Modelling of new generation plasma optical devices

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1 NUKLEONIKA 216;61(2):27212 do: /nuka ORIGINAL PAPER Modllng of nw gnraton plasma optcal dvcs Irna V. Ltovko, Aly A. Goncharov, Andrw N. Dobrovolsky, Lly V. Nako, Irna V. Nako Abstract. Th papr prsnts nw gnraton plasma optcal dvcs basd on th lctrostatc plasma lns confguraton that opns a novl attractv possblty for ffctv hgh-tch practcal applcatons. Orgnal approachs to us of plasma acclrators wth closd lctron drft and opn walls for th craton of a cost- -ffctv low-mantnanc plasma lns wth postv spac charg and possbl applcaton for low-cost, low-nrgy rockt ngn ar dscrbd. Th prlmnary prmntal, thortcal and smulaton rsults ar prsntd. It s notd that th prsntd plasma dvcs ar attractv for many dffrnt applcatons n th stat-of-th-art vacuum-plasma procssng. Ky words: anod layr plasma lns plasma acclrator plasma jt spac charg Introducton I. V. Ltovko Plasma Tchnology and Plasma Physcs Dpartmnt, Insttut for Nuclar Rsarch NASU, 47 Nauk pr., 365 Kv, Ukran, Tl.: , Fa: , E-mal: ltovko@ramblr.ru, ltovko@knr.kv.ua A. A. Goncharov, A. N. Dobrovolsky, L. V. Nako, I. V. Nako Gas Elctroncs Dpartmnt, Insttut of Physcs NASU, 46 Nauk Av., Kv, 328, Ukran Rcvd: 2 Sptmbr 215 Accptd: 3 Dcmbr 215 Th crossd lctrc and magntc flds, nhrnt to th cylndrcal lctrostatc plasma lns (PL) confguraton, provd an attractv mthod for stablshng a stabl plasma dscharg at a low prssur [1]. On partcularly ntrstng rsult of ths background work was th obsrvaton of th ssntal postv potntal at th floatng substrat. Ths suggstd that an lctrostatc PL can possbly b usd for focusng and manpulatng hgh-currnt bams of ngatvly chargd partcls (lctrons and ngatv ons) that s basd on th us of th dynamcal cloud of postv spac charg undr th condtons of lctron s magntc nsulaton. An attractv possblty of th applcaton of dynamcal postv spac chargd plasma lns wth a magntc lctron nsulaton and non-magntsd ons, for focusng and manpulatng wd-aprtur hgh-currnt ngatvly chargd partcls bams, has bn shown n our prvous works [2, 3]. Hr w dscrb th orgnal approach to us plasma acclrators wth a closd lctron drft, whch (unlk th tradtonal acclrators wth mtal and dlctrc walls [4]), hav opn (gasous) walls and can b appld for th craton of cost-ffctv low-mantnanc plasma dvcs. Thy mght b basd on a plasma lns confguraton for th producton of acclratd on bams convrgng towards th z-as, and for th dsgn of postv spac charg plasma lns [5]. It has bn shown that, basd on th da of th contnuty of currnt transfrrng at th systm n th fram of Unauthntcatd Download Dat 2/11/18 6:2 AM

2 28 I. V. Ltovko t al. on-dmnsonal modl, act analytcal solutons dscrbng lctrc potntal and lctron dnsty dstrbuton along an acclraton gap can b found. Plasma acclrator wth gas walls and closd lctron drft St-up and prlmnary prmntal rsults Acclrators wth closd lctron drfts and opn (gas) walls hav not bn studd tll now, n contrast to th wll-known and wdly usd plasma acclrators wth an anod layr and acclrators wth closd lctron drfts and dlctrc walls [4]. Th acclrator wth closd lctron drfts can, howvr, b ntrstng for th optmsaton of hgh currnt flows of chargd partcls and can b attractv for th laboraton of low-cost, ffctv and low mantnanc plasma lns wth a postv spac charg cloud. Th plot prmntal plasma acclrator wth closd lctron drfts and opn walls s shown n Fg. 1a. Such a cylndrcal Hall-typ plasma-on sourc, whch producd on-plasma flows convrgng towards th symmtry as of th systm, was cratd for th ploraton. Th damtr of anod was 6.7 cm, and that of cathod was 3.2 cm. A dstanc btwn anod and cathod was qual to 1.75 cm. Magntc fld H = O was cratd by prmannt magnts. Th appld voltag was blow 2 kv. Th workng prssur was n a rang of 1 5 to 1 3 Torr, and th workng gas was pur argon. Th formaton suffcnt amount of ons was possbl du to th prsnc of magntc fld, whch solat anod from cathod. Fgur 1b shows volt-ampr charactrstcs masurd for dffrnt work gas prssur. Two opratng mods wr obsrvd and th currnt- -voltag charactrstcs of th acclrator n ths mods wr dfnd. W hav low-currnt opraton mod at a low prssur of th workng gas, whn all onsaton procsss occur n an anod layr. At a prssur ncras, th anod layr sz grows up and th acclrator procds to a hgh-currnt mod wth total currnt rangng up to 2 A. In ths mod, th dscharg currnt s gratr by svral ordrs, but dscharg s not localsd nar th anod any mor, and can fll up th whol nnr volum. In a hgh-currnt quas-nutral plasma mod of th acclrator opraton, a plasma jt s usually obsrvd, as shown n Fg. 2a. Ths prlmnary rsults show that potntal drop appars along th jt as and can b usd for th on bam acclraton. Fgur 2b shows an on bam currnt dnsty dpndnc on currnt dscharg along th jt as. It should b notd that th powr on plasma flow ncrass wth an ncras n th dscharg currnt dnsty. On should also not that th on currnt dnsty at th jt as can rach up to 2 3% of th total dscharg currnt. That opns a novl attractv Fg. 1a. Eprmntal unt: 1 cathod, 2 anod, 3 prmannt magnts systm. Fg. 2a. Plasma jt n a hgh-currnt opraton mod. Th plum s obsrvd prpndcular to th acclraton drcton. Fg. 1b. Th total dscharg currnt vs dscharg potntal for dffrnt work gas prssurs. Fg. 2b. Dpndnc of a bam currnt dnsty vs. dscharg currnt dnsty. Unauthntcatd Download Dat 2/11/18 6:2 AM

3 Modllng of nw gnraton plasma optcal dvcs 29 (5) = 4(n n ) whr for on dnsty w can wrt th prsson (6) n( ) M /2 d sn( s) / ( ) ( s) Consdrng th fact that on currnt s quals on th cathod and takng nto account a boundary condton = =, whr a s an anod potntal, w obtan th closd systm of quatons. In som cass, t s possbl to fnd act analytcal solutons of ths systm. For ampl, nglctng a dffuson n th cas whn n >> n, whch corrsponds to a low-currnt mod, w can gt th soluton n a dmnsonlss form: Fg. 3. Schm for a thortcal modl: 1 anod, 2 cathod, 3 magntc systm. possblty to us ths knd dvc as a prototyp of small rockt ngns. Modl and analytcal solutons In ordr to analys th proprts of th consdrd acclrator, w usd a on-dmnsonal hydrodynamc modl. A schm usd n ths modl s schmatcally shown n Fg. 3. In th consdrd systm, lctrons ar magntsd, ons ar non-magntsd and mov from th anod to th systm as. W can assum that a currnt dnsty n th gap volum s th sum of th on and lctron componnts: (7) = (( 1) 2 1) / 2 + 1, = / d 2 whr d s th gap lngth. Potntal dstrbuton (Eq. (7)) for dffrnt valus of paramtr s shown n Fg. 4a. On can s that at = ½, th total appld potntal falls nsd th acclratng gap. In ths optmal cas, th gap lngth s: (8) d= 2 a / Undr assumpton that all lctrons orgnatd (1) j + j = j d whr j and j ar on and lctron currnt dnsty, rspctvly. Consquntly, j n( ) d (2) whr s th onsaton frquncy, = /m 2 H s th lctron transvrs moblty, E() = s th lctrc fld, s potntal, n s th frquncy of lastc collsons wth nutrals and ons, H s th lctron cyclotron frquncy, T s an lctron tmpratur that can b found from th quaton of th lctrons hatng n an lctrc fld [4], that s, (3) j( ) n E( ) nt T( ) j( ) = j( s) ds whr < 1. Thus, takng nto account th valus from Eqs. (1) and (2), w obtan th prsson (4) n( )d n nt jd Anothr quaton for th analysd systm dscrpton s th Posson s quaton: s Fg. 4a. Potntal dstrbuton for dffrnt valus n a low-currnt mod. Fg. 4b. Potntal dstrbuton for dffrnt valus n a hgh-currnt quas-nutral plasma mod. Unauthntcatd Download Dat 2/11/18 6:2 AM

4 21 I. V. Ltovko t al. from th gap only by mpact onsaton, and go to th anod du to classcal transvrs moblty, th prvous prsson can b rprsnt n th form: (9) Ths prsson concds wth th on for classcal anod layr [6] accurat wthn 2. It should b notd that n th cas whn paramtr > ½ (th gap lngth s smallr than ), th potntal drop s not compltd. For th cas < ½, whn th gap lngth d >, th potntal drop cds th appld potntal. Ths can b du to an lctron spac charg domnatng at th acclrator t. On can tnd now our dscrpton takng nto consdraton n and n changs along th gap, whch corrsponds to a hgh-currnt mod. As bfor, w wll study th cas T = only. Thn for dmnsonlss Eqs. (4), on can wrt th quaton (1) whr b = a n /j d d and c = dn /j d ar dmnsonlss paramtrs. For smplcty, w wll consdr quas-nutral plasma n n. Thn substtutng a dmnsonlss qualty (6) n Eq. (1), on gts (11) Takng nto account th qualty of th consdrd ntgrals and boundary condton, on obtans th prsson for th potntal dstrbuton: (13) () = 1 a 2 /4f 2 + a 2 ( 1) 2 /4f 2 whr a = c/b. It should b notd that t s corrspondng to th paramtr 1/ ntroducd abov. From Eq. (13), w can fnd that th bhavour of th potntal dstrbuton dpnds on a rato p = a 2 /4f 2. It should also b notd that th paramtr f dscrbs th nflunc of th on dnsty (s Fg. 4b). If w now drv Eq. (1), w could obtan an quaton for th lctron dnsty: (14) (n ())/n () = (a )/ Th soluton of Eq. (14), at th gvn rlaton (13), has a form: (15) 2 / a c n()d s sbn() 1 whr f = dm/2 a. Aftr som transformatons and takng nto account th fact that on currnt quals j d upon th cathod, Eq. (11) could b rwrttn n a form 1 1 (12) d sn( s) 2 bf ( ) ( s) d sn( s) c 2f n( ) C( 1) a whr C s a constant. On should not that f a = 2f 2, th lctron dnsty dos not chang along th gap and th soluton (13) s rducd to th valu n()d s sbf d s n()/ s () () s gvn by Eq. (7). Th condton mntond abov could b rwrttn n a form (16) d / 2 d = 2 or d = 2 2 d 2 = 1 whr d = d/ E s lctron lftm, and d = d/ d s on lvng tm. Indd Eq. (16) s som gnralsaton condton of a slf-sustand dscharg n th crossd E H flds, takng nto consdraton both lctron and on dynamcs pcularty. Rsults of smulatons n hydrodynamc and hybrd modls Now lt us consdr a mor gnral dscrpton, assumng that lctron hatng losss occur mostly by dffrnt knds of collsons. Introducng a charactrstc tm of nrgy losss, w can wrt a dfnton for th tmpratur: (17) T = j d E (1 t/ )/n and for a stady-stat (17a) (18) T = j d E /n m bbbb Thus Eq. (4) can b rwrttn n th form Makng ths quaton and Posson s quaton dmnsonlss, that s, ntroducng dmnsonlss paramtrs, w can obtan a systm of quatons (19) and (19a) j n d n dj d d a bn( ) c n( s)ds1 n ( ) f ns ( )d s/ ( ) ( s ) =g whr th ntroducd nw dmnsonlss paramtrs ar a = a /d 2 and g = a /4d 2 n, whl paramtrs b, c and f corrspond to thos ntroducd abov. In a gnral cas, th consdrd quaton systm dos not hav analytcal solutons and rqurs numrcal calculatons. If w assum a zro lctrc fld on th cathod, w got solutons (s Fg. 5a) smlar to obtand abov (s Fg. 4a). As on can s from Fg. 5b, th lctron dnsty changs by a small amount along th gap, thus our abov consdraton that n s constant along th gap s untru. Not also that f w assum that = d, thn Eq. (17) wll b rducd to th form: T = j d / n, consquntly n Eq. (4), th tmpratur trm dsappars. Thrfor, w com back to potntal dstrbuton (Eq. (7)). For a mor dtald study of th nflunc of on dynamcs on th systm procss, w appld a on-dmnsonal hybrd modl usd for calculatons of a span mod wth nutral-partcl onsaton. In ths modl, ons and nutral dynamcs s dscrbd by kntc quatons, whr rght parts tak nto account only a sngl onsaton: Unauthntcatd Download Dat 2/11/18 6:2 AM

5 Modllng of nw gnraton plasma optcal dvcs 211 modl. On can asly s that takng nto account span mod wth sngl onsaton dos not hav a grat nflunc on th rsultng potntal dstrbuton (Fg. 6a). Th lctron dnsty dstrbuton (Fg. 6b) looks mor consstnt along th gap n a hybrd modl n a comparson wth that found from a hydrodynamc modl. It s th rsult of an nflunc of nutrals and onsaton on th systm procsss, whch wr not takn nto account n th hydrodynamc modl. Nvrthlss, th hydrodynamc modl dscrbs th systm qut wll and allows gt act analytcal solutons. Fg. 5a. Potntal dstrbuton obtand from th numrcal smulatons. Fg. 5b. Elctron dnsty dstrbuton obtand from th numrcal smulatons. (2) whr f and f ar th dstrbuton functon of nutrals and ons, rspctvly. Ths functons satsfy boundary condtons: (21) f f nf t f f f E n f t M n fd, j fd M f (,, t) p 3/2 (2 MT) 2T for postv vlocts f(,, t) for ngatv vlocts In such a cas < > = ma (T )p( U /T ), whr ma th mamal onsaton cross-scton, (T ), an avrag lctron thrmal vlocty, U th th onsaton potntal. For lctrons, w can us a hydrodynamc modl, as bfor: j j j d E (22) j ne jd E 4n n Th computd rsults ar shown n Fg. 6(a,b) n a comparson wth thos from a hydrodynamc Conclusons For th frst tm, th orgnal approach to us plasma acclrators wth closd lctron drfts and opn walls, applcabl for th craton of cost-ffctv low-mantnanc plasma dvcs for producton of on bams convrgng towards th z-as, was dscrbd. Th plot unt of such a plasma acclrator was cratd and tstd. Th frst prmntal rsults wr obtand for a low-currnt and a hgh- -currnt mods. Basd on th da of contnuty of currnt transfr n th consdrd systm, act analytcal solutons, whch dscrb an lctrc potntal dstrbuton along th acclraton gap, wr found. It was shown Fg. 6a. Potntal dstrbutons obtand from th hydrodynamc and hybrd modls. Fg. 6b. Elctron dnsty dstrbutons obtand from th hydrodynamc and hybrd modls. Unauthntcatd Download Dat 2/11/18 6:2 AM

6 212 I. V. Ltovko t al. that th potntal dstrbuton s parabolc for dffrnt opraton mods (.., n a low-currnt mod as wll as n a hgh currnt quas-nutral plasma mod) and t slghtly dpnds on th lctron tmpratur. It was found that, undr condtons at whch all lctrons wr producd wthn th gap by mpact onsaton only and propagatd towards th anod (du to classcal moblty n a transvrs magntc fld), th full potntal drop n th acclratng gap appars wthn th anod layr thcknss. In a cas whn th gap lngth s smallr than th anod layr thcknss, ths potntal drop s not compltd. For th cas whn th gap lngth s largr than th anod layr, th consdrd potntal drop cds th appld voltag. For a hgh-currnt quas-nutral mod, a gnral condton of a slf-sustand dscharg n th crossd E H flds, takng nto consdraton both lctron and on dynamcs pcularty. Th smulaton rsults obtand from th hydrodynamc and hybrd modl ar n a good accordanc, and thr bhavour s smlar to act analytcal solutons. Th prsntd plasma dvc s attractv for th craton of cost-ffctv and low-mantnanc plasma lns wth a postv spac charg ndd for focusng ngatv ntns charg partcls bams (lctrons and ngatv ons). It crats opportunty to dsgn low-cost and low-nrgy small rockt ngns and can b usful for many othr hgh-tch practcal applcatons. Acknowldgmnt. Th work s partly supportd by th grant of NAS of Ukran no and no. PL Ths work was prformd at th Insttut for Nuclar Physcs and Insttut of Physcs NASU n Kv, Ukran. Rfrncs 1. Goncharov, A. A., & Brown, I. G. (27). Plasma dvcs basd on th plasma lns: A rvw of rsults and applcatons. IEEE Trans. Plasma Sc., 35(4), Goncharov, A., Dobrovolsky, A., Dunts, S., Evsyukov, A., Ltovko, I., Gushnts, V., & Oks, E. (211). Postv-spac-charg lns for focusng and manpulatng hgh-currnt bams of ngatvly chargd partcls. IEEE Trans. Plasma Sc., 39(6), Gushnts, V., Goncharov, A., Dobrovolsky, A., Dunts, S., Ltovko, I., Oks, E., & Bugav, A. (213). Elctrostatc plasma lns focusng of an ntns lctron bam n an lctron sourc wth a vacuum arc plasma cathod. IEEE Trans. Plasma Sc., 41(4), Morozov, A. I. (28). Introducton to plasma dynamcs. Moscow: Fsmatlt. 5. Ltovko, I., Goncharov, A., Dobrovolsky, A., Najko, L., Najko, I., Gushnts, V., & Oks, E. (215). Computr modlng plasma optcal dvcs (nw rsults). Probl. Atom. Sc. Tchn. (VANT), 95(1), Grshn, D., Lskov, L., & Kozlov, N. (1983). Plasma acclrators. Moscow: Mashnostron. Unauthntcatd Download Dat 2/11/18 6:2 AM