Three-dimensional Hybrid-PIC Simulation of Microwave Neutralizer

Transcription

1 Thr-dimnsional Hybrid-PIC Simulation of Microwav Nutralizr IEPC Prsntd at th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity Washington, D.C. USA Octobr 6 10, 2013 K. Kubota 1 Japan Arospac Exploration Agncy, Chofu, Tokyo, , Japan H. Watanab 2, I. Funaki 3 Japan Arospac Exploration Agncy, Sagamihara, Kanagawa, , Japan N. Yamamoto 4, H. Nakashima 5 Kyushu Univrsity, Kasuga, Fukuoka, , Japan and T. Miyasaka 6 Gifu Univrsity, Gifu, Gifu, , Japan Abstract: In ordr to analyz a microwav nutralizr in ion s tim/spac scals, wakly coupld simulations of a Hybrid-PIC (Particl-In-Cll) and an lctromagntic PIC simulation wr conductd. Th ionization rat with rspct to microwav discharg was obtaind from th lctromagntic PIC solvr, and was xportd to th Hybrid-PIC whr ions and lctrons wr dalt with particls and fluid, rspctivly. Two anod potntials of 20 and 38 V wr xamind to simulat a transition from a low currnt mod to a high currnt mod. Th lctron tmpratur insid an orific was fixd to 3 V at th low currnt mod, and was artificially incrasd to 4 V at th highr anod potntial of 38 V. It was found that th grown ion dnsity insid th orific at th high currnt mod lads to incras in th ion dnsity around th antnna, and hnc to incras in ion production rat by microwav discharg. As a rsult, th lctron currnt collctd by th virtual anod was incrasd from 22 ma to 98 ma. B C E H j m = magntic flux dnsity = thrmal vlocity = lctric fild = lmntary charg = magntic fild = currnt dnsity = mass of particl Nomnclatur 1 Rsarchr, Institut of Aronautical Tchnology, kubota.knichi@jaxa.jp 2 Rsarch Fllow, JAXA s Enginring Digital Innovation Cntr, watanab.hiroki@jaxa.jp 3 Associat Profssor, Institut of Spac and Astronautical Scinc, funaki@isas.jaxa.jp 4 Associat Profssor, Dpartmnt of Advancd Enrgy Enginring Scinc, yamamoto@as.kyushu-u.ac.jp 5 Profssor, Dpartmnt of Advancd Enrgy Enginring Scinc, nakasima@as.kyushu-u.ac.jp 6 Associat Profssor, Dpartmnt of Human and Information Systms, miyasaka@gifu-u.ac.jp 1 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

2 n P p R T t u v x = numbr dnsity = input powr = prssur = gas constant = tmpratur = tim = vlocity of fluid = vlocity of a particl = coordinat β = Hall paramtr φ = lctric potntial μ = mobility ν = collision frquncy subscripts a : anod : lctron h : havy particl (nutral and ion) i : ion T I. Introduction h ion ngin μ10 installd on th Japan s astroid xplorr HAYABUSA stablishd th availability of microwav discharg for lctrostatic propulsion systm. On that xplorr, four ion ngins wr quippd, and ach ngin gnratd a thrust of 8 mn, a spcific impuls of 3,200 sconds, and consums an lctric powr of 350 W. In 2005, th HAYABUSA landd on astroid ITOKAWA, and accomplishd th first vr round trip spac flight btwn Earth and an astroid. 1 In th actual opration, howvr, th lif tim of on of th ion ngins was rstrictd to 14,000 hours bcaus of an unxpctd troubl with a microwav nutralizr, 2 in spit of th succssfully compltd nduranc ground-tst through 20,000 hours. In ordr to clarify th causs of prformanc dgradation, th prototyp modl nutralizr usd in th nduranc tst was rviwd, and it was concludd that th prformanc dgradation was attributd to mtal flaks and contamination of th dilctric. 3 Also, th othr ground tsts for thr diffrnt gomtris of nutralizrs showd that th prformanc and th rosion rat of ach wall strongly dpnd on th gomtry. 4 It is considrd that th contamination and th rosion wr attributd to sputtring by ions, thus th ncssity to grasp th ion s bhavior is gtting incrasd for th improvmnt of robustnss of th microwav ion ngin. Rcntly, nt currnt into ach composing lmnt wr masurd in ordr to undrstand ion s bhavior. 