Model of Hollow Cathode Operation and Life Limiting Mechanisms

Transcription

1 EPC-3-43 Modl of Hollow Cathod Opraton and Lf Lmtng Mchansms ra Katz John R. Andrson Jams E. Polk Dan M. Gobl Jt Propulson Laboratory Pasadna, CA 9119, USA ntroducton Hollow cathods ar a crtcal componnt of most lctrostatc and Hall ffct on thrustrs. Grddd on thrustrs such as th 3cm NSTAR thrustr hav two hollow cathods. On hollow cathod provds lctrons to onz th propllant n th dscharg chambr. Th othr provds lctrons to nutralz th on bam xtror to th ngn. Th rcord lf of a hollow cathod was th Spac Staton plasma contactor tst run at NASA/GRC [1]. Durng ths tst, th cathod prformanc changd aftr 3, hours of opraton, and th cathod fnally fald to rstart aftr 8, hours. Ths nduranc s mprssv, and xcds almost all dmands on a hollow cathod for solar lctrc propulson mssons. Howvr, on mssons to th outr plants, lctrc thrustrs wll b rqurd to oprat for mor than 5 yars. Bcaus of ths nd, w hav bgun a systmatc nvstgaton to modl th procsss that can caus hollow cathod prformanc dgradaton and falur. n th papr blow w apply rsults from th xtnsv travlng wav tub vacuum barum mprgnatd cathod ltratur to th hollow cathods usd n on thrustrs. W show that th obsrvd spac staton cathod lf s n gnral agrmnt wth publshd barum vaporaton rats. Whl t may appar surprsng that th hollow cathod dsgn dosn t rstrct th vaporaton of barum, w show that n hollow cathods barum s onzd mmdatly, and thus surfac barum s not balancd by nutral vapor phas barum atoms. Ths pctur has mmdat mportant consquncs for assssng hollow cathod barum nsrt lf. t suggsts that vry rducton n th nsrt opratng tmpratur by about 4º C wll xtnd th nsrt lf by a factor of two, a wll known rul of thumb for cathods opratng n vacuum. W dscuss furthr masurmnts ncssary to valdat ths conjctur for gas fd hollow cathods. Background Th Spac Staton hollow cathod plasma contactor tst trmnatd whn th hollow cathod fal to start and th tp tmpratur xcdd th prtst lmt at 8, hours. Th spac staton cathod tp tmpratur startd at about 1º C gradually droppd to about 115º C and aftr 3,8 hrs, jumpd to 13º C, whr t rmand untl th cathod wouldn t start aftr 8, hours. Th jump n cathod startng voltag, and opratng tp tmpratur 1

2 aftr ar both symptoms of a lack of fr barum, n th nsrt. Fr barum rducs th nsrt work functon and also ads th n dscharg ntaton. n ths papr w assum 3,8 hours as th tm of ffctv dplton for ths cathod. Prvous nvstgatons of barum nsrt lf n hollow cathods focusd on th rvrsbl, qulbrum chmcal ractons as barum oxd vaporats from th barum calcum alumnat mxtur n a porous tungstn nsrt. Th 1-D modl of Kovalsk [] ncluds th barum transport and dffuson n th hollow cathod xnon gas flow. Th proposd loss mchansm was barum flow through th orfc. Th loss rat was qut low, bcaus th xnon gas vlocty, approxmatly 4 m/s, was much slowr than barum thrmal vlocty. Evn wth dffuson, th barum vapor prssur abov th nsrt was suffcntly hgh to rduc th loss rat an ordr of magntud compard wth losss n a vacuum. Howvr, th spac staton hollow cathod xprnc s n bttr agrmnt wth publshd dplton rats of barum cathods opratd n vacuum. An xprmntal study of barum mprgnatd cathod lf n vacuum [3] showd th tmpratur dpndnc of barum dplton consstnt wth a.9v hat of vaporzaton. A mor rcnt study [4] showd that th sam barum vaporaton nrgy from 411 mprgnats for a wd rang of cathods. Thy rvwd th ltratur and found th total varaton from.8v to 3.V, rgardlss of th matrx mtal. Th small varaton of masurd hat of vaporaton, and ts nsnstvty to th matrx matral, promptd us to apply th vacuum rsults to xnon gas fd hollow cathods. Applcaton to th Spac Staton Hollow Cathod n ths papr w prsnt a modl of barum transport and loss n a typcal lctrc propulson hollow cathod that ncluds th ffct of th nsrt rgon plasma. Orfc Plasma Condtons Th currnt was 1 amprs durng th spac staton hollow cathod tst. Ths was th uppr nd of a larg dynamc rang, and th currnt dnsty n th orfc was qut hgh. W hav usd a nw 1-D, varabl cross scton modl to dtrmn th prssur and plasma dnsty boundary condtons at th upstram nd of th orfc. Ths modl [5] xtnds th prvous modl of th nsrt rgon [6] to nclud charg xchang collsons, a radal dnsty profl, and axal varaton n all paramtrs. Th modl shows that th axal varaton of on currnts to orfc walls s n agrmnt wth publshd shaps of orfc roson [7]. For th spac staton cathod, assumng an orfc tmpratur of 1º C, th modl prdcts th nsrt rgon nutral xnon dnsty of 5.4x1 m -3 and a plasma dnsty at nd of th orfc of 3.4x1 1 m -3. About.1 amprs of on flow upstram from th orfc nto th nsrt rgon. W assum that th nutral gas dnsty s farly unform throughout th nsrt rgon, but th plasma dnsty drops rapdly away from th orfc. nsrt Rgon Plasma f w assum constant nutral dnsty, unform lctron tmpratur, th nsrt

