults obtaind for a givn valu of z 0 ( z 0 10 cm ) and varying prssur valus ar in Figur 8. Th wll pronouncd wall shath at th nd of th profils (z approaching z 0 cm ), with a strong drop of th dc potntial thr, shows discharg bhavior in a fr-fall rgim and, thus, th ncssity of accounting for th inrtia trms in th momntum quations of th positiv ions, as it has bn don in Sction. Th minimum of T and th maximum of n in th filtr rgion ar accompanid with a chang in th gradint of th potntial of th dc fild thr, i.. with a chang in th dc lctric fild. 4. Conclusion Basd on an xtnsion of th D fluid-plasma modl from [16] towards dscription of th fr-fall rgim discharg maintnanc, dvlopd in th study, rsults for th spatial structur of low-prssur hydrogn dischargs with localizd rf powr dposition and an xtrnal magntic fild positiond outsid it ar discussd. Th charactristics of th rmot plasma maintnanc in rgions without and with an xtrnal magntic fild, as dtrmind by th nonlocality of th discharg bhavior, Figur 8. Axial profils (at x 0 ) of th potntial of th dc lctric fild: at a givn valu of th gas prssur p 4mTorr and diffrnt positions of th cntr z 0 of th magntic filtr, and for a givn valu of th cntr of th magntic filtr z 0 10 cm and diffrnt valus of th gas prssur. ar outlind. Slight dcras of th lctron tmpratur accompanid with strong drop of th lctron dnsity charactrizs th plasma xpansion in rgions without xtrnal magntic fild whras strong drop of th lctron tmpratur accompanid with formation of a maximum of th lctron dnsity charactrizs th plasma xpansion through an xtrnal magntic fild. Th analysis of th rsults could b mployd in conclusions for optimization of th discharg as a sourc of volumproducd ngativ ions rgarding us for addional plasma hating in big fusion machins (ITER siz tokamaks). Elctron cooling by th magntic filtr is th rsult usually strssd on with rgards to th rquirmnts for local production of ngativ hydrogn ions. In addition, th formation of th maximum of th lctron dnsity in th filtr rgion can b also usd for raching high dnsity of th ngativ ions. For achiving this, a propr position of th magntic filtr with rspct to both th powr dposition rgion and th xtraction rgion should b chosn. 5. Acknowldgmnts Th work is within th programm of th Bulgarian Association EURATOM/INRNE (task.1.1). Copyright 01 SciRs.

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