THE EFFECTS OF CLUSTERING MULTIPLE HALL THRUSTERS ON PLASMA PLUME PROPERTIES

Transcription

1 THE EFFECTS OF CLUSTERING MULTIPLE HALL THRUSTERS ON PLASMA PLUME PROPERTIES Brian E. Bal * and Alc D. Gallimor Plasmadynamics and Elctric Propulsion Laboratory Dpartmnt of Arospac Enginring Th Univrsity of Michigan Ann Arbor, MI 489 USA William A. Hargus, Jr. Air Forc Rsarch Laboratoris Edwards Air Forc Bas Edwards, CA 9354 USA ABSTRACT Clustrs of Hall thrustrs hav bn proposd as a mans of achiving lctric propulsion systms capabl of oprating at vry high powr lvls. To facilitat tsting in xisting vacuum facilitis, initial tsts hav focusd on a clustr of low-powr Busk BHT--X3 Hall thrustrs. A combination of tripl Langmuir probs and floating missiv probs is usd to study th ffcts of multi-thrustr opration on th lctron numbr dnsity, lctron tmpratur, and plasma potntial in th plasma plum. Th rsultant numbr dnsity is shown to b a rsult of linar suprposition of th plums of individual thrustrs, whil th lctron tmpratur in th clustr plum is masurd to b slightly highr than that causd by opration of a singl thrustr. Th plasma potntial downstram of th clustr is shown to oby th Boltzmann rlation. In th rgion btwn th thrustrs, th plasma potntial incrass as a function of downstram distanc and may rsult in rflction of som low-nrgy charg xchang ions back toward th clustr. A mchanism that may lad to slightly rducd ion bam divrgnc through focusing of ions dirctd toward th thrustr cntrlin is discussd. Introduction Both NASA and th Unitd Stats Air Forc (USAF) ar conducting rsarch into lctric propulsion (EP) systms oprating at powr lvls in xcss of kw. Th Air Forc will us highpowr systms for orbit transfr vhicls and rscu vhicls capabl of rpositioning assts that hav xhaustd thir propllant load or faild to mt thir oprational orbit. 1, NASA prdicts that high-powr EP systms will b usd in both a high thrust mod to rduc mission tims and in a high spcific impuls mod to nabl dp spac missions that rquir high vlocity incrmnts ( V). 3,4 NASA s rcntly announcd Projct Promthus will sk to dvlop spac nuclar ractors capabl of mting th powr dmands of in-spac propulsion. 5 Th commncmnt of this projct incrass th liklihood that high-powr EP systms will bcom viabl for dp spac missions whr th availability of solar powr is diminishd, as wll as for th nar-earth missions of intrst to th Air Forc. * Ph.D Candidat, Studnt Mmbr AIAA Associat Profssor, Associat Fllow AIAA Rsarch Scintist, Snior Mmbr AIAA On lctric propulsion dvic that is of intrst for ach typ of mission discussd abov is th Hall thrustr du to its low spcific mass, high thrust dnsity, and high rliability. Although th nvisiond powr lvl is somwhat byond th currnt stat-of-th-art, thr ar two approachs bing considrd for raching high powrs. Th first, known as th monolithic approach, is to dsign a singl thrustr capabl of oprating at th dsird powr lvl. Th scond, complmntary approach involvs clustring svral modratly powrd thrustrs togthr to rach th dsird powr lvl. Th clustrd approach, which is th on bing pursud by th USAF, may b xpctd to hav a slightly lowr total fficincy and highr dry mass than a comparabl monolithic dvic sinc larg thrustrs hav historically outprformd smallr thrustrs. A clustr of thrustrs, howvr, has svral advantags ovr a singl unit including