3 rgon plasma, ncludng lctron mpact onzaton of xnon atoms, and rsonant charg xchang collsons btwn xnon ons and atoms can b modld analytcally. Wth th assumpton of quas nutralty n = n n, th local onzaton rat lnks th stady stat contnuty quatons for nutral xnon, xnon ons, and lctrons. n& u n =, n& + j = whr s th lctron charg, n s th plasma numbr dnsty, j nu s th lctron currnt, u s th axal spd (subscrpts,, stand for nutral, on and lctron, rspctvly) and n& s th on gnraton rat T n& = 4σ ( T ) n n πm whr m s th lctron mass, n s th nutral xnon numbr dnsty, and σ ( T ) s th mpact onzaton crossscton for xnon avragd ovr a Maxwllan dstrbuton of lctrons at tmpratur T (n V) [6], σ ( T ) [ 3.97 (.368T )] + (.643T ) 1.17 Exp 1 T W assum that nrtal trms ar nglgbl n both th on and lctron momntum quatons, an assumpton supportd by th calculatons blow. W also assum that th on currnt s small compard wth th lctron currnt. Th lctron momntum quaton taks th famlar form of a gnralzd Ohm s law, as dos th on momntum quaton. n j u u ) = D n + n µ E ( = D n + n µ E whr for ach spcs th dffuson coffcnt, D, and th moblty, µ, ar dfnd as kt kt D = τ, D = τ M m µ = τ, µ = τ M m whr τ s th collson tm. By lmnatng th axal lctrc fld, E, th on momntum and lctron momntum quatons can b combnd nto a sngl quaton µ µ j n( u u ) = D + D n + µ µ µ j = Da n + µ whr D a s th ambpolar dffuson coffcnt. Whl n th orfc th last trm s non-nglgbl, n th nsrt rgon w nglct both t and th nutral drft vlocty. Th on moblty s lmtd by rsonant charg xchang wth nutral xnon. n th orfc th on man fr path for charg xchang collsons s svral mcrons. Th ambpolar dffuson coffcnt s 1 τ = σ n u CEX scat 1 T + T D = a σ CEX n M uscat whr σ CEX s th xnon nutral-on charg-xchang cross scton and u scat s an ffctv on spd ncludng drft and thrmal vlocts. For rlatvly slow dffuson, such as n th nsrt rgon, u scat can b approxmatd by th on thrmal spd, u th. T uth =. M 3

4 Th collson tm for lctrons s gvn by 1 τ = υ + υ whr υ n s th lctron-on collson frquncy and υ n s th lctron-nutral collson frquncy. Th lctron-on coulomb scattrng from Rfrnc [8] s υ =.9x1 1 nλt n Λ = 3 Ln 3 T and a numrcal ft to th lctronnutral scattrng cross scton avragd ovr a Maxwllan lctron dstrbuton [9]. υ = σ ( T n n ) n T m T σ n ( T ) 6.6x1 1.6 T Sttng th dffuson loss rat qual to th on producton rat ylds [ D a n] = n&. gnorng th axal and radal varatons n lctron tmpratur and nutral dnsts, w obtan n 1 n n C n = r r r z 8T nσ ( T ) π m C = Da W can solv th dffuson quaton analytcally by sparatng varabls n = n() f ( r) g( z) 1 f 1 f 1 g + + C + α = + α f r rf r g z Th soluton s th product of a zro = ordr Bssl functon tms an xponntal α z ( r, z) = n() J ( C + α r) n Prvous nvstgatons hav rportd an xponntal fall of plasma dnsty [1], n agrmnt wth abov prdctd bhavor. Assumng that th on dnsty gos to zro at th wall, w obtan 1 C + α =, R whr λ 1 s th frst zro of th zro ordr Bssl functon and R s th ntrnal radus of th nsrt. Sttng α =, ths gnvalu lads to th followng quaton that dtrmns th maxmum possbl lctron tmpratur: R λ 1 λ nσ 8T π m ( T ) D = Th lctron tmpratur from ths modl agrs wll wth 1.1 V masurd by Malk, Montard, and Hans [11] for th UK5 hollow cathod. For th spac staton hollow cathod, th prdctd plasma tmpratur s slghtly hghr, 1. V. Th corrcton for fnt α s lss than on pr cnt. Th 1. V plasma quckly onzs any vapor phas barum atoms. Usng plasma dnsty from th orfc modl, th onzaton man fr path for a thrmal barum atom s 4x1-5 m, much lss than th nsrt nnr damtr. Th moblty of th barum ons s much gratr than nutral barum atoms, and th prdomnat lctrc flds that pull lctrons out of th cathod drv th barum upstram away from th orfc, th oppost drcton than n th Kovalsk modl []. Ths flow drcton s consstnt wth rports of th prsnc of barum upstram of th cathod nsrt a 4

