39th AIAA/ASME/SAE/ASEE Joint Propulsion Confrnc an Exhibit -3 July 3, Huntsvill, Alabama AIAA 3-47 FUNCTION OF A HOLLOW ANODE FO AN ANODE LAYE TYPE HALL THUSTE Shinsuk YASUI*, Kn KUMAKUA**, Naoji YAMAMOTO*,Kimiya KOMUASAKI**, an Yoshihiro AAKAWA* Univrsity of Tokyo, Tokyo 3-8656, JAPAN * Dpartmnt of Aronautics an Astronautics ** Dpartmnt of Avanc Enrgy Email: yasui@al.t.u-tokyo.ac.jp ASTACT Th amplitu of ischarg currnt oscillation has bn masur for various hollow ano wihs an axial positions using a kw class ano layr typ Hall thrustr. As a rsult, thr was plasma nsity thrshol for stabl ischarg. Structur of lctrical shath insi a hollow ano was numrically analyz using fully kintic D3V Particl -in-cll (PIC an Dirct Simulation Mont Carlo (DSMC mtho. Th comput shath ara was not so snsitiv to th hollow wih. NOMENCLATUE : magntic inuction D: ano hollow wih E: lctric fil strngth : lctronic charg I: lctric currnt m: particl mass n: numbr nsity : man raius of th ischarg channl S: ano surfac ara T: tmpratur t: tim v: vlocity V: voltag x: position Z: istanc btwn ano tip an channl xit ε : fr spac prmability λ D: Dby lngth µ: magntic prmability τ : man fr tim ϕ : spac potntial r, θ, z: cylinrical coorinat SUSCIPTS : ano xit : ischarg : lctron i : ion n : nutral w : wall INTODUCTION Discharg instability in ano layr typ hall thrustrs woul b on of th srious problms to b ovrcom. A hollow ano is commonly us to stabiliz th ischarg for ths thrustrs as shown in Fig.. -3 Howvr, th function of th hollow ano has not bn clarifi yt an optimization has not bn on. Hollow Fig. Ano layr typ Hall thrustr. In this rsarch, th function of hollow ano is invstigat xprimntally an analytically. Th goal of th stuy is to mol th ano shath, which has a grat ffct on th stabl ischarg of ano layr typ hall thrustrs, an fin out a scaling law for th ano sign. In th xprimntal stuy, a kw class ano layr typ hall thrustr with a hollow ano has bn sign an fabricat in univrsity of Tokyo. 4 (Fig. Amplitu of ischarg currnt oscillation has bn masur for various hollow wihs an axial positions. As for th computational stuy, th structur of lctrical shath insi a hollow ano was numrically simulat using fully kintic D3V Particl-in-Cll (PIC an Dirct Simulation Mont Carlo (DSMC mthoologis. 5-8 Effcts of gomtric paramtrs on th shath structur ar invstigat. Copyright 3 by th Amrican Institut of Aronautics an Astronautics, Inc. All rights rsrv.
Oprating an gomtric paramtrs It has a hollow annular ano ma of cuppr. W fin Z as th istanc btwn th thrustr xit an th tip of ano, an D as th wih of propllant channl as inicat in Fig. 4. Z an D ar vari (Z=~4[mm], D=~3[mm] in this stuy. X is us as a propllant, an th mass flow rat is st at.[a q ]=.37[mg/s]. Discharg voltag is st at 4[V]. Unr such conitions, th amplitu of ischarg currnt oscillation has bn masur for various magntic inuctions. Fig. kw class ano-layr Hall Thrustr. EXPEIMENT Thrustr Th cross sction of thrustr is shown in Fig. 3. It has two guar rings ma of stainlss stl. Thy ar kpt at th catho potntial. Th innr an outr iamtrs of a ischarg chambr ar 48mm an 6mm, rspctivly. A solnoial coil is st at th cntr of th thrustr to apply raial magntic fil in th ischarg chambr. Magntic inuction is variabl by changing coil currnt. As an lctron sourc, a filamnt catho (% thoriat tungstn of φ.7[mm] 5[mm] 3 was us to minimiz ischarg fluctuations originat from catho opration instability. Fig. 4 Dfinitions of Z an D. Discharg Stability Figur 5 shows masur amplitu of ischarg currnt oscillation an th ischarg currnt. Hr, th amplitu of ischarg currnt oscillation is fin as, τ τ I _.. ( M S I I I =, ( I = ( I I τ τ Oscillation amplitu was snsitiv to magntic inuction. Although, th oscillation is small at <.4[T], th thrust fficincy is poor in this rang of bcaus of larg ischarg currnt. Thrfor, th sirabl opration conition is limit in a quit narrow rang of. Tabl shows a map of th gomtric paramtrs Z an D. In th map, ischarg stability is not. Th cass whn oscillation amplitu is lss than. ar fin stabl. Typically, stabl ischarg has not bn raliz for any in th cas of small Z an small D. Fig. 3 Th cross sction of thrustr.
Discharg currnt, A Discharg currnt 3.5 3.5.5.5 Oscillation amplitu.4..8.6.4. Oprating Point.5..5..5.3.35.4 Magntic flux nsity, T Oscillation amplitu Fig. 5 Oscillation charactristics. D=3[mm], Z=[mm]. Tabl Discharg stability for various D an Z. Z[mm] D[mm] 3 4 3 : Stabl : Unstabl. Masur oscillation amplitu is plott in Fig. 6. Thr is a common trn that oscillation bcoms unstabl with th incras in as sn in Fig. 5. Howvr, th thrshol of varis pning on th gomtric paramtrs Z an D. Oscillation amplitu.4..8.6.4. DZ3 DZ4 DZ DZ3 DZ4 D3Z D3Z D3Z3 D3Z4.6.8. Fig. 6 lation btwn oscillation amplitu an. Z=-4[mm], D=-3[mm], =.6-.[T] Unifi paramtr Using a on imnsional lctron iffusion mol with a classical iffusion cofficint insi th ischarg chambr, lctron currnt can b xprss as µ I = µ ne ( πd = ne ( πd + µ µ m n = mv n n ( mn < σ v > ne D ne D n ( π = ( π m < σ v > ne Assuming uniform istributions of lctric an magntic fils, lctron tmpratur, nutral an lctron numbr nsitis an lctron currnt nsity, Eq.( can b intgrat in th z irction as m IZ mn v V n = < σ > mv n n Thn, lctron nsity in th ischarg chambr is xprss as Imv n n n = Z m < σ v > mv n ( (3 (4 All of th oprating an gomtric paramtrs xcpt D ar contain in Eq. (4. Figur 7 shows th rlation btwn th oscillation amplitu an n assuming that nutral tmpratur is,[k] an lctron tmpratur is [V]. I is takn as I. Oscillation amplitu.4..8.6.4. 7 8 DZ3 DZ4 DZ DZ3 DZ4 D3Z D3Z D3Z3 D3Z4 Fig. 7 lation btwn n an oscillation amplitu. Z=-4[mm], D=-3[mm], =.6-. [T] In orr to hav clar insight from ths ata, w hav to assum aitional acclration zon lngth Z pning on D as n 3
Imv n ( Z Z m v mv n n = + < σ > n (5 As illustrat in Fig. 8, Z woul b incras with D bcaus of pntrations of th plasma acclration zon into th hollow. Z was uc by fitting a curv to a st of ata for ach D. Thy ar list in Tabl. Oscillation amplitu.4..8.6.4 DZ3 DZ4 DZ DZ3 DZ4 D3Z D3Z D3Z3 D3Z4. (a D=[mm]. (b D=[mm]. (c D=3[mm]. Fig. 8 Substantial acclration zon. Tabl Th fitt valu of Z. Z [mm] D=[mm] D=[mm] D=3[mm] 4 Th rarrang plots using n xprss in Eq. (5 is shown in Fig. 9. Oscillation amplitu was incras sharply at critical n of about 5 7 [m -3 ]. 7 4 7 6 7 8 7 8 Fig. 9 lation btwn n an oscillation amplitu taking into account of th substantial acclration zon. Z=-4[mm], D=-3[mm], =.6-.[T] In th rgion whr ischarg is oscillating, lctron iffusion cofficint woul b no mor classical, but anomalous. Thrfor, actual lctron nsity will b smallr than prict on in that rgion. CALCULATION Computational Mthos an Physical Mols It is vry ifficult to masur th istributions of lctric potntial an plasma nsity insi a hollow ano, structur of lctrical shath structur insi th hollow ano was numrically comput using fully kintic D3V Particl-in-Cll (PIC an Dirct Simulation Mont Carlo (DSMC mthoologis. Figur shows th flow chart of calculation. On thousan of ral particls ar trat as on macro particl an both of lctron an ion macro particls ar trat kintically. Elctric an magntic forcs ar implmnt via th PIC mtho an collisions ar via th DSMC mtho. Th cylinrical coorinat systm (r, z, θ was appli to th rgion insi th hollow ano as shown in Fig.. Particl s position is xprss in two-imnsional spac r an z, whil its vlocity is xprss in thr-imnsional spac. That is, particls mov in all irctions, but th azimuthal coorinat is always iscar. An orthogonal calculation gri is st, with th axial lngth of th cll gtting smallr towar th ano xit in orr to obsrv th sharp fall of lctron nsity in th vicinity of ano xit. Th minimum cll lngth is in th sam orr of th Dby lngth. n 4
Nxt Tim Stp No Start Prparation Cll Systm, Magntic Fil Initial Conition, ounary Conition Implmnt Elctric Fil Particl Injction Particl Movmnt Intr-Particl Collision Dnsity Calculation Spac Potntial Calculation Elctric Fil Calculation Is Th Particl Numbrs Constant? Finish Ys Fig. Flow chart of th calculation. Z Fig. Th coorinat an th calculation gri. Assumptions ar list blow. Magntic fil lins ar align in th raial irction uniformly insi th hollow ano an on t hav axial or azimuthal componnts. =.[T]. Only singly charg ionization is consir. Mass ratio m n /m is cras from 4-6 to /, to sp up havy particl s motion. Potntial iffrnc btwn ano an plasma at th ano xit bounary is st 5 V. Elctrons ar f from th ano xit with a T =[V] half-maxwllian vlocity istribution. Th lctron nsity on that bounary n is a variabl paramtr in this calculation. Collisions consir in this simulation ar shown in Tabl 3. Th man fr tim an collision frquncy in th tabl ar typical valus whn th particls ar at thir thrmal vlocity. Th simulation tim stp is bas on lctron - nutral collision man fr tim τ n. Tabl 3 Collisions consir in th simulation. Collision Man Fr Tim lativ Collision Frquncy Elctron Nutral.38-9 [s]. Elastic Scattring Elctron Nutral.83-8 [s]. Ionization Elctron Nutral 6.683-8 [s] 3.5 - Excitation Elctron Ion.87-7 [s] 7. -3 Coulomb Elctron Elctron.57-5[s].33-4 Coulomb Nutral Nutral Scattring 3.83-5 [s] 5.3-5 All th particls mov accoring to th ynamic quations. Th ynamic quations for charg particls ar xprss as, Elctrons: Ions : vz m = ( EZ vθ v vθ m = E r + m x vθ m xz = v, = v z Z x vz mi = EZ v mi = E xz = vz x = v = v v v m x θ (6 (7 Spac potntial is calculat using th Poisson s quation as, ϕ + Z x x ϕ = ( ni ε n sults an Discussions Comput istributions of lctron an ion numbr nsitis, lctric potntial ar shown in Fig.. In th rgion nar th hollow xit, quasi-nutral plasma is crat. As a rsult, lctric shath is rtar an th surfac ara of th shath is nlarg in th hollow ano. (8 5
(a Elctron numbr nsity (b Ion numbr nsity. (c Elctric potntial. Fig.. Comput istributions of lctron an ion numbr nsitis, lctric potntial Figur 3 shows potntial istributions for th cass D=,3,6[mm]. Th pth of quasi-nutral plasma rgion was incras with D, whil it was not so snsitiv to D. (a D=[mm]. (b D=3[mm]. CONCLUSIONS In th xprimnt, it was foun that thr was a plasma nsity thrshol for stabl ischarg. Th comput shath structur insi a hollow ano show that lctric shath is istort bcaus of th xistnc of quasi-nutral plasma nar th hollow xit. Th pth of quasi-nutral plasma rgion in th hollow was not so snsitiv to th hollow wih. EFEENCES [] Chouiri, E. Y., Funamntal iffrnc btwn th two Hall thrustr variants, Physics of Plasmas Vol.8, No. Novmbr. [] Smnkin A.V., Tvrokhlbov S.O., Garkusha V.I., Kochrgin A.V., Chislov G.O., Shumkin.V., Soloukhin A.V., Zakharnkov L.E., Oprating Envlops of Thrustrs with Ano Layr, IEPC-3, 7th Intrnational Elctric Propulsion Confrnc, Pasana, USA, Octobr. [3] Smnkin, A., Kochrgin, A., Garkusha, V., Chislov, G., usakov, A., HETT/EPDM Flight Ano Layr Thrustr Dvlopmnt, IEPC-97-6, 5th Intrnational Elctric Propulsion Confrnc, Clvlan, USA, August 997. [4] Yamamoto, N., Nakagawa, T., Komurasaki, K., Arakawa, Y., Extning Stabl Opration ang in Hall Thrustrs, AIAA--3953 38th AIAA/ASME/SAE/ASEE Joint Propulsion Confrnc & Exhibit, Inianapolis, USA, July. [5] Hirakawa, M., Particl Simulation of Plasma Phnomna in Hall Thrustrs, IEPC-95-64, 4th Intrnational Elctric Propulsion Confrnc, Moscow, ussia, Sptmbr 995. [6] Szabo, J. J., Fully Kintic Hall Thrustr Moling, IEPC--34, 7th Intrnational Elctric Propulsion Confrnc, Pasana, USA, Octobr. [7] Szabo, J. J., Fully Kintic Hall Thrustr Moling of a Plasma Thrustr, PhD Thsis, Massachustts Institut of Tchnology,. [8] Szabo, J., ostlr, P., On an Two Dimnsional Moling of th HT-, IEPC--3, 8th Intrnational Elctric Propulsion Confrnc, Toulous, Franc, March 3. (c D=6[mm]. Fig. 3 Elctric potntial istribution in th cas of n = 7 [/m 3 ]. Th corrlation btwn plasma nsity on th ano xit bounary an shath structur insi th hollow ano is our nxt concrn. 6