2 improvd systm rliability and th ability to throttl th systm by simply turning on or off th appropriat numbr of thrustrs. Throttling th systm in this way allows a clustr to prform at lowr powrs without oprating any of th individual thrustrs at off-dsign conditions. This charactristic of a clustr may prov bnficial on missions whr ithr th availabl powr or th propulsiv nds chang as a function of tim. For xampl, a high-powr clustr of Hall thrustrs could b usd for th initial LEO-GEO transfr of a gosynchronous communications satllit. Upon raching its final dstination, on lmnt of th clustr could thn b usd for north-south station kping. A final, vry important advantag of oprating multipl thrustrs is th high dgr of systm scalability. In principl, onc th tchnical issus involvd with oprating a clustr ar undrstood, a singl flight-qualifid ngin could support a wid rang of missions by simply clustring togthr th appropriat numbr of thrustrs. Bfor a clustr of Hall thrustrs can b usd in flight, thr ar svral tchnical issus that must b addrssd. 1, On of th most prssing issus is th nd to undrstand th intraction of th plasma plums with ach othr and with th spaccraft. In an ffort to addrss this issu, tsting of four -watt Busk BHT--X3 thrustrs has bgun at both th Air Forc Rsarch Laboratory (AFRL) and at th Univrsity of Michigan s Plasmadynamics and Elctric Propulsion Laboratory (PEPL). 6-8 Figur 1 shows th clustr in opration at AFRL. Figur 1: A low-powr Hall thrustr clustr in opration. Th currnt work focuss on dtrmining th rlations ncssary to prdict th plum proprtis of a clustr basd on masurmnts or simulations of a singl thrustr plum. To this nd, th plum of th clustr is charactrizd using a combination of lctrostatic tripl probs and missiv probs to masur th lctron numbr dnsity, lctron tmpratur and plasma potntial. In addition, a thr-axis gaussmtr is usd to masur th magntic fild downstram of th clustr. Exprimntal Stup Clustr Th clustr usd in this xprimnt is composd of four Busk BHT--X3 -watt class Hall thrustrs. An arlir vrsion of this thrustr is rportd to oprat at an anod fficincy of 4% and spcific impuls of 13 sconds whil providing 1.4 mn of thrust at th nominal oprating conditions. 9 Each thrustr has a man diamtr of 1 mm. Th thrustrs ar arrangd in a x grid with approximatly 11.4 cntimtrs btwn th cntrlins of adjacnt thrustrs. Typical oprating conditions for th BHT- ar givn in Tabl 1. Paramtr Valu Discharg Voltag (V) 5 ±.5 Discharg Currnt (A).8 ±.3 Cathod Voltag (V) -8.5±1. Magnt Currnt (A) 1. ±.3 Kpr Currnt (A).5 ±.5 Kpr Voltag (V) 13 ± 1 Anod Mass Flow (sccm) 8.5 ±.85 Cathod Mass Flow (sccm) 1. ±.1 Tabl 1: Typical thrustr oprating conditions. Vacuum Chambr All data rportd in this papr ar rcordd in Chambr 6 at AFRL. Chambr 6 is a 1.5 x.4 mtr cylindrical, stainlss stl vacuum chambr that is vacuatd by four cryopanls maintaind at 5 Klvin by four APD cold hads, HC-8C hlium comprssors, and an APD cryopump. This systm provids a pumping spd of 6, litrs pr scond of xnon with a typical bas prssur of 8x -7 Torr as masurd by a MKS Modl 9 hot cathod gaug. During thrustr opration, th chambr prssur riss to approximatly 6.1x -6 Torr for singl thrustr opration and.3x -5 Torr for four-thrustr opration. Both rportd prssurs ar corrctd for xnon.