5 It was found that a sid wall is gathring most of currnts than othr parts, and an antnna is gathring many lctrons. For furthr undrstandings on th discharg phnomna, a numrical solvr to simulat th motion of ions in th nutralizr is bing dvlopd in this study. In ordr to simulat th nutralizr with th ion s tim/spac scals, a Hybrid-PIC(Particl-In-Cll) modl was mployd, whr ions and lctrons ar modls as particls and fluid, rspctivly. In this papr, th dtails of th numrical modl ar dscribd, and th plasma proprtis such as dnsity and lctric potntial ar discussd. In ordr to dal with on of th most charactristic phnomna of a microwav nutralizr, w focus on a transition of discharg mod. It is widly known that a microwav nutralizr has two opration mods rfrrd to as low currnt mod and high currnt mod, i.. whn a bias voltag xcds a crtain thrshold, a discharg currnt riss discontinuously. 6 In spit of th importanc of th mod chang, howvr, littl is known about th transition mchanism. To undrstand th mod transition, two working conditions blow and abov th thrshold voltag ar xamind undr som assumptions, and its charactristics and validity ar discussd. II. Numrical Modl A. Gomtry and Computational Rgion Figur 1 illustrats a schmatic viw of a nutralizr simulatd in this study, which was assmbld at Kyushu Univrsity. Although this gomtry is not xactly th sam as th nutralizr of μ10, qualitativ bhavior of th microwav plasma will rmain unaltrd. It has a symmtric discharg chambr with a diamtr of 18 mm. A 2 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

3 microwav is fd through a coaxial lin followd by an L shapd antnna insrtd to th discharg chambr. Bcaus of th asymmtric shap of th antnna, a thr dimnsional simulation is rquird to undrstand ralistic physics. Elctrons producd by microwav discharg ar supposd to b xtractd though th orific with a diamtr of 5 mm and an axial lngth of 8 mm. Th configuration was approximatd by th Cartsian grids for simplicity as dpictd in Fig.2, whr th blu colord clls rprsnt a computational rgion. A grid intrval was uniformly st to 0.5 mm which is much shortr than th man fr path of ions. With this grid, although th boundary surfac cannot b capturd xactly, this rsolution will b nough to mt th prsnt purpos to undrstand ovrall charactristics of th discharg fild. Th cavity in th back yok through which th antnna is insrtd was filld by clls blonging to th back yok for furthr simplicity. Th computational rgion was xtndd by 4 mm toward th plum rgion, and a virtual anod was locatd at th boundary surfac of x = 28 mm. In actual xprimnt of this nutralizr, an anod plat was locatd at 20 mm from th orific xit, thus dirct comparison btwn th computational and xprimntal rsults is impossibl. According to a diagnosis, howvr, thr is littl potntial drop in a plum rgion, although thr may xist an lctron shath about 5-10 V on an anod plat. 7 Th outr rgion btwn th orific xit and th virtual anod was rmovd from th computational rgion to rduc th calculation cost. Magntic fild shown in Fig. 3 is applid by a surrounding ring-shapd magnt in ordr to gnrat lctron s cyclotron motion, which is intndd to nhanc plasma production. Th lctrons ar trappd by th magntic fild and ioniz background nutrals. Figur 1. Schmatics of Microwav Nutralizr. Figur 2. Computational Grid. Figur 3. Magntic fild. Figur 4. Flow Chart of Calculation. 3 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

