Study of a coaxial vacuum arc thruster plume and its interaction with applied magnetic field

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1 Study of a coaxial vacuum arc thrustr plum and its intraction with applid magntic fild IEPC /ISTS-2015-b-82 Prsntd at Joint Confrnc of 30th Intrnational Symposium on Spac Tchnology and Scinc 34th Intrnational Elctric Propulsion Confrnc and 6th Nano-satllit Symposium, Hyogo-Kob, Japan M. Jimnz Diaz 1, L. Garrigus 2, G. J. M. Haglaar 3, F. Gaboriau 4, L. Liard 5 LAPLACE (Laboratoir Plasma t Convrsion d'enrgi), Univrsité d Toulous, UPS, INPT Toulous 118, rout d Narbonn, F Toulous cdx 9, Franc CNRS; LAPLACE; F Toulous, Franc L. Hrrro 6 and A. Blancht 7 COMAT Arospac, Flourns, Franc A hybrid modl whr ions ar tratd as particls and lctrons with fluid quations for magntizd lctron flux is adaptd in ordr to simulat a vacuum arc sourc. This sourc is a candidat for solid propllant propulsion systm of micro- and nano-satllits. W show prliminary rsults of th plum and intrlctrod rgion proprtis with and without th influnc of an imposd magntic fild. W compar th rsults with xprimntal data, and w find that th magntic collimation is ovrstimatd in th simulation. Nomnclatur B = total applid magntic fild, M = lctron, ion mass = ion (drift) vlocity, ion vlocity for injction boundary, lctron thrmal vlocity = prpndicular and paralll lctron mobility = Hall cofficint and cyclotron frquncy, = lctron, ion dnsity = lctron, ion tmpratur = lctron-ion, lctron-nutral collision frquncy = lctron, ion currnt = discharg, ion currnt dnsity = nutral gas dnsity = lctron to ion currnt ratio at cathod surfac = man ion charg = Potntial, Arc Voltag = lctron, ion Larmor radius = (virtual) prob radius for ion angular distribution 1 Postdoc at LAPLACE, Toulous, Franc, manul.jimnz@laplac.univ-tls.fr 2 Snior Scintist at CNRS, LAPLACE, Toulous, Franc, laurnt.garrigus@laplac.univ-tls.fr 3 Snior Scintist at CNRS, LAPLACE, Toulous, Franc, grjan.haglaar@laplac.univ-tls.fr 4 Associat Profssor, Paul Sabatir Univrsity, LAPLACE, Toulous, Franc, frddy.gaboriau@laplac.univ-tls.fr 5 Associat Profssor, Paul Sabatir Univrsity, LAPLACE, Toulous, Franc, laurnt.liard@laplac.univ-tls.fr 6 Projct Managr, COMAT AEROSPACE, Toulous, l.hrrro@comat-arospac.com 7 Propulsion Enginr, COMAT AEROSPACE, Toulous, l.hrrro@comat-arospac.com 1

2 I. Introduction Th growing nd for smallr (nano/micro) satllits dmands mor compact, mor prcis propulsion systms. Vacuum arc tchnology [1], [2], [3] is abl to produc plasma plums with high dirctd ion vlocity and low powr consumption (du to th charactristic low arc voltag), whil gas fding rlis on th cathod consumption. Ths faturs mak vacuum arcs potntial candidat for plasma sourcs of micro-thrustr as shown alrady in [4]. Th vacuum arc thrustr VAT main charactristics, namly dirctivity and spcific impuls, improv whn an xtrnal magntic flux is applid [4]. Th vacuum arc or cathodic arc has bn xtnsivly studid by [1], and [3] amongst othrs, and it has applications in coating, ion sourc, high currnt intrruptrs, tc. Th currnt is drivn by cathod spots with sizs in th micromtr rang, allowing rlativly high currnts ( A) with low arc voltags ( V). Figur 1. Schmatic viw of potntial distribution in a vacuum arc. Rgion (I), it is considrd part of th cathod spot, th rgion whr ionization and acclration occur. Rgion (II) is th intrlctrod rgion, th rgion whr vlocity is constant and th charg stat distribution frzs. A schmatic viw of th potntial distribution is shown in Figur 1. Hr w distinguish two rgions: Rgion (I) is considrd part of th cathod spot, it is th rgion whr ionization and acclration of th ions du to lctron ion friction taks plac. Rgion (II), it is whr ions kp moving at constant vlocity and constant man ion charg (i.. a frozn charg stat distribution [5]). Th spac scal of rgion (I) is in th ordr of 1μm, whras th intrlctrod rgion (II) is in th ordr of mm or cm. Th lctron dnsitis also chang from bginning of rgion (I) to rgion (II) by a numbr of ordrs of magnitud,.g. w can find dnsitis of clos to cathod surfac, whras in th intrlctrod rgion, w can find vals of dnsity starting at. Although th ionization dgr is vry high (clos to 99%), macroparticls and nutral spcis ar important and can affct th proprtis of th discharg, as shown in [6]. This schmatic viw is valid whn a point sourc cathod spot is considrd and whn cathod and anod surfacs ar facing ach othr, so that currnt lins ar prpndicular to ach lctrod surfac. Furthrmor it nglcts phnomna such as ionization and rcombination in th intrlctrod rgion, gomtrical ffcts, anod spot formation, among othr ffcts. W hav xtndd th hybrid modl dscribd in [7] to analyz th magntic arc plasma plum. Th modl is two dimnsional and lctron anisotropy transport as inducd by th magntic fild is dscribd ffctivly via paralll and prpndicular mobility with rspct th magntic fild lins [7]. W ar furthr improving th modl to transform it in an usful tool for th dsign of vacuum arc thrustr, as thos currntly bing dvlopd in th Comat Arospac company. W found that th ion sourc dscribd in [10] is similar to on of th possibl candidats considrd by Comat. Furthrmor, a comparison with xprimntal rsults in [10] is usful as mans of validation. Bcaus of th quasi-stady and pulsd natur of th plasma, masurmnts nd to b undrstood as an avrag ovr a sris of pulss. Th modl aims to obtain insight into ths avrag rsults. Som rasons to justify th tratmnt of rsults as an avrag ovr pulss is that th natur of cathod-spot producs givs ris to nois of high frquncy (.g. arc voltag, ), and th initial position of cathod spot aftr th triggring changs from puls to puls, du to diffrnt ffcts. W show how th magntic fild affcts th plum divrgnc and th plasma potntial distribution for a givn ion vlocity distribution at a rgion clos to th cathod spot. In following sctions, w dscrib th modl and th simulations, and w conclud showing and discussing rsults and th comparison with xprimntal data. II. Dscription of Modl and Simulations This hybrid modl is basd in th work of [7]. W hav includd modifications that allow for a suprsonic ion jt at th inlt, whil rtaining th capability of magntizd th lctron flux by mans of an anisotropic mobility. In th following sction, w dscrib first th main assumptions in th modl, thn w summariz th hybrid modl, togthr with th injction boundary condition and th gomtry and main simulation input paramtrs. 2

3 A. Assumptions Th modlling of vacuum arc is a difficult task that involvs multipl physics phnomna and diffrncs in tim and spac scals of 8 ordrs of magnitud. Th following assumptions simplify th modl: - Tim dpndnt modl, but starting tim placd away from triggring tim. - Th cathod spot is not modlld. Thir proprtis, for th injction boundary such as lctron to ion currnt, β, ion vlocity, flux strngth, ar imposd and dpnd upon prior knowldg.g. kintic calculations or xprimntal data. In our cas with stimat ths proprtis for a cathod mad of coppr. - Ions ar not magntizd:, with Larmor radius. - Elctrons ar magntizd:, with Larmor radius. - No ffct of th slf-magntic fild is considrd. - Th injction boundary or inlt is placd bhind th mixing rgion and thr is a constant distribution of th spots in th group spot. - Elastic collisions only affct th lctron mobility. - Ionization occurs bfor th injction boundary. Thr is no ionization in th intrlctrod rgion, which can b th cas for high currnt and high magntic filds. - Th lctron tmpratur is constant (.g. 3 V) in th whol computational domain. - Gomtry of lctrods undr chargd particls bombardmnt dos not chang. - Cartsian gomtry is usd in th modl (s Figur 2), although cylindrical is also availabl. B. Dscription of th modl In th hybrid modl, tratmnt of th ion spcis drivs from particls tracing as don in PIC simulation, whras lctron transport is simplifid and dscribd with fluid quations. For furthr information w rfr to [7]. Elctron fluid dscription Th lctron fluid quation, and corrsponding lctron flux rad n t S (1), n ( n T ) (2). Hr S is th background ionization sourc (if any),, th anisotropic mobility tnsor dfind with rspct to magntic flux lins by its paralll and prpndicular componnts m v, (3) with th collision frquncy of lctrons with ions and nutrals, v, hall paramtr and th cyclotron frquncy c B / m. Th modl allows for arbitrary (2D axisymmtric) magntic fild configuration with a mthod appropriat for ExB configurations [7]. Not, th lctron tmpratur is not solvd but st i.. in th whol domain. Plasma Cofficints Th collision frquncy of lctron and ions is givn by: Whr Coulomb logarithm is approximatd to lnδ = 7, lctron tmpratur in V, and lctron dnsity in. For mor dtails s also [8]. Th collision frquncy of lctrons and nutrals is givn by 3