3 Positioning Systm and Nomnclatur Th naming convntion and coordinat systm usd throughout this xprimnt ar shown in Fig.. As shown, th thrustrs ar labld as TH 1-4 bginning in th uppr lft-hand cornr and procding countrclockwis. Th origin of th coordinat systm is dfind as th midpoint of th clustr in th displayd X-Y plan. Th Z coordinat masurs th distanc downstram of th thrustr xit plan. a nt currnt from th discharg. A schmatic of th tripl prob circuit is shown in Fig. 3. As shown in this diagram, lctrod is allowd to float whil th voltag btwn lctrods 1 and 3, V d3, is applid by a laboratory powr supply with floating outputs. For th xprimnts discussd hr, V d3 is st to 1 volts. Th potntial btwn probs 1 and, V d, is masurd by an HP 3497A data acquisition systm, as ar th floating potntial, V f, and th currnt, I. 1 3 I I Vf Vd + Vd3 Figur 3: Tripl prob circuit. Figur : Clustr nomnclatur and coordinat systm. A thr-dimnsional positioning systm is usd to swp probs through th clustr plum. Th X and Z positions ar adjustd using a singl two-axis Parkr Dadal tabl with approximatly 3 cm of travl in ach dirction. Th Y position is controlld using a vrtically mountd Parkr Dadal linar stag with a 45 cm rang of motion. Tripl Prob Th tripl Langmuir prob usd for ths xprimnts consists of 3 tungstn lctrods insulatd from ach othr by an alumina rod. Each lctrod is.5 mm (. ) in diamtr and 5. mm (. ) long. Th spacing btwn th cntrlins of adjacnt lctrods is approximatly mm. Th prob is sizd to critria that allow th standard thin shath assumptions of prob thory to b applid. 11 Ths critria, which ar discussd lswhr, 6 ar ncssary to nsur propr opration of th prob. Th symmtric tripl prob, originally dvlopd by Chn and Skiguchi, 1 is a convnint plasma diagnostic for collcting larg amounts of data du to th limination of th voltag swp rquird by othr lctrostatic probs. Additionally, sinc th prob as a whol floats, th disturbanc to th ambint plasma is minimizd compard to singl probs, which draw Th rlations usd to dtrmin plasma proprtis from masurd prob data ar prsntd in Eqn. 1 and. In ths quations, n is th lctron numbr dnsity, which is qual to th ion numbr dnsity through th quasinutrality assumption. Th lctron tmpratur is rprsntd by T and ion and lctron masss by m i and m, rspctivly. Th symbol A dnots th ara of a singl lctrod, is th lctron charg, and k b is Boltzmann s constant. Various rror analyss indicat that th uncrtainty in th calculatd lctron tmpratur and numbr dnsity ar gnrally lss than 3% and 5%, rspctivly Th rlativ uncrtainty btwn multipl data points rcordd using th sam prob is blivd to b significantly lowr than th absolut uncrtainty. n mi = kbt 1 A 3 Vd 1 xp kbt Vd 1 xp kbt 1 I xp V d xp 1 kbt 3 = 1 (1) () 3

4 Emissiv Prob Plasma potntial masurmnts ar conductd using a floating missiv prob similar to th on dscribd by Haas t al. 14 Th mitting portion of th prob consists of a.17 mm (.5 ) diamtr tungstn filamnt loop, th nds of which ar insrtd into doubl bor alumina tubing along with.58 mm (. ) diamtr molybdnum wir lads. Short lngths of tungstn wir ar insrtd into th alumina tub to insur contact btwn th mitting filamnt and molybdnum lads. Th diamtr of th mitting filamnt loop is approximatly 3 mm. Figur 4 shows a sktch of th missiv prob. ~3 mm Tungstn Filamnt Molybdnum Lads Alumina Insulator Figur 4: A schmatic of th missiv prob. Th thory of th missiv prob is wll stablishd and rsults in th conclusion that a thrmionically mitting filamnt will assum th local plasma potntial whn its mittd lctron currnt is sufficint to nutraliz th plasma shath. 