5 rgon. n what follows w assum that th vaporatd barum atoms ar onzd and transportd upstram wth nglgbl stckng tm on th hot downstram rgons of th nsrt. To fnd th xponntal coffcnt, α, of th nsrt plasma dcay, w balanc th masurd hollow cathod nput powr wth th onzaton losss n th nsrt. Th Spac Staton tst cathod opratd at 1 Amprs and 1.5 volts [1]. From our 1-D modl, w fnd that about 67 watts wr dsspatd n th orfc by Ohmc hatng whch not only hatd th orfc plat, but also gnratd and hatd th plasma that lft th cathod. Th powr that travrss th cathod shath s th total dscharg powr mnus th powr dsspatd n th cathod aprtur: = 1 A V = 1.5 V V = 15 W φ φ shath shath = = 83W = 6.9 V Ths lavs a maxmum of 6.9 V for th shath potntal, nglctng any rsstv drop n th nsrt rgon. Th shath currnt conssts of lctrons and ons. Th powr that th lctrons gan from th shath gos nto onzaton and lctron convcton. Th nrgy mpartd n th onzaton collson s sum of th onzaton potntal (1.1 V) and th scondary lctron kntc nrgy ( V) that s convctd away. = + 5 φ shath = T = 1.1(1 ) + 37 Solvng for th on and lctron currnt through th shath at 1 A of dscharg currnt, w fnd that = 9.6 A =.4 A Analytcally, th nsrt on currnt gnraton s qual to th ntgral of th on gnraton rat ovr th nsrt volum. = = ndv & π 4σ ( T ) n n ( r, z) T πm rdrdz Applyng th analytcal soluton for th lctron dnsty drvd arlr, w can rwrt on currnt gnraton n trms of th avrag radal dnsty and solv for th on currnt. n = R λ n(,) J R π R J1 = n(,) λ ( λ ) πr = 4σ ( T ) n n α r πrdr T πm For th pak dnsty, n(,), w us th upstram orfc plasma dnsty from th 1-D orfc cod. Solvng ths quaton for α, w fnd th plasma falls off upstram on a scal lngth of.7 cm, roughly consstnt wth th masurmnts of nsrt surfac chang rportd by Sarvr-Vrhy [1]. 5

6 Fgur 1. Dcras n saturaton msson currnt wth tm for dffrnt cathod tmpraturs. Fgur from Pallul and Shroff [3] Work Functon (V) Work Functon Jsat J Schotky Emsson Currnt (A/cm ) nsrt Tmpratur (K) Fgur. Work functon and saturaton msson currnts wth and wthout th Schotky lctrc fld nhancmnt trm. 6

7 nsrt Lf (hours) 16, 14, 1, 1, 8, 6, 4,, nsrt Tmpratur ( o C) Fgur 3. Expctd nsrt lf for th spac staton cathod as a functon of nsrt tmpratur nsrt lf Pallul and Shroff [3] masurd dcras n nsrt msson n vacuum as a functon of tm and tmpratur (s Fg. 1). Thy found that th tmpratur dpndnc was consstnt wth th.9v hat of vaporzaton, and that th rat vard as th squar root of tm, consstnt wth Knudsn dffuson through th pors. As barum vaporats, th msson currnt dnsty that th cathod can support dcrass, prsumably du to rducd surfac covrag. Followng Pallul and Shroff, w hav calculatd th saturatd msson currnt dnsty at th bgnnng of lf, shown n Fgur, and hav ncludd a Schotky corrcton usng th on currnt and plasma lngth scal calculatd abov. At 15º C (153 K), th Schotky fld nhancd saturatd lctron currnt dnsty that th cathod could mt s about 35 A/cm, whl th calculaton abov ndcats that th cathod was drawng lss than 1 A/cm of lctron currnt from th mttng surfac. n Fgur 3 w plot th tm that th spac staton cathod could support th dscharg currnt as a functon of th nsrt tmpratur basd on th Pallul and Shroff vacuum data. At an ntrnal nsrt tmpratur of about 15º C, th Schotky nhancd msson currnt dnsty would hav droppd blow th opratng cathod currnt aftr about, hours. Ths would rqur an ncras n nsrt tmpratur at that pont to mantan th dscharg currnt, whch s consstnt wth th xprmntal rsults rportd by Sarvr- Vrhy. Ths nsrt tmpratur, 15ºC, s about 7ºC gratr than th cathod tp tmpraturs as rportd by Sarvr- Vrhy, and wthn th rang of tmpraturs masurd by varous mans 7

