Space Potential Fluctuation in an Anode-layer Hall Thruster

Transcription

1 Spac Potntial Fluctuation in an -layr Hall Thrustr IEPC-5-4 Prsntd at th 9 th Intrnational Elctric Propulsion Confrnc, Princton Univrsity, Octobr 3 Novmbr 4, 5 Shigru Yokota *, Kimiya Komurasaki, and Yoshihiro Arakawa Th Univrsity of Tokyo, Dpartmnt of Aronautics and Astronautics, Hongo 7-3-, Bunkyo, Tokyo , JAPAN Abstract: Th lctrical shath structur insid a hollow anod and plasma dynamics in a discharg channl wr numrically computd using a fully kinticd3v Particl-in-Cll (PIC) / Dirct Simulation Mont Carlo (DSMC) cod. By trating both lctrons and ions as particls, tmporal and spatial variations of th nonnutral plasma structur nar th anod surfac wr analyzd. As a rsult, brathing mod ionization oscillation obsrvd in an anod-layr thrustr was wll rproducd. Th potntial drop ovr th anod surfac was fluctuatd with plasma dnsity fluctuation. Rsulting variation of substantial anod ara was found nhancing th oscillation. Nomnclatur B = magntic flux dnsity D = anod hollow width = lctric charg E = lctric fild strngth I d = discharg currnt m = particl mass n = numbr dnsity t = tim V d = discharg voltag x = position Z = distanc btwn anod tip and channl xit = fr spac prmability = spac potntial = collision frquncy r, z, = cylindrical coordinat = anod xit = lctron i = ion n = nutral Subscripts * Graduatd Studnt, Th Univrsity of Tokyo, yokota@al.t.u-tokyo.ac.jp Associat Profssor, Th Univrsity of Tokyo, komurasaki@al.t.u-tokyo.ac.jp Profssor, Th Univrsity of Tokyo, arakawa@al.t.u-tokyo.ac.jp Octobr 3 Novmbr 4, 5

2 I. Introduction ischarg instability in anod layr hall thrustrs would b on of th srious problms to b ovrcom. A Dhollow anod is commonly usd to stabiliz th discharg for ths thrustrs. -3) Howvr, th mchanism of discharg stabilization using a hollow anod has not bn clarifid yt and optimization of anod dsign has not bn don. Th goal of our study is to modl th anod shath, which has a grat ffct on th stabl discharg of anod layr hall thrustrs, and find out a scaling law for th anod dsign. In th computational study, th structur of lctrical shath insid a hollow anod was numrically simulatd using fully kintic D3V Particl-in-Cll (PIC) and Dirct Simulation Mont Carlo (DSMC) mthodologis. 4-9) Th rsults ar compard with th masurmnt using a -kw class anod layr hall thrustr. II. Discharg Currnt Oscillation A kw-class anod layr hall thrustr with a hollow anod has bn dsignd and fabricatd as shown in Fig.. It has two guard rings mad of stainlss stl. Thy ar kpt at th cathod potntial. Th innr and outr diamtrs of a discharg chambr ar 48mm and 6mm, rspctivly. Magntic flux dnsity is variabl by changing th currnt of a solnoid coil st at th cntr of th thrustr. Dtaild dscription is availabl in Rfs. 3,4). Figur. Th Univrsity of Tokyo Layr Hall Thrustr. Figur. Photograph of th Hollow. A photograph of th Hollow is shown in Fig.. It has an annular hollow anod mad of cuppr. W dfin Z as th distanc btwn th thrustr xit and th tip of anod, and D as th width of propllant channl. Z and D ar varid (Z=~4mm, D=~3mm) in this study. Xnon is usd as a propllant, and th mass flow rat is st at.a q =.37mg/s. Discharg voltag is st at 4V. Figur 3 shows masurd amplitud of discharg currnt oscillation and th tim-avragd discharg currnt I d. Hr, th amplitud of discharg currnt oscillation is dfind as, ( ) d d d I I t. () Oscillation amplitud was snsitiv to magntic flux dnsity B. Although th oscillation is small at B<.4T, th thrust fficincy is poor in this rang of B bcaus of larg lctron backflow currnt. Thrfor, th dsirabl opration condition is limitd in a quit narrow rang of B. Masurd oscillation amplitud is plottd for various anod gomtris in Fig. 4. Thr is a common trnd that oscillation bcoms unstabl with th incras in B as sn in Fig. 3. Th thrshold of B is about.-.5[t]. Octobr 3 Novmbr 4, 5

3 Discharg currnt, A Discharg currnt Oscillation amplitud Dsirabl opration Magntic flux dnsity, T Oscillation amplitud Figur 3. Oscillation charactristics. D=3mm, Z=mm. 4) Oscillation amplitud DZ3 DZ4 DZ DZ3 DZ4 D3Z D3Z D3Z3 D3Z4...3 Magntic flux dnsity, T Figur 4. Rlation btwn oscillation amplitud and B. Z= 4mm, D= 3mm, Vd=4V. 4) III. Computation Mthod It is vry difficult to masur th distributions of lctric potntial and plasma dnsity insid a hollow anod bcaus plasma dnsity is xpctd vry small and th plasma is lctrically non-nutral. Thrfor, structur of lctrical shath insid th hollow anod and plasma dynamics in th discharg channl wr numrically start computd using fully kintic D3V Particl-in-Cll Cll Systm (PIC) and Dirct Simulation Mont Carlo (DSMC) mthodologis. By trating both lctrons and ions Initial condition as a particl, non-nutral plasma structur in th Particl Movmnt shath rgion nar th anod surfac can b Intr-Particl Collision analyzd. Figur 5 shows th flow chart of calculation. 6-9 Spac Potntial Calculation of ral particls ar tratd as on macro particl and all of macro particls ar tratd Elctric Fild Calculation kintically. Elctric and magntic forcs ar implmntd via th PIC mthod and collisions ar Particl Acclration via th DSMC mthod. Th cylindrical coordinat Data Sampling systm (r, z, ) was usd as shown in Fig. 6. Particl s position is xprssd in two-dimnsional t= t+ t spac r and z, whil its vlocity is xprssd in thr-dimnsional spac. That is, particls mov in finish all dirctions, but th azimuthal coordinat is always discardd. Figur 5. A flow chart of th calculation. An orthogonal calculation grid is st, with th axial lngth of th cll gtting smallr toward th discharg channl in ordr to obsrv th sharp fall R of lctron dnsity in th vicinity of anod xit. Th minimum cll lngth is in th sam ordr of th Dby lngth. Figur 7 shows th magntic flux dnsity Z distribution usd in th calculation, that is idntical to th actual distribution in th thrustr. 4) BB is variabl. Figur 6. Th coordinat and th calculation grid. 3 Octobr 3 Novmbr 4, 5

4 anod 5 5 Z,mm Figur 7. Assumd magntic flux dnsity distribution. Tabl. Collisions considrd in th Hall Thrustr and thir typical collision frquncy. Collision Man Fr Rlativ Tim, ps - X Elastic Scattring X Ionization X Excitation X + Coulomb Coulomb X X Scattring Only singly chargd ionization is considrd and mass ratio m /m n is dcrasd from 4-6 to /, to spd up th calculation. Potntial diffrnc btwn anod and plasma at th thrustr xit boundary is st at 5V. Propllant mass flow rat is st at.a q to simulat th xprimnt. Elctrons ar fd from th anod xit with a T =V half-maxwllian vlocity distribution. Considrabl collisions in th Hall thrustr ar shown in Tabl. Th man fr tim and collision frquncy in th tabl ar typical valus whn th particls ar at thir thrmal vlocity. Th thr highst frquncy collisions ar considrd in this simulation. Th simulation tim stp (typically. - s) is st basd on Larmor frquncy, and that is much smallr than - X collision man fr tim. In addition, amorous diffusion is considrd in this cod. Th frquncy of th Bohm diffusion is B Bohm. () 6 m Thrfor, total collision frquncy is dfind as total lastic ionization xcitation Bohm. (3) All th particls mov according to th dynamic quations. Th dynamic quations for lctrons ar xprssd as, and for ions, mz E ( r Br ). (4) r z mr E mr. (5) mr zb mr. (6) i r z mz E. (7) mr E. (8) i r Spac potntial is calculatd using th Poisson s quation as, r ( ni n). (9) z r r r 4 Octobr 3 Novmbr 4, 5

5 IV. Cod Validation A. Th collision part Th collision sction is th most important part of this cod and th PIC-DSMC cod is compard with th dtrministic solution. For asy comparison, th original DSMC cod is modifid to calculat in on cll. In this cod, particls ar confind in a crtain cll and rflct on th cll boundary. Th othr parts ar sam as th original DSMC cod. Th quation to solv th collision part dtrministically is dn n NnN v. () dt V Th nutral numbr which is dcay is gnratd lctron numbr and th sum of ths two particls numbr is constant. N n N const. () v is a function of lctron nrgy and th quation of th total lctron nrgy consrvation is de dt N E N E () ion ion x x whr, N ion is ionization rat, N x is xcitation collision numbr, Eion is ionization nrgy and E x is nrgy loss of xcitation collision. Th rsult is shown in Fig.8. 8 DSMC Dtrministic Tim, s Figur 8. Nutral numbr history in a cll. A comparison of th DSMC cod solution with th dtrministic solution Th charactristic tim is dfind as a tim which nutral numbr dcrass to /. Th dtrministic solution indicats th charactristic tim is about.5-8 s and DSMC solution indicats that is about s. This slight diffrnc is causd by small nrgy lctron. In DSMC cod, scondary lctron, which is gnratd by ionization, has oftn too small nrgy to occur ionization. On th othr hand, in dtrministic solution, lctron nrgy is avragd in ach tim stp. Figur 9 shows lctron nrgy distributions at s, s, and. -8 s. At t= s, lctron nrgy distribution is Boltzmann distribution. As tim incrass, small nrgy lctron numbr incrass by ionization and xcitation collision and lctron nrgy coms off from Boltzmann distribution. This nrgy distribution diffrnc 5 Octobr 3 Novmbr 4, 5

6 maks ionization rat small. As a rsult, th charactristic tim of DSMC cod is longr than that of dtrministic on DSMC Dtrministic solution.5 DSMC Dtrministic solution.5 DSMC Dtrministic solution Elctron nrgy, V 3 4 Elctron nrgy, V 3 4 Elctron nrgy, V (a) t= s (b) t=5. -9 s (c) t=. -8 Figur 9. Nutral numbr history in a cll. B. An rror margin by macro-particl Th probabilistic solution is stpwis bcaus on nutral macro-particl is a clustr of ral nutrals. Figur shows nutral numbr history in two cass; in on cas, 6 macro particls ar in a cll, in th othr cas, 833 macro particls ar in a cll, initially. For finr rsolution, numbr of nutrals includd in a macro particl should b minimizd. In ordr to find out an adquat macro particl numbr in a cll, th charactristic tim is assumd to b an indx. Figur shows th charactristic tim in th ach macro particl numbr cas. This indicats th charactristic tim is about s and mor than macro particls ar ncssary in a cll for accurat rsult macro particls 833 macro particls Tim, s Figur. Nutral numbr history in a cll. On is a cas a macro particl contains 5. 9 ral nutrals. Th othr is Macro particl numbr in a cll Figur. Th variations in charactristic tim C. Comparison of DSMC rsults with xprimntal rsults Finally, calculatd rsults ar tstd with xprimntal rsults. Figur shows th calculatd discharg currnt historis. In th cas of BB=mT, strong discharg oscillation was obsrvd. This is ionization oscillation. Oscillation frquncy(5khz) and th wav shap ar vry clos to th masurd on. Avragd discharg currnt is.8a. In this rgion, th main lctron backflow mchanism has transitd from classical diffusion to Bohm diffusion in th xprimnt. 6 Octobr 3 Novmbr 4, 5

7 .5.5 5kH Discharg currnt, A.5.5 5kH Tim,s (a) Computd rsult Figur Tim, s (b) Exprimntal rsult Discharg currnt history. V. Rsults Figur 3 shows th computd avrag discharg currnt and it s oscillation amplitud. Th amplitud was high at BB.5T. This trnd agrs wll with th masurd on as sn in Figs. 3 and 4. Calculatd two-dimnsional distributions of lctron numbr dnsity ar shown in Fig.. In th cas of BB.4T =.T, magntic confinmnt against th lctron backflow is not nough and larg lctron currnt flows in th discharg channl. In th cas of BB=.4T, lctron is trappd by th magntic fild, and dnsity paks in th middl of discharg channl. Plasma has pntratd into th anod cavity rsulting in larg substantial anod surfac ara that contacts th plasma. Thn, lctrons would b abl to rach th anod smoothly without a larg shath drop. Th ionization raction insid th hollow anod contributs to this profil. Th fraction of propllant gas that is ionizd in th hollow anod is about 3%. In th cas of BB.5T (Fig.4 (c) and (d)) th discharg is oscillating. Th island of high-dnsity lctrons sn insid (Fig.4 (a) and (b)) th distributions ar stabl. For B B Avrag discharg currnt Oscillation amolitud Magntic flux dnsity,mt Figur 3. Computd discharg currnt oscillation amplitud (a)b B =.T (b)b B =.4T (c)b B =.5T T (d) B B =.T Figur 4. Computd lctron numbr dnsity distributions. Contour max. 8 m -3, min. 8 m -3. (a) and (b) ar stady solutions. (c) and (d) ar snapshots of oscillating profils. 7 Octobr 3 Novmbr 4, 5

8 th hollow anod is moving back and forth in th z-dirction. Although th gas is ionizd insid th hollow anod, th dnsity distribution is discontinuous and ionization instability has sn obsrvd. Figur 5 shows lctron currnt dnsity distribution on th anod surfac. Th anod lngth ffctiv for lctron currnt is about mm for D=3mm. Figur 6 shows th computd plasma potntial distributions. In th cas of B.4T, a potntial drop appars at th xit of discharg channl. Th plasma potntial is linarly varid though th anod xit In th cas of BB.5T, potntial starts to dcras at th anod xit. This rapid potntial dcras at th anod xit is idntical to th on without an anod hollow. Th lctron dnsity tnds to b small du to th rapid acclration by th lctric fild rsulting in shortag of plasma dnsity on th anod surfac B =.4[T] B =.5[T] Z, mm Figur 5. Discharg currnt distribution on th anod surfac. (a)b B =.T (b) B B =.4T (c)b B =.5T T (d) B =.T Figur 6. Computd lctric potntial distributions. Contour max 5V, min V. (a) and (b) ar stady solutions. (c) and (d) ar snapshots of oscillating profils. Figur 7 shows th computd lctron tmpratur distributions. In th cas of BB.5T, high tmpratur rgion is limitd in a thin layr locatd at th xit of anod. This is du to th strong lctric fild as sn in Fig. 6. This rapid incras in tmpratur contributs to th high ionization rat insid th hollow anod, and brings th ionization oscillation insid th hollow anod. To supprss th ionization oscillation, linar variation in plasma potntial though th anod xit would b ncssary. As sn in Figs. 6-7, ionization and acclration occurs in a thin layr at th anod xit in th high magntic (a)b=.t (b) B=.4T (c)b=.5t (d) B=.T Figur 7. Computd lctron tmpratur distributions. Contour max V, min V. (a) and (b) ar stady solutions. (c) and (d) ar snapshots of oscillating profils. flux dnsity cass. This is a typical fatur of anod layr typ or shath typ thrustr. Th condition in which th layr appars will b a function of oprating and gomtric paramtrs of th thrustr. Thn, optimization of th hollow anod gomtry for typical oprational condition would b on way to supprss th 8 Octobr 3 Novmbr 4, 5

9 oscillation. Anothr way would b to hav a discharg indpndnt of th main discharg to assist th ionization in th hollow anod. VI. Conclusions Th fully kintic PIC-DSMC cod can rproduc both stabl and unstabl opration mods obsrvd in th xprimnt. In th stabl opration cas, which corrsponds to th low magntic flux dnsity cas, th plasma pntratd into th anod cavity. This larg substantial anod ara would contribut to stabl opration. In th unstabl opration cas, which corrsponds to th high magntic flux dnsity cas, ionization oscillation and spac potntial fluctuation was obsrvd insid th hollow anod. This would b causd by th non-linar variation of plasma potntial at th anod xit. To supprss th ionization oscillation, linar variation in plasma potntial though th anod xit would b ncssary. Rfrncs Smnkin A.V., Tvrdokhlbov S.O., Garkusha V.I., Kochrgin A.V., Chislov G.O., Shumkin B.V., Solodukhin A.V., Zakharnkov L.E., Oprating Envlops of Thrustrs with Layr, IEPC-3, 7th Intrnational Elctric Propulsion Confrnc, Pasadna, USA, Octobr. Smnkin, A., Kochrgin, A., Garkusha, V., Chislov, G., Rusakov, A., RHETT/EPDM Flight Layr Thrustr Dvlopmnt, IEPC-97-6, 5th Intrnational Elctric Propulsion Confrnc, Clvland, USA, August Yamamoto, N., Nakagawa, T., Komurasaki, K., Arakawa, Y., Effct of Discharg Oscillations on Hall Thrustr Prformanc, ISTS -b-7, 3rd th Intrnational Symposium on Spac Tchnology and Scinc, Shiman, Japan, May. 4 Yasui, S., Yamamoto, N., Komurasaki, K., Arakawa, Y., Effct of Shath Structur on Oprating Stability in an Layr Thrustr, Procdings of Asian Joint Confrncs in Propulsion and Powr 4, pp , Soul, Kora, March 4. 5 Hirakawa, M., Particl Simulation of Plasma Phnomna in Hall Thrustrs, IEPC-95-64, 4th Intrnational Elctric Propulsion Confrnc, Moscow, Russia, Sptmbr Szabo, J. J., Fully Kintic Hall Thrustr Modling of a Plasma Thrustr, PhD Thsis, Massachustts Institut of Tchnology,. 7 Szabo, J., Rostlr, P., On and Two Dimnsional Modling of th BHT-, IEPC--3, 8th Intrnational Elctric Propulsion Confrnc, Toulous, Franc, March 3. 8 Kumakura, K., Yasui, S., Komurasaki K., Arakawa, Y., Plasma Modling of a Hollow for an Layr Typ Hall Thrustr IEPC--86, 8th Intrnational Elctric Propulsion Confrnc, Toulous, Franc, March 3. 9 Octobr 3 Novmbr 4, 5