15 For this xprimnt, th currnt ncssary to hat th prob is providd by a programmabl Sornsn modl DLM 4-15 powr supply with floating outputs. At ach location in th plum, th currnt is stadily incrasd and th potntial with rspct to ground at th ngativ trminal of th supply is rcordd using th HP data acquisition unit mntiond abov. This mthod allows for vrification of a wll-dfind platau in th voltag-currnt trac, which indicats plasma shath nutralization. Th shap of a typical trac, such as th on shown in Fig. 5, can b xplaind as follows. At zro applid currnt, th prob assums th local floating potntial. As th currnt to th prob is incrasd, th masurd potntial initially dcrass as a voltag appars across th prob and causs th potntial at th ngativ trminal to mov blow th floating potntial. As th prob currnt is incrasd furthr, th filamnt bgins to mit lctrons causing th masurd potntial to ris sharply bfor approaching an asymptot at th local plasma potntial. Considring that th voltag drop across th mitting filamnt nvr xcds 6 V, th uncrtainty in th plasma potntial masurmnts is stimatd to b ±3 V. Masurd Potntial (V) Hating Currnt (A) Figur 5: Sampl missiv prob trac. Gaussmtr Th magntic fild downstram of th clustr is rcordd using an FW Bll modl 73 thr-axis gaussmtr. All masurmnts ar rcordd without th thrustrs in opration. Although rcnt work has shown th magntic fild strngth profils insid an oprating thrustr to dviat from th applid profils du to filds inducd by th azimuthal lctron drift, 16 th diffrnc is xpctd to b ngligibl for th lowpowr thrustrs studid hr bcaus of th low currnt lvls involvd. Th magntic fild profils prsntd in this papr ar thrfor blivd to b ralistic rprsntations of thos that occur downstram of an oprational clustr. Rsults and Discussion Magntic Fild Magntic fild data ar rcordd in th XZ plan of thrustrs and 3, and in th YZ plan of thrustrs 3 and 4. Th rsults ar shown in Figs. 6 and 7, rspctivly. Th diffrncs in ths plots ar attributabl to th diffrnt dirction of magnt currnt flow btwn thrustrs and 4. Thrustrs and 3 ar opratd with th lctromagnts in th nominal configuration whil th currnt flow was rvrsd in thrustr 4. Rvrsing th polarity of lctromagnts in altrnat thrustrs of a clustr has bn suggstd as a mans of cancling th disturbanc torqus that typically rsult from th slight ExB drift of th bam ions. 1,,17 Th data prsntd in Figs. 6 and 7 will b usd to tst th prviously publishd thory that th plasma potntial profils of a clustr can b prdictd from magntic fild data. 8 4

5 B (G): that would b xpctd downstram of a larg monolithic thrustr. Z (mm) X(mm) Figur 6: Th magntic fild strngth and stramtracs downstram of TH & 3. Z(mm) 5 15 Dnsity (m -3 ) 1.E E E E+17 4.E E+17.8E+17.E E E+17 1.E E E+16 6.E+16 5.E+16 Z(mm) B (G): Y(mm) 4 6 Figur 7: Magntic fild profils downstram of thrustrs 3 & 4. Th polarity of magnt 4 has bn rvrsd from th normal configuration. Plasma Dnsity A tripl Langmuir prob is usd to masur th plasma numbr dnsity at 5 mm intrvals in th clustr plum. Data ar rcordd in both th XZ plan of thrustrs and 3 and th YZ plan of thrustrs 3 and 4. For both plans, data ar rcordd with ach thrustr oprating alon and with two thrustrs oprating simultanously. Du to th good agrmnt btwn th two data sts, only th data rcordd in th YZ plan of thrustrs 3 and 4 ar rportd hr. Th plasma dnsity profils downstram of thrustrs 3 and 4 ar shown in Fig. 8. As this plot shows, th maximum numbr dnsity 5 mm downstram of th clustr xit plan is roughly 1x 18 m -3. This valu dcrass rapidly in th downstram dirction and by Z=5 mm th maximum plasma dnsity has dcrasd by mor than an ordr of magnitud to about 5x 16 m -3. Figur 8 shows a wll-dfind jt structur downstram of ach individual thrustr. By about 5 mm downstram th plums hav mrgd to th point that th dnsity is narly constant across th width of th clustr and rsmbls th