8 durng th tst. As long as th currnt dnsty that th surfac can mt s wll n xcss of th msson currnt rqurd to support th dscharg, th xpctd nsrt lf would doubl for vry 4ºC dcras n opratng tmpratur. As sn n Fg.3, droppng th nsrt tmpratur 1 C to about 115 C would hav ncrasd th cathod lftm n ths tst to n xcss of 1, hours whl mantanng th dscharg currnt. Ths nsrt tmpratur rducton could hav bn achvd by smpl gomtry and flow changs n th hollow cathod. Concluson Th fundamntal rsult of ths analyss s that durng th 8, hour lf tst, th spac staton hollow cathod nsrt was opratng at a tmpratur far n xcss of th mnmum ncssary to support th msson currnt dnsty. Ths causd xcssv vaporaton of barum from th nsrt, whch was transportd upstram away from th plasma to rgons whr msson can not occur du to spac charg ffcts. Consquntly, aftr a suffcnt tm th cathod could not support th dscharg currnt rqurd du to barum dplton n th plasma contact ara of th nsrt. Modfyng th cathod to oprat at a lowr nsrt tmpratur would hav rsultd n a sgnfcantly longr lf. W ar crtan that ths s not surprsng nformaton to th tst dsgnrs. Th contactor cathod was dsgnd for a larg dynamc rang n dscharg currnt, and th tst was conductd at th hghst nd of that rang. Undr lss dmandng condtons, at lowr currnts or wth a cathod dsgn chang, th lf would hav bn much gratr. Th hollow cathods usd n th NSTAR thrustr ar of smlar dsgn, but oprat at lowr tmpraturs. n th NSTAR Extndd Lf Tst [1], ths cathods contnu to oprat stably and wth rproducbl msson prformanc for ovr 7, hours, wth no chang n startng voltag. Th modl prsntd s mprcal n natur. Drct masurmnts of nsrt opratng tmpraturs ar ndd on futur tsts, as ar masurmnts of barum dplton as a functon of tm. f th assumpton s born out that mprgnat lf n gas fd hollow cathods s smlar to that n vacuum cathods at th sam tmpratur, th on thrustr communty wll bnft from th xtnsv ltratur of vacuum cathod lf tst data and modls. Rfrncs [1] Sarvr-Vrhy, T.R., Dstructv Evaluaton of a Xnon Hollow Cathod Aftr a 8, Hour Lf Tst, AAA , July [] Kovlsk, S. D., Lf Modl of Hollow Cathods Usng a Barum Calcum Alumnat mprgnatd Tungstn Emttr, EPC 1-76, Octobr 1. [3] Pallul, P., t al., Exprmntal Study of mprgnatd-cathod Bhavor, Emsson, and Lf, J. Appl. Phys. 51(5), p , May 198. [4] Gartnr, G., t al., Supply and Loss Mchanssms of Ba Dspnsr Cathods, Appld Surfac Scnc v. 146, p. -3,

9 [5] Katz,., t al., A Modl of Hollow Cathod Plasma Chmstry, AAA [6] Katz,., t al., Modl of Plasma Contactor Prformanc, Journal of Spaccraft and Rockts, v. 34, n. 6, p , [7] Polk, J. E., t al., An Ovrvw of th Rsults from an 8 Hour war Tst of th NSTAR on Thrustr, AAA , Jun [8] Book, D. L., NRL Plasma Formulary, Naval Rsarch Laboratory, [9] Mkllds, t. al., A 1-D Modl of th Hall-Effct Thrustr wth an Exhaust Rgon, AAA 1-355, July 1. [1] Sgfrd, D. E., t. al., An nvstgaton of Mrcury Hollow Cathod Phnomna, AAA 78-75, Aprl [11] Malk, A. K., t al., Spctroscopc Masurmnts of Xnon Plasma n a Hollow Cathod, J. Phys. D: Appl. Phys. 33, p ,. [1] Sngupta, A., t al., Prformanc Charactrstcs Of Th Dp Spac 1 Flght Spar on Thrustr Long Duraton Tst Aftr 1,3 Hours Of Opraton, AAA -3959, July 9