4 whr th collision frquncy of lctron with nutrals is stimatd as = m 2 for coppr, whras th gas dnsity is st as. Ion Particl Dscription Ions ar dscribd as macroparticls (in th ordr of 1 million) using a particl in cll (PIC) modl. Ions ar injctd uniformly ovr th injction boundary using a shiftd Maxwllian flux (s [9]). Ion dnsitis ar calculatd from th position of macroparticls and coupld with th lctron dscription via Poisson s quation to calculat th potntial distribution. Not, th ions movs intracting with th slf-consistnt potntial (computd via Poisson s quation). Thus th magntic fild affcts indirctly th ion dynamics by affcting dirctly th lctron flux. Poisson s quation Th potntial distribution is obtaind from th Poisson quation as with appropriat boundary conditions (s furthr). a) b Figur 2. Gomtry in [10] (cylindrical coordinats). b) Gomtry in our modl (Cartsian coordinats). 4

5 Magntic Fild Calculation Th magntic fild is calculatd via amprs law, with coils of lngth 10 mm placd such that th magntic fild lins ar prpndicular to th injction boundary. In th cas whr th coils ar activatd, th currnt in th coil is such that th minimum absolut valu of th magntic flux at injction boundary B = 3.6 mt, and th maximum B = 4.0 mt. C. Dscription of th simulation gomtry and boundary conditions Th gomtry of th simulation configuration is givn in Figur 2.b. This configuration is chosn to rsmbl that in [10], which is cylindrical symmtric. W hav translatd this gomtry into our Cartsian coordinats; th rason for this is to allow for asymmtris in th injction of ions at th injction boundary. Actually, in an axial symmtric simulation th injction of ions would occur homognously across an annular surfac, thus nhancing th ion currnt at th cntr. In rality any symmtry is braking th random distribution injction of ions rlatd with th random movmnt of cathod spots. In th nd, th distribution of ion insrtion is a proprty that dpnds upon a high numbr of conditions and furthr study is ndd to improv th dscription in th modl. In th gomtry for th simulation, th width of injction boundary is approximatd by that of th cathod diamtr as 20 mm, th anod aprtur ntranc is st to 16 mm of width, and it is sparatd from injction boundary by 3 mm. It is surroundd by dilctric wall plac 2 mm away from th injction boundary dg. Th anod aprtur xit is of 35 mm width. Th plum rgion bhind th anod aprtur is surroundd by an opn boundary. This opn boundary sts th lctron currnt qual to th ion currnt whil avoiding th dscription of th shath by imposing quasinutrality. Th coil has a lngth of 10 mm and it is placd surrounding. Th dimnsions of th computational domain ar of 60 mm x 80 mm. An opn matrial layr with thicknss of 8 mm covrs th dg of th computational domain. Th main paramtrs in th simulation ar st according to a coppr lctrod: th lctron to ion currnt at th injction boundary, injction ion vlocity, th flux at th wall is st such that an ion currnt of 120 A is injctd, and consquntly th lctron currnt is Th atomic ion mass of coppr is 63.55, whras th man ion charg. Th lctron tmpratur is st as. Th anod potntial it st at 0 V. Th duration of th puls is 100 s. III. Rsults and Discussion Cas without applid magntic fild: Th distribution of th potntial along x and y is shown in Figur 3. a. Hr w s how a maximum for th plasma potntial dvlops at th injction boundary. This mans a rduction in th arc voltag (s Figur 1). This maxima rsults from th dmandd chang in lctron currnt from th injction boundary toward th anod as th plasma xpands (in th othr dirction onc passing th anod aprtur). Not that bcaus th hydrodynamic acclration of ions and lctrons, an incras of potntial toward th anod is not rquird to support th lctron currnt. Instad, th intrlctrod lctric fild dpnds mor on th path of lctron currnt lins, which is mainly affctd by th gomtry of th vacuum arc and th applid magntic fild lins [11]. Bcaus th high currnt of 1000 A, and small intrlctrod gap of 3 mm and th anod facing th injction on ions, w bliv th injction boundary is so clos to th anod that th potntial nds to dcras and dirct lctrons toward th anod aprtur. In ordr to furthr undrstand this, w nd to furthr xplor input paramtrs such as anod aprtur diamtr, arc currnt, and intrlctrod gap lngth and compar it with xprimntal data. Th total ion dnsity distribution is shown in Figur 3. c, with th angular distribution of th ion currnt (normalizd to maximum valu) givn in Figur 3. d. Th angular distribution is obtaind along a curv of radius, = 40 mm, as shown in Figur 2. As w can s th ion currnt dos not follow a cosin function, w bliv this is th rsult of th homognous profil chosn for th ion flux at th injction boundary. Th oscillations ar rlatd with th random injction and th low numbr of macroparticls. Including a largr numbr of macroparticls would show in th oscillation dcras or thy ar an ffct of th mannr ions ar injctd. 5

6 a) b) c) d) Figur 3. a) Two dimnsional distributions in x (mm) and y (mm) of potntial (V). Two currnt lins ar shown. b) Potntial along th currnt lins starting at injction boundary positions y = 47.5 mm and y=37 mm. c) Total ion currnt dnsity (A/m 2 ) distribution and d) corrsponding angular distribution of ion currnt (along curv of radius 40 mm shown in c) ). No magntic fild cas. Cas with applid magntic fild: Similarly to prvious cas, th potntial dpnds on th lctron currnt path and its strngth. Th lctron currnt path is strongly changd bcaus of anisotropic lctron mobility, and continuity of currnt at anod. This is th rason for th potntial wll in Figur 4.a. As w follow th currnt path (s Figur 4.b) th potntial incrass toward th anod, thrfor th arc voltag is highr with applid magntic fild [11]. Howvr, this arc voltag incras is highr than xpctd for such a low magntic fild. Th potntial wll has bn masurd across th plasma cross-sction in magntic filtrs [12]. Howvr, th potntial minimum clos to th injction boundary looks 6

7 a) b) c) d) Figur 4. Sam conditions as in Figur 3, with applid magntic fild. much highr than xpctd for a magntic fild of only 3.6 mt. Furthr xploration of th physics and xprimntal data ar ndd to bttr undrstand th potntial wll. Th angular distribution of th normaliz ion currnt, in Figur 4.d, shows how th plasma bam is collimatd. Comparison: In Figur 5, w hav compard th angular distribution btwn both cass, and also with xprimntal data from [10]. Th currnt is normalizd with rspct th absolut currnt masurd at th prob in [10] as. As w can s our modl ovrstimats th magntic contraction of th plasma bam. W nd to study in furthr dtail which part of th modl is rsponsibl for this ovrstimation. In, w show th angular distribution of ion vlocity as sam points as for th currnt. W do not apprciat an incras of ion vlocity along th axis. 7

8 Figur 5. Comparison of angular distribution of th normalizd ion currnt as dfind in [10]. Exprimntal points ar also obtaind from [10]. Rp = 40 mm in modl. Rp = 50 mm in [10]. Figur 6. Angular distribution of th ion vlocity: without magntic fild (dashd lin) and with magntic fild (solid lin). 8