profil Y(mm) Figur 8: Elctron numbr dnsity in th plum of thrustrs 3 and 4. Figurs 9-11 show plasma dnsity profils at axial distancs of 5, 15, and 5 mm downstram of th clustr xit plan. Th black lins in ths plots ar obtaind by linar suprposition of th data rcordd with thrustr 3 and thrustr 4 running indpndntly. Th masurmnts of plasma dnsity takn with both thrustrs oprating simultanously agr with th calculatd valus to wll within th margin of rror of th tripl prob diagnostic. This implis that th dnsity in a clustr plum, n, can b prdictd by summing th contributions of ach individual thrustr, n j, as shown in Eqn. 3. n = n j (3) j Dnsity (m^-3) 1.4E+18 1.E+18 1.E+18 8.E+17 6.E+17 4.E+17.E+17 TH4, Z=5 TH3, Z=5 3&4, Z=5 Suprposition.E Figur 9: Plasma dnsity at Z=5 mm. Th data show good agrmnt with linar suprposition. 5

6 Dnsity (m^-3) 1.8E E E+17 1.E+17 1.E+17 8.E+16 6.E+16 4.E+16.E+16 TH4, Z=15 TH3, Z=15 3&4, Z=15 Suprposition.E Figur : Plasma dnsity at z=15 mm. Z(mm) 5 15 Tmp. (V) Dnsity (m^-3) 7.E+16 6.E+16 5.E+16 4.E+16 3.E+16.E+16 1.E+16.E+ TH4, Z=5 TH3, Z=5 3&4, Z=5 Suprposition Figur 11: Plasma dnsity at z=5 mm. Elctron Tmpratur Th lctron tmpratur contours rcordd downstram of thrustrs 3 and 4 ar displayd in Fig. 1. Th tmpratur varis btwn roughly 3 V at Z=5 mm along th thrustr cntrlins to lss than 1 V nar th boundaris of th sampld rgion. Th data show slight discrpancis in th lctron tmpratur in th nar-fild of ach individual thrustr. Masurmnts rcordd downstram of thrustrs and 3 (not shown) indicat similar diffrncs, thus th variations ar not blivd to b a rsult of th rvrsd magntic fild profils mntiond prviously. Rathr, th discrpancis ar probably du to tolrancs in th manufacturing procss or diffrncs in th cumulativ tim of opration btwn th dvics. Th diffrnc in th lctron tmpratur in front of ach thrustr dcrass as a function of downstram distanc and by roughly Z=9 mm th diffrnc btwn th two units bcoms ngligibl Y(mm) Figur 1: Elctron tmpratur profils downstram of thrustrs 3 and 4. Elctron tmpratur tracs masurd at axial locations of 5, 15, and 5 mm ar shown in Figs , rspctivly. Th black lin in ach figur is calculatd using Eqn. 4 and rprsnts a first attmpt to prdict th lctron tmpratur in th clustr plum. Th simplistic approach of calculating a dnsity wightd avrag, as indicatd by Eqn. 4, sms to slightly undrprdict th masurd tmpratur, particularly in th rgion btwn th thrustrs. Th lctron tmpraturs masurd during thrustr opration ar consistntly highr than thos rcordd during singl thrustr opration; howvr th diffrnc is gnrally lss than. V, which is within th uncrtainty of th diagnostic. Elctron Tmp. (V) kbt = n j j TH4, Z= TH3, Z= 3&4, Z= Wightd Avrag j k T n b j j (4) Figur 13: Th lctron tmpratur profils masurd for singl- and multi-thrustr opration 5 mm downstram of th xit plan. 6

7 1.4 Elctron Tmp. (V) TH4, Z=15 TH3, Z=15 3&4, Z=15 Wightd Avrag Figur 14: Elctron tmpratur profils 15 mm downstram of th clustr xit plan. Elctron Tmp. (V) TH4, Z=5 TH3, Z=5 3&4, Z=5 Wightd Avrag Figur 15: Th lctron tmpratur 5 mm downstram of th thrustrs. Plasma Potntial An missiv prob is usd to masur th plasma potntial at 5 mm intrvals in th clustr plum. Rsults obtaind with thrustrs 3 and 4 oprating simultanously ar shown in Fig. 16. An intrsting fatur shown in this plot is th uniqu plasma potntial profil in th ara btwn th thrustrs. Btwn approximatly Y=-3 and Y=3 mm, th plasma potntial incrass with downstram distanc indicating that thr xists a rgion whr th lctric fild vctor is orintd in th upstram dirction. This can b sn clarly in Fig. 17, which shows th plasma potntial profils at various axial locations. Th rvrsd lctric fild could potntially caus ions producd in th ara btwