Effects of Electron Model on Three-Grid Ion Engine Analyses

Transcription

1 Effcts of Elctron Modl on Thr-Grid Ion Engin Analyss IEPC Prsntd at th 32nd Intrnational Elctric Propulsion Confrnc, Wisbadn Grmany Takshi Miyasaka 1 and Katsuo Asato 2 Gifu Univrsity, Gifu, , Japan Fakhuradzi B. Baharudin 3 Gifu Univrsity, Gifu, , Japan Hitoshi Sugiyama 4 Gifu Univrsity, Gifu, , Japan and Ikkoh Funaki 5 JAXA, Sagamihara, Kanagawa, , Japan Abstract: To invstigat th ffcts of th lctron modl in ion ngin analysis, w carrid out thr-dimnsional particl simulations using th full-pic and hybrid PIC cods. Comparison of th rsults obtaind using th two cods nabld us to undrstand th influnc of th Boltzmann rlation on th lctric potntial distribution. Th rsults rval that th numbr dnsity of nutralizing lctrons in th vicinity of th cntrlin of th hol downstram of a dcl grid obtaind using th hybrid-pic cod is highr than that obtaind using th full-pic cod. Th high numbr dnsity of lctrons in this rgion dcrass th lctric potntial. k m i m n i n T w 0 = lmntary lctric charg = Boltzmann constant = ion mass = lctron mass = ion numbr dnsity = lctron numbr dnsity = lctron tmpratur = axial vlocity = lctric potntial = prmittivity of fr spac Nomnclatur 1 Associat profssor, Dpartmnt of Human and Information Systms, miyasaka@gifu-u.ac.jp. 2 Profssor, Dpartmnt of Human and Information Systms, asato@gifu-u.ac.jp. 3 Graduat studnt, Dpartmnt of Human and Information Systms, p @du.gifu-u.ac.jp. 4 Graduat studnt, Dpartmnt of Human and Information Systms, q @du.gifu-u.ac.jp. 5 Associat profssor, ISAS, funaki@isas.jaxa.jp. 1

2 I. Introduction Ion ngins ar promising for us as spac propulsion systms, and numrous xprimntal and numrical studis on ion ngins hav bn carrid out. Th 10 ngin was usd as th main ngin of th astroid prob Hayabusa. 1 Owing to thir high spcific impuls, ion ngins ar xpctd to b usd in long-trm mission satllits and probs. It is important to valuat th ngin liftim for such long-trm missions. Howvr, ral-tim valuation bcoms incrasingly difficult with incrasing opration tim. Thrfor, mthods for numrically prdicting th liftim ar rquird. In prvious numrical analyss of ion ngins, 3-7 various typs of modls hav bn mployd and th ion ngin prformanc was prdictd wll. To us numrical analysis as a tool for valuating th ngin liftim, a cod that prdicts grid rosion quantitativly is rquird. 2 Grid rosion is causd by th impact of "collidd ions" producd by collisions btwn nutrals and th constitutiv part of th ion bam. Figur 1 shows a schmatic of th impact of collidd ions on th accl and dcl grids. Th tracking of ion motion and collisions nabls us to stimat th rat of grid rosion (s Fig. 2). Howvr, th calculation tim bcoms hug bcaus thr-dimnsional analysis is rquird. In most cods, th lctron numbr dnsity is stimatd from th Boltzmann rlation. Bcaus th Boltzmann rlation is indpndnt of th tim stp, which is dtrmind by th charactristic spd of lctrons, much highr than that of ions, th calculation cost is rducd. Thus, th Boltzmann rlation is appropriat for thr-dimnsional analysis. Howvr, th Boltzmann rlation is a modl for th lctron numbr dnsity distribution. Thus, th validity of th modl should b confirmd bfor th quantitativ valuation of grid rosion. To invstigat th applicability of th Boltzmann rlation to th valuations of grid rosion, w hav bn prforming particl analyss on ion ngins using full particl in cll (full-pic) mthod, 8 in which ions and lctrons ar tratd as particls. 9,10 In our prvious studis, 9 analyss of th two-grid ion ngins usd in th xprimnts carrid out by Hayakawa 11 wr prformd. Th calculatd grid currnts agrd wll with thos obtaind xprimntally, and a charactristic rosion pattrn rfrrd to as "pits & groovs" was obsrvd in th stimatd rosion distribution of th downstram surfac of th accl grid. Figur 1. Schmatic of impact of collidd ions on accl and dcl grids. Figur 2. Distribution of collidd ion particls. In th prsnt study, a full-pic analysis of a Hayabusa typ thr-grid ion ngin was carrid out. To invstigat th ffct of th Boltzmann rlation in thr-grid ion ngin analyss, a hybrid-pic analysis using th Boltzmann rlation was also prformd. By th comparison of th lctric potntial distribution and th numbr dnsity distribution of lctrons obtaind from th two analyss, th applicability of th Boltzmann rlation to thr-grid ion ngins is discussd. II. Numrical procdurs Full-PIC and hybrid-pic analyss wr prformd with th sam oprational conditions and ngin gomtris. Th propllant was assumd to b xnon. Th following numrical procdurs wr applid in th prsnt analyss (s Fig. 3). A. Full-PIC analysis Th motion of chargd particls is calculatd by th full-pic mthod. Both ions and lctrons ar tratd as particls and mov according to rlativ quations of motion. For th quantitativ valuations in this study, th 4thordr Rung-Kutta-Gill mthod is mployd for th tim intgration of th quations of motion. Th tim stp rquird for lctron motion is much lowr than that for ion motion, rsulting in a hug calculation tim. Thus, to shortn th calculation tim, an artificial lctron mass, assumd to b tims smallr than th ion mass, is 2

3 introducd. In past work, 10 it was found that for a ratio of ion mass to lctron mass of highr than 10000, th lctron distribution was narly indpndnt of th ratio. Elctric potntial distributions ar obtaind by solving th Poisson quation by th FEM (finit lmnt mthod). n i n. (1) 0 Th numbr dnsitis of chargd particls obtaind by calculating th quation of motion ar usd in calculation of Eq. (1). Elastic and charg-xchangd collisions btwn th ions constituting th ion bam and th nutrals ar calculatd. This analysis also trats multipl collisions btwn collidd ions and nutrals. Owing to th high numbr dnsity of nutrals compard with that of ions, th numbr dnsity distribution of nutrals is fixd throughout th analyss. Th distribution is calculatd by th DSMC (dirct simulation of Mont Carlo) mthod in advanc. Bcaus of th low ratio of th numbr dnsity of collidd ions to that of th ions constituting th ion bam, if a collision occurs, a collidd ion and a collidd nutral ar addd to th simulation. B. Hybrid-PIC analysis Th numrical procdurs in th hybrid-pic analysis ar almost th sam as thos in th full-pic analysis xcpt for th tratmnt of th lctron motion. In th hybrid-pic analysis, th numbr dnsity distribution of lctrons is stimatd from th Boltzmann rlation. n n, rf xp kt, rf Th lctric potntial and lctron numbr dnsity of th plasma at th upstram boundary, p and n, p, ar usd as th rfrnc valus p,rf and n, rf in Eq. (2), rspctivly. Th lctric potntial and dnsity of lctrons, and n,, at th downstram boundary ar rspctivly usd as p,rf and n, rf for th nutralizing lctrons. In this study, p and ar 1510 and 0 V, rspctivly. Th lctric potntials on th scrn grid, on th accl grid, and on th dcl grid, s, A, and D, ar st to 1500, -400, and 0, rspctivly. By itrativ calculation using Eqs. (1) and (2), slf-consistnt lctric potntial and lctron numbr dnsity distributions ar obtaind for th ion numbr dnsity distribution obtaind from th quation of motion. rf. (2) Figur 3. Schmatic of numrical procdur Figur 4. Schmatic of thr-dimnsional calculation domain and conditions C. Calculation domain and numrical conditions Th gomtric paramtrs ar chosn to b similar to thos in th 10 ion ngin. To shortn th calculation tim, th thr-dimnsional calculation domain is limitd to a rctangular paralllpipd by applying som symmtry conditions, as shown in Fig. 4. Mirror rflction conditions ar applid to th boundary surfacs xcpt for th 3

4 surfac at y= y max, whr a lin symmtry condition is applid. A rctangular grid with 43, 39, and 181 grid points in th x-, y-, and z-dirctions, rspctivly, is usd. Uniform grid sizs ar st in th x- and y-dirctions and a nonuniform grid siz is st in th z-dirction. At th upstram boundary, th ion numbr dnsitis of th plasma n i, p = n, p ar applid. Elctrons with th Maxwll distribution for a tmpratur of 5 V and ions with a fixd axial vlocity flow into th calculation domain. Th ion numbr dnsity of th plasma is dtrmind from th bamlt currnt. In th prsnt analyss, th bamlt currnt was st to 0.3 ma. On th downstram boundary surfac, th numbr dnsity of nutralizing lctrons is st to th avrag ion dnsity of th bamlt. Nutralizing lctrons flow into th nutralizing rgion with th Maxwll distribution for a tmpratur of 5 V. III. Rsults and discussion A. Elctric potntial and numbr dnsity of lctrons distributions Figur 5 shows a comparison btwn th lctric potntial distributions at y = 0 mm obtaind by th full-pic and hybrid-pic analyss. Th two distributions agr wll xcpt for in th nutralizing rgion downstram of th dcl grid. In th vicinity of th hol cntr and downstram of th dcl grid, th lctric potntial for th full-pic analysis is highr than that for th hybrid-pic analysis. Figur 6 shows th lctric potntial distributions in th x-y plan along th whit lin shown in Fig. 5 for both analyss. In Fig. 6, a diffrnc in th lctric potntial can b clarly obsrvd. Figur 7 shows a comparison btwn th numbr dnsity distributions of lctrons at y = 0 mm obtaind by th two analyss. Th numbr dnsity of lctrons in th vicinity of th hol cntr and downstram of th dcl grid for th full-pic analysis is lowr than that for th hybrid-pic analysis. Th diffrnc can also b obsrvd clarly in Fig. 8. Ths rsults indicat that th low numbr dnsity in this rgion causs th high lctric potntial for th full-pic analysis. Namly, in this rgion, th lctric potntial distribution is affctd by th Boltzmann rlation. Th motion of ions is dtrmind by th lctric potntial distribution. Ths rsults suggst that th Boltzmann rlation may influnc th rat of grid rosion. a) b) Figur 5. Two-dimnsional distributions of lctric potntial (y=0) obtaind by a) full-pic analysis and b) hybrid-pic analysis. a) b) Figur 6. Two-dimnsional distributions of lctric potntial along whit lin in Fig. 5 obtaind by a) full-pic analysis and b) hybrid- PIC analysis. a) b) Figur 7. Two-dimnsional distributions of lctron numbr dnsity (y=0) obtaind by a) full-pic analysis and b) hybrid-pic analysis. a) b) Figur 8. Two-dimnsional distributions of lctron numbr dnsity along whit lin in Fig. 5 obtaind by a) full-pic analysis and b) hybrid-pic analysis. 4

5 B. Vlocity distribution of lctrons To invstigat th diffrnc btwn th distributions of th lctron numbr dnsity obtaind by th full-pic and hybrid-pic analyss, th vlocity distributions of lctrons obtaind by th full-pic analysis wr invstigatd. Figur 9 shows th calculatd axial vlocity distributions of lctrons at points (A) and (B) in th upstram rgion, as shown in Figs. 5 and 7. Each distribution agrs wll with th Maxwll distribution f, whr f n m 2 kt 1 mw xp 2 k T 2. (3) a) b) Figur 9. Axial vlocity distributions of lctrons at a) (A) and b) (B) obtaind by full-pic analysis and vlocity distributions f.. Figur 10 shows th axial distributions of th lctron numbr dnsitis and lctric potntials along th cntrlin of th grid hol in th nutralizing rgion obtaind by th two analyss (s Fig. 7). Th numbr dnsity distribution of lctrons stimatd from th Boltzmann rlation for th lctric potntial obtaind by th full-pic analysis is also givn in Fig. 10. Th lctron numbr dnsity for th full-pic analysis is much lowr than that stimatd from th Boltzmann rlation. Th axial vlocity distribution of lctrons at point (C) in Fig. 10, whr th lctric potntial is highr than that on th boundary, is shown in Fig. 11. Th distribution at (C) diffrs from th Figur 10. Axial distributions of ion and lctron numbr dnsitis and lctric potntials along th cntrlin of th grid hol in th nutralizing rgion obtaind by full-pic and hybrid-pic analyss. Figur 11. Axial vlocity distribution of lctrons at (C) obtaind by full-pic analysis and vlocity distributions f and g. 5

6 Maxwll distribution f. Th lctrons flowing from th downstram boundary with th Maxwll distribution ar acclratd by th positiv diffrnc btwn th lctric potntials at (C) and at th boundary. Thus, th ratio of lctrons in th low-vlocity rgion dcrass. Figur 11 rvals that th high ratio of lctrons in th high-vlocity rgion satisfis th vlocity distribution including th ffct of th diffrnc btwn th lctric potntials g, givn by g n, rf m 2 kt 1 2 mw rf xp 2 k T. (4) Th lctric potntial and lctron numbr dnsity for th hybrid analysis ar slf-consistnt solutions of Eqs. (1) and (2). Bcaus of th supprssion of th positiv lctric potntial in th nutralizing rgion, th lctron numbr dnsity for th hybrid-pic analysis bcoms low compard with that stimatd from th Boltzmann rlation using th lctric potntial in th full-pic analysis. Howvr, diffrncs btwn th distributions of th lctric potntial and lctron numbr dnsity for th full-pic and hybrid-pic analyss ar obsrvd in Fig. 10. IV. Conclusion Diffrncs btwn th lctric potntials and lctron numbr dnsitis obtaind by a full-pic analysis and a hybrid-pic analysis mploying th Boltzmann rlation wr obsrvd in th nutralizing rgion of a simulatd thrgrid ion ngin. In this rgion, th lctron numbr dnsity obtaind by th full-pic analysis diffrs from that obtaind using Boltzmann rlation. This diffrnc btwn th lctron numbr dnsitis is causd by th non- Maxwllian lctrons in th positiv-lctric-potntial rgion in th full-pic analysis. Acknowldgmnts This work was supportd by Japan Arospac Exploration Agncy undr cooprativ rsarch projct. Th authors would lik to thank mmbrs of th JIEDI (JAXA Ion Engin Dvlopmnt Initiativs) projct for thir supports. Rfrncs 1 Funaki, I., Kuninaka, H. and Toki, K., "Plasma Charactrization of a 10-cm Diamtr Microwav Discharg Ion Thrustr," J. Propulsion and Powr, Vol. 20, No.4, 2004, pp Kuninaka, H, "Rsarch and Dvlopmnt of JIEDI (JAXA Ion Engin Dvlopmnt Initiativs) Tool for Numrical Evaluation of Ion Engin Grid Liftim," JAXA Spcial Publication, JAXA-SP , pp.5-9, 2007 (in Japans). 3 Nakano, M, "Thr-dimnsional Simulations of Ion Engin Grid Erosion," Advancs in Applid Plasma Scinc, Vol. 6, 2007, pp Nakayama, N. and Wilbur, P.J., "Numrical Simulation of Ion Bam Optics for Multipl-grid Systms," J. Propulsion and Powr, Vol. 19, No.4, 2003, pp Wang, J., Cao, Y., Kafafy, R., Martinz, R., and Williams, J., "Ion Impingmnt Limits of Sub-Scal Ion Optics: Comparison of Simulation and Exprimnt," AIAA papr , Tartz, M., Hartmann, E., Dltschw, R., and Numann, H., "Validation of a Grid Erosion Simulation by Short-tim Erosion Masurmnts," Procdings of th 26th Intrnational Elctric Propulsion Confrnc, IEPC , Okawa, Y., Takgahara, H., "Particl Simulation on Ion Bam Extraction Phnomna in an Ion Thrustr," Procdings of th 26th Intrnational Elctric Propulsion Confrnc, IEPC , Birdsall, C.K. and Langdon, A.B., Plasma Physics via Computr Simulation, MacGraw-Hill, Miyasaka, T, Kobayashi, T., and Asato, K., "Charactristics of Ions Impacting Grid Surfacs in an Ion Engin," Vacuum, Vol. 85, No. 5, 2010, pp Miyasaka, T, Kobayashi, T., and Asato, K., "Numrical Prdiction of Grid Erosion of Ion Engin," Trans. of th Japan Soc. for Aronautical and Spac Scincs, Arospac Tchnology Japan [onlin journal], Vol. 8, No. ists27, 2010, pp.pb_61-pb_66, URL: [citd 9 March 2011]. 11 Hayakawa, Y., "Currnt Distribution on a Two-grid-ion-xtraction-systm Gridlt," JAXA Spcial Publication: JAXA-SP , pp.20-27, 2007 (in Japans). 6