9 IV. Conclusions W hav shown th capabilitis of th hybrid modl for dscribing th intrlctrod and plum rgions of a magntizd vacuum arc. Mor studis ar ndd to validat th modl, and in-hous masurmnts ar plannd for this purpos. For futur work, improvmnts on physical phnomna considrd can involv: - Improvmnt of injction profil by using information from intgratd total ion currnt as in [13]. - Mor ralistic magntic fild configuration. - Positiv anod drop. - Enhancmnt of th prpndicular lctron mobility via instabilitis (i.. Bohm diffusion, s [14]). - Includ multi ion spcis. - Th ffct of nutrals via charg-xchang, and th rduction of ion man charg. - Effct of slf-magntic fild du to high currnt. - Includ lctron nrgy quation. - Ionization in th intrlctrod rgion. Th hybrid modl prsntd hr is a fast tool (simulation tim in ordr of 24 hours using a dsktop computr), flxibl from th prspctiv of gomtry gnration and it is a promising tool for dsign and obtaining insight into magntizd vacuum arc thrustr. Acknowldgmnts This works is supportd by th Rgion Midi Pyrénés Programm Arosat Rfrncs [1] R. L. Boxman, D. M. Sandrs, and P. J. Martin, Handbook of Vacuum Arc Scinc and Tchnology: Fundamntals and Applications Noys Publications, [2] E. Hantzsch, A Simpl Modl of Diffus Vacuum arc Plasmas, Contrib. Plasma Phys., vol. 30, no. 5, pp , Jan [3] A. Andrs, Th volution of ion charg stats in cathodic vacuum arc plasmas: a rviw, Plasma Sourcs Sci. Tchnol., vol. 21, no. 3, p , Jun [4] M. Kidar, J. Schin, K. Wilson, A. Grhan, M. Au, B. Tang, L. Idzkowski, M. Krishnan, and I. I. Bilis, Magntically nhancd vacuum arc thrustr, Plasma Sourcs Sci. Tchnol., vol. 14, no. 4, p. 661, Nov [5] A. Andrs, Th Intrlctrod Plasma, in Cathodic Arcs, Springr Nw York, 2008, pp [6] A. Andrs, E. M. Oks, and G. Y. Yushkov, Production of nutrals and thir ffcts on th ion charg stats in cathodic vacuum arc plasmas, Journal of Applid Physics, vol. 102, no. 4, p , Aug [7] G. J. M. Haglaar, Modlling lctron transport in magntizd low-tmpratur discharg plasmas, Plasma Sourcs Sci. Tchnol., vol. 16, no. 1, p. S57, Fb [8] M. Kidar, I. Bilis, R. L. Boxman, and S. Goldsmith, 2D xpansion of th low-dnsity intrlctrod vacuum arc plasma jt in an axial magntic fild, J. Phys. D: Appl. Phys., vol. 29, no. 7, p. 1973, Jul [9] L. Garrigus, J. Barills, J. P. Bouf, and I. D. Boyd, Modling of th plasma jt of a stationary plasma thrustr, Journal of Applid Physics, vol. 91, no. 12, pp , Jun [10] Y. Cohn, R. L. Boxman, and S. Goldsmith, Angular distribution of ion currnt mrging from an aprtur anod in a vacuum arc, IEEE Transactions on Plasma Scinc, vol. 17, no. 5, pp , Oct [11] V. N. Zhitomirsky, R. L. Boxman, and S. Goldsmith, Transport of a vacuum arc plasma bam through th aprtur of an annular anod, IEEE Transactions on Plasma Scinc, vol. 33, no. 5, pp , Oct [12] E. Byon, J.-K. Kim, S.-C. Kwon, and A. Andrs, Effct of ion mass and charg Stat on transport of vacuum arc plasmas through a biasd magntic filtr, IEEE Transactions on Plasma Scinc, vol. 32, no. 2, pp , Apr [13] J. E. Polk, M. J. Skrak, J. K. Zimr, J. Schin, N. Qi, and A. Andrs, A Thortical Analysis of Vacuum Arc Thrustr and Vacuum Arc Ion Thrustr Prformanc, IEEE Transactions on Plasma Scinc, vol. 36, no. 5, pp , Oct [14] A. Andrs, S. Andrs, and I. G. Brown, Transport of vacuum arc plasmas through magntic macroparticl filtrs, Plasma Sourcs Sci. Tchnol., vol. 4, no. 1, p. 1, Fb