4 B. Outlin of Numrical Modl In this nutralizr, most of th lctrons producd by ionization collisions btwn lctrons and nutrals ar jctd from an orific and rachs th virtual anod. On th othr hand, most of th ions ar rcombind on conductor surfacs with lctrons fd from an ion sourc, and rturn back to bulk plasma as nutrals; hnc th ions plays an important rol as a charg carrir in th microwav nutralizr. This indicats that th physics should b modld in ion s tim/spac scal to simulat th ssntial physics of th microwav nutralizr. Physical proprtis ncssary to modl ar classifid into thr catgoris. First is th ion s motion itslf, and scond is th static lctric fild btwn th nutralizr and th virtual anod. Third is th intraction btwn th microwav and th lctrons, i.. th procss of lctron s hating by microwav. Th lctric powr fd through th microwav antnna is absorbd mainly by th lctrons, and th nrgizd lctrons transfr th powr to nutrals by collisions. In particular, whn an lctron passs through ECR(Elctron Cyclotron Rsonanc) rgion, th powr absorption bcoms significant. To simulat such a rsonanc phnomnon, proprty of an lctron as a particl should b includd in th numrical modl, bcaus kintic ffcts play an important rol in th rsonanc rgion. In this study, th first and th scond is modld by Hybrid-PIC(Particl-In-Cll) modl which trats ions and lctrons as particls and fluid, rspctivly. Th assumption of fluid lctron will b obstacl for th modling of powr absorption by ECR. It will b rasonabl, howvr, to undrstand ovrall lctron s bhavior in a discharg chambr, bcaus it was xprimntally confirmd that an lctron s nrgy distribution function is Maxwllian undr a condition of a low powr blow 10 W. 6 Rgarding th third, intraction btwn th microwav and th lctrons is sparatly analyzd with an lctromagntic PIC solvr dvlopd at Kyushu Univrsity. 8 In this solvr, only th lctrons ar tracd with PIC mthod, and th ions as wll as th nutrals ar tratd as background gass. Hraftr, lt us rfr to this solvr as Elctron-PIC. This solvr provids th production rat of ions and th lctron tmpratur, which ar xportd to th Hybrid-PIC solvr. It has to b notd that th ffct of static lctric fild is ignord in this solvr, thus w can xtract phnomnological intraction btwn th microwav and th lctrons from th rsults of th Elctron-PIC. In ordr to considr th ionization rlatd with lctron s acclration by static lctric fild, Townsnd ionization was implmntd in a spcifid rgion. Sinc th plasma in th nutralizr is considrd to b wakly ionizd, th nutrals wr tratd as background gas whos dnsity was fixd to a rsult obtaind from th prliminary DSMC(Dirct Simulation Mont Carlo) analysis. Th ffct of Coulomb collision btwn lctrons and ions, howvr, was implmntd in th Hyrid-PIC and th Elctron-PIC, bcaus it cannot b ignord in comparison with th collisions btwn lctrons and nutrals. Th ovrall flow chart of this simulation is summarizd in Fig. 4. C. Hybrid-PIC Modl In this modl, th motion of ions is tracd with PIC mthod. dxi dvi vi, E vi B (1) dt dt mi Th charg xchang collision and lastic collision with nutrals ar takn into account in th ion PIC. Th plasma was assumd to b wakly ionizd, thus an ion was vanishd onc it rachd a wall to simulat ion s rcombination with an lctron on a wall. Th production rat of ions causd by th microwav discharg is importd from th Elctron-PIC cod dscribd in th nxt sction. In addition, sinc th Elctron-PIC dos not tak static lctric fild into account, ionization by lctrons which acclratd by static lctric fild around orific xit, i.. Townsnd ionization, has to b implmntd sparatly. This ionization was considrd in th Hybrid-PIC, and was incorporatd insid th orific and in th plum rgion. Thn, ions wr producd in ach cll in accordanc with a raction rat dfind as follows. k n n (2) f n Th forward raction cofficint k f is a function of lctron s man nrgy, and was obtaind by Bolsig+. 9 In this simulation, th lctron s man nrgy was dfind as a sum of a thrmal nrgy and a man kintic nrgy. Th motion of lctrons is xprssd by th following drift-diffusion modl, μ // p u // μ E//, u U β U b (3) n whr μ p μ K B B B E φ, μ, U μe, μ, β, b. m ν n 2 1 β 16B m ν B h h 4 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

5 Th mobility prpndicular to th magntic fild includs th ffct of Bohm diffusion, whr th constant of K B is fixd to Th lctron s collision frquncy includs th collision with ions as wll as with nutrals. With this modl and th currnt consrvation law, j n ui u 0 (4) a Poisson quation to yild static lctric fild can b drivd. n μ μ b φ b μ φ β μ φ b,,, μ μ, μ, β μ, (5) nui b p b p p b Ths formulations ar basd on th assumption that th static lctric fild and th microwav lctric fild can b dscribd sparatly, i.. th lctric fild discussd hr rprsnts only a tim-avragd static lctric fild, bcaus th harmonic microwav lctric fild can b vanishd by tim-avraging. Such tratmnt of th lctric fild is sn in th litratur about th microwav discharg simulation Assuming quasi-nutrality, th lctron numbr dnsity is qual to th ion numbr dnsity obtaind from th ion PIC. Th position and th vlocity of ions wr tim-marchd with lap-frog mthod. Equation 5 was discrtizd with a finit lmnt mthod, and was solvd with a dirct mthod, bcaus th diagonal dominanc of obtaind linar systm is not assurd du to high Hall paramtr. It was assumd that all walls ar groundd, i.. th lctric potntial of th all walls is zro. Howvr, sinc th Hybrid-PIC modl assums quasi-nutrality, th boundary condition for th lctric potntial on th walls has to b paid attntion. In th vicinity of th walls contacting with plasma, thr is a shath rgion, whr a stp potntial drop xists and th assumption of quasi-nutrality bcoms invalid. To tak th shath into considration, a shath modl should b applid to th boundary condition of th lctric potntial. In this study, th following quality is usd as a shath modl, 1 φ sh nu n nc xp (6) 4 kt whr n and φ sh dnot a normal vctor toward a wall surfac and a shath potntial, rspctivly. On th othr hand, a potntial valu of th virtual anod was spcifid xplicitly. D. Elctron-PIC Modl Th govrning quations of th Elctron-PIC ar th quation of motion of lctrons and Maxwll quation. 8 dx dt dv v, E v B (7) dt m H E E μ0, H ε0 j (8) t t Hr μ 0 and ε 0 ar th prmability and prmittivity of vacuum, rspctivly. Contrary to th Hybrid-PIC formulation, th lctric fild in Eq. 7 dnots microwav lctric fild. In th PIC of lctrons, lastic, xcitation, and ionization collisions btwn lctrons and nutrals wr implmntd by mans of Null-collision mthod. 14 By counting th ionization collisions, w can stimat th ion production rat pr unit tim at ach cll. In addition, w implmntd Coulomb collision btwn lctrons and background ions, bcaus its collision frquncy is comparabl to that btwn lctrons and nutrals. Th lctron tmpratur was dtrmind by NM S 2 T V (9) 3R NM 1 NM whr N M M m1 N ( m) M ( m) N m1 i1 ( m) M N ( m) i, V, S v. N M v ( m) i m1 i1 Hr, M dnots th numbr of nsmbl sampling, and N (m) is th numbr of supr particls in a cll for a sampl of m. Sinc this solvr dos not includ th ffct of static lctric fild, th shath rgion should b tratd in a spcial mannr. On th boundaris, if an lctron s nrgy is mor than a shath voltag stimatd by th Hybrid-PIC, th lctron was vanishd on th wall, and if not, th lctron was rflctd without nrgy loss. 2 5 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

6 Th powr of microwav was controlld by th strngth of lctric fild applid at th root of th antnna in th Elctron-PIC, i.. th strngth of th lctric fild at th root of th antnna was adjustd vry priod so that a tmporary input powr injctd into th plasma approachs a spcifid powr, which can b formulatd as, P' E E P θp P' θ 1 (10) t t 2 P' whr θ, P, and P ar a proportional constant, a spcifid input powr, and a tmporary input powr calculatd by tim-intgral of a Poynting flux at th root of th antnna. Hr, th tmporary input powr is assumd to b proportional to th squar of lctric fild at th root of th antnna. E. Calculation Conditions Th calculation conditions ar listd in Tabl 1. In th prliminary DSMC simulation of nutrals, th mass flow rat of a working gas (X) was fixd to 0.5 sccm. On th boundaris, a diffus rflction condition was imposd, whr th wall tmpratur was assumd to b 373 K. Th microwav frquncy assumd in th Elctron-PIC was 2.45 GHz, thus ECR rgions appar at a magntic flux dnsity of T as shown in Fig. 2. Th Elctron-PIC was tim-intgratd for 10 ns in ach analysis, whr th initial lctron tmpratur was st to 2 V in all cass. Th ion production rat and th lctron tmpratur wr tim-avragd during th lattr 5 ns. Ths tim-avragd data wr importd in th Hybrid-PIC only in th rgion upstram of th orific ntranc. Th ionization rat intrior of th orific was calculatd by Eq. 2, and ionization in th plum rgion was not modld. Aftr convrgnc of th Hybrid-PIC, th ion(lctron) numbr dnsity was fd back to th Elctron-PIC. In this papr, two potntial valus of th virtual anod wr xamind. Th xprimntal rsults of our nutralizr discussd latr showd that a transition to a high currnt mod appars at a bias voltag of 35 V whn dcrasing th voltag, and at 37.8 V whn incrasing th voltag. Thrfor th potntial valus of 20 and 38 V wr chosn to simulat both a low currnt mod and a high currnt mod. According to th plasma diagnosis with lctron xtraction, 15 th lctron tmpratur in th orific and plum rgion is about 3 V at a low currnt mod, vn though th lctron tmpratur within th discharg chambr is 2 V. This will b du to th Joul hating by lctrons acclratd toward downstram rgion. It is infrrd that th lctron tmpratur in th orific and th plum rgion is incrasd at a high currnt mod. Hnc, in th rgion downstram of orific ntranc (x > 16 mm), whn th anod potntial φ a is 20 and 38 V, th lctron tmpratur was artificially fixd to 3 and 4 V, rspctivly. Th wight of a supr-particl was st to in th Elctron-PIC, and in th Hybrid-PIC, and whn φ a = 20 V and 38 V, rspctivly. Tabl 1. Calculation Conditions. Cas1 Cas2 Working gas X Mass flow rat 0.5 sccm Microwav frquncy 2.45 GHz Input powr 8 W Initial lctron tmpratur of Elctron-PIC 2 V Potntial of virtual anod 20 V 38 V Elctron tmpratur in x > 16mm 3 V 4 V 6 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

7 III. Rsults and Discussion A. Nutral Dnsity Figur 5 shows th numbr dnsity and axial vlocity distributions of th nutrals obtaind by th DSMC analysis. Around th antnna, th dnsity is about m -3. This valu is consistnt with rough stimation of a numbr dnsity by us of th mass flow rat and a conductanc modifid with Clausing s factor. Sinc th prsnt aspct ratio of th orific is L/D=1.6, th Clausing s factor is stimatd about 0.4. Thn, assuming T = 373 K in th nutralizr and p = 0 Pa in th plum rgion, th stimatd numbr dnsity in th nutralizr is m -3, thus th simulatd rsult sms rasonabl. Th man fr path of nutrals is about 12 mm, which lads to a Knudsn numbr about unity. Th numbr dnsity diminishs gradually though th orific, and rapidly dcrass down to m -3 in th plum rgion. Figur 5. Numbr dnsity of nutrals, m -3. B. Plasma Proprtis Th ion dnsity distributions at th symmtric plum (z = 0 mm) ar shown in Fig. 6. In both cass, high ion dnsity rgion is formd btwn th tip of th antnna and th front yok. According to a photograph takn from downstram sid in Rf.6, th intnsity of mission is highst around th antnna, which will assur th validity of th simulation rsult. A cut off dnsity of 2.45 GHz microwav is m -3, thus th plasma around th antnna is in th stat of ovr-dns condition, which was also confirmd xprimntally by mans of a prob masurmnt. 4,6 Th obliqu distribution of th high dnsity rgion is du to th high ionization rat in this rgion. Figur 7 shows th ionization sits during 5 ns obtaind by Elctron-PIC. In this figur, ionization sits btwn -2 < z < 2 mm ar plottd. It can b sn that many ionization collisions occur btwn th tip of th antnna and th front yok. It is considrd that highly nrgizd lctrons ar trappd to th magntic fild, and dirctly ioniz nutrals during bouncing motions, which is suggstd by th lctron tmpratur distribution shown in Fig. 8 obtaind by Elctron-PIC. Th lctron tmpratur amounts to 5 V around th antnna, and a band of high tmpratur rgion of 3-4 V is formd btwn th antnna and th front yok. In th Cas2, th dnsity has a pak btwn th antnna and th back yok. It is considrd that producd lctrons tnd to b accumulatd in this rgion, sinc th tip of th antnna is rlativly clos to th high magntic fild rgion around th back yok. In spit of th sam calculation condition of Elctron-PIC in both cass, th amount of ion productions by microwav discharg is considrably incrasd in Cas2. This will b attributd to additional ions supplid from th orific rgion. In th orific and th plum rgion, th Townsnd ionization maks th ion dnsity incrasd up to m -3 in both Cass. Evn though th amount of ion production insid th orific was lss than th half of ion production by microwav discharg, th Townsnd ionization has a significant impact on th microwav discharg. Th rsult implis that th incras in th ion production rat at th high currnt mod is not strongly rlatd with th lctron s nrgy but with th grown dnsity, bcaus th lctron tmpratur around th antnna is narly th sam in both cass. Figur 9 shows th lctric potntial distributions. It can b sn that th high potntial rgion appars btwn th antnna and th front yok lik th dnsity distribution. Th similarity btwn th dnsity and th potntial distribution suggsts that th dnsity is approximatly linkd with th lctric potntial by Boltzmann rlation along th magntic fild. Th ions producd btwn th antnna and th front yok is radially acclratd by this potntial gradint. In th rgion downstram of th orific ntranc, howvr, th potntial gradually incrass toward th virtual anod. Thrfor ions producd by th microwav discharg hardly rach th orific xit. Most of th ions jctd toward th plum rgion originat from Townsnd ionization around th orific xit. 7 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

8 (a)cas1: Low currnt mod (φ a = 20 V) (b)cas2: High currnt mod (φ a = 38 V) Figur 6. Numbr dnsity of ions, (a): in m -3, (b): in m -3. (a)cas1: Low currnt mod (φ a = 20 V) (b)cas2: High currnt mod (φ a = 38 V) Figur 7. Ionization collision sits obtaind by Elctron-PIC during 5 ns: Ionization sits btwn -2 mm < z < 2 mm ar plottd. Ionization sits insid th orific ar ignord in ths figurs. (a)cas1: Low currnt mod (φ a = 20 V) (b) Cas2: High currnt mod (φ a = 38 V) Figur 8. Elctron tmpratur, V : In x < 16 mm, th lctron tmpratur obtaind by Elctron-PIC is shown. In x > 16 mm, th lctron tmpratur was artificially fixd to 3 V and 4 V in Cas1 and Cas2, rspctivly. 8 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

9 (a)cas1: Low currnt mod (φ a = 20 V) (b)cas2: High currnt mod (φ a = 38 V) Figur 9. Elctric Potntial, V. (a)cas1: Low currnt mod (φ a = 20 V) (b)cas2: High currnt mod (φ a = 38 V) Figur 10. Currnt into ach componnt. Figur 11. Voltag-Currnt Charactristics. C. Currnt Distribution Th ions producd mainly btwn th tip of th antnna and th front yok ar acclratd radially by th static lctric fild, and flow in th chambr wall. From th simulation rsults, th ion and lctron currnts into ach componnt wr calculatd as shown in Fig. 10 (also s Fig. 1). Th lctron currnt was stimatd by mans of Eq. 9 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

10 6. It is rmarkabl that, in Cas1, th lctron currnt is dominant at th antnna du to th high lctron tmpratur around th antnna, i.. highly nrgizd lctrons can ovrcom th shath potntial on th antnna. This fatur was also obsrvd in th xprimnt of μ10 nutralizr. 5 Th amount of th lctron currnt is quit larg on th orific du to its larg surfac ara and assumd high lctron tmpratur. On th othr hand, in Cas2, lctron currnts into ach componnt ar almost zro du to a larg shath potntial on th walls, sinc th highr bias voltag lads to highr lctric potntial within th discharg chambr. Comparing th Cas1 with th Cas2, incrasing rat of th ion currnt into th orific is th highst in all componnts. This is attributd to th nhancd ionization insid th orific. D. Voltag-Currnt Charactristics Th nutralization currnt is compard with th xprimntal data obtaind by authors at Kyushu Univrsity. In th xprimnt, an anod plat was locatd 20 mm apart from th orific xit. Figur 11 shows th obtaind voltagcurrnt charactristics, and simulatd valus ar also plottd. Th simulatd valus wr stimatd by intgrating lctron flux dfind by Eq. 6 on th virtual anod. It should b notd that th bias voltag of th simulation dos not corrspond to th bias voltag of th xprimnt bcaus of th diffrnt plum lngth and xistnc of an anod shath. Evn though th potntial gradint in th plum rgion is quit modrat, th sum of th potntial drop in th rmaining plum rgion and an anod shath drop will b 5-10 V. 7 Thrfor th currnt should b compard with th xprimnt at a highr bias voltag about 5-10 V. Th simulation rsults, howvr, ar plottd at a potntial of th virtual anod bcaus of th uncrtainty of th potntial drop in th rmaining plum rgion and th anod shath. Th simulation rsult of Cas1 agrs wll with th xprimntal data, vn allowing for th uncrtain surplus potntial drop bcaus th discharg currnt is almost constant at th low currnt mod. Th agrmnt with th xprimntal valu suggsts that thr is littl ionization procsss in th rmaining plum rgion. On th othr hand, in Cas2, th simulation undrstimats th xtraction currnt in light of th rmaining plum rgion. Th xprimntal valu, howvr, will contain th lctrons producd in th rmaining plum rgion. Thrfor, th undrstimation of th currnt may b justifid. For furthr undrstanding, not only a simulation of th discharg chambr but also a plum analysis will b ncssary. IV. Conclusion Th thr dimnsional Hybrid-PIC solvr has bn dvlopd to simulat a microwav nutralizr in th ion s tim/spac scals. Th microwav discharg was modld with anothr lctromagntic cod rfrrd to as Elctron- PIC, which can provid th Hybrid-PIC with th local ion production rat and th lctron tmpratur. In th orific and th plum rgion, Townsnd ionization was takn into account in plac of th ionization rat givn by th Elctron-PIC to simulat ionization with rgard to acclratd lctrons. In ordr to dal with on of th most charactristic phnomna of a microwav nutralizr, w focusd on a transition of discharg mod; from low currnt mod to high currnt mod. Undr th condition of a mass flow rat of 0.5 sccm, a microwav powr of 8 W, and a microwav frquncy of 2.45 GHz, a bias voltag applid to a virtual anod was st to 20 V and 38 V to simulat th low currnt mod and th high currnt mod, rspctivly. In both cass, thr appars a high dnsity rgion btwn th antnna and th front yok du to high ionization rat causd by nrgizd bouncing lctrons. In th rgion downstram of th orific ntranc, th ion dnsity is gradually incrasd and amounts to ovr m -3 du to Townsnd ionization, which rsult in a positiv gradint of lctric potntial toward downstram rgion. At th low currnt mod, th lctrons losss ar significant on th orific surfac bcaus of its larg surfac ara and th assumd high lctron tmpratur insid th orific. At th antnna, an lctron currnt is dominant du to th high lctron tmpratur around th antnna. A simulatd lctron xtraction currnt of 22 ma agrs wll with th xprimntal data vn allowing for th potntial drop in th rmaining plum rgion ignord in th simulation. At th high currnt mod, th lctron losss bcom rducd du to a high shath potntial sustaind by th high bias voltag. A simulatd lctron xtraction currnt of 98 ma undrstimats th xprimntal valu, which is probably du to th lctron production in th rmaining plum rgion. 10 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013

11 Rfrncs 1 Nishiyama, K., Hosoda, S., Koizumi, H., Shimizu, Y., Funaki, I., Kuninaka, H., Bodndorfr, M., Kawaguchi, J., and Nakata, D., Hayabusa s Way Back to Earth by Microwav Discharg Ion Engins, AIAA , Hosoda, S., and Kuninaka, H., Th Homward Journy of Astroid Explorr Hayabusa Powrd by th Ion Engin, Journal of Plasma and Fusion Rsarch, Vol. 86, pp , (in Japans) 3 Ohmichi, W., and Kuninaka, H., Dgradation Mchanism of ECR Nutralizr and Countrmasur, IEPC , Satori, S., Funaki, I., and Kuninaka, H., Plasma Diagnostics of Microwav Nutralizr, Journal of th Japan Socity for Aronautical and Spac Scincs, Vol. 47, pp , (in Japans) 5 Ohmichi, W., and Kuninaka, H., Ion Currnt Distribution of ECR Microwav Discharg Nutralizr, AIAA , Funaki, I., and Kuninaka, H., Ovrdns Plasma Production in a Low-Powr Microwav Discharg Elctron Sourc, Japans Journal of Applid Physics, Vol. 40, pp , Kuninaka, H., and Nishiyama, K., Dvlopmnt of 20cm Diamtr Microwav Discharg Ion Engin μ20, AIAA , Masui, H., Tashiro, Y., Yamamoto, N., Nakashima, H, and Funaki, I., Analysis of Elctron and Microwav Bhavior in Microwav Discharg Nutralizr, Transactions of th Japan Socity for Aronautical and Spac Scincs, Vol. 49, pp , Haglaar, G. J. M., Pitchford, L. C., Solving th Boltzmann quation to obtain lctron transport cofficints and rat cofficints for fluid modls, Plasma Sourcs Scinc and Tchnology, Vol. 14, pp , Fif, J. M., Nonlinar Hybrid-PIC Modling and Elctrostatic Prov Survy of Hall Thrustrs, Ph. D. Dissrtation, Aronautics and Astronautics Dpt., Massachustts Institut of Tchnology, Cambridg, MA, Yasaka, Y., Fukuyama, A., Hatta, A., and Itatani, R., Two-dimnsional Modling of Elctron Cyclotron Rsonanc Plasma Production, Journal of Applid Physics, Vol.72, No. 7, pp , Williamson, M. C., Lichtnbrg, A. J., and Librman, M. A., Slf-consistnt Elctron Cyclotron Rsonanc Absorption in a Plamsa with Varying Paramtrs, Journal of Applid Physics, Vol. 72, No. 9, Yasaka, Y., and Uda, N., Practical Schm for Thr-dimnsional Simulation of Elctron Cyclotron Rsonanc Plasma Ractors, Journal of Applid Physics, Vol. 89, No. 7, pp , Vahdi, V., and Surndra, M., A Mont Carlo Collision Modl for th Particl-In-Cll Mthod: Applications to Argon and Oxygn Dischargs, Computr Physics Communications, Vol. 87, No. 179, Onodra, N., Takgahara, H., Nishiyama, K., Funaki, I., and Kuninaka, H., Elctron Emission Mchanism of Microwav Discharg Nutralizr, Journal of th Japan Socity for Aronautical and Spac Scincs, Vol. 49, pp , (in Japans) 11 Th 33rd Intrnational Elctric Propulsion Confrnc, Th Gorg Washington Univrsity, USA Octobr 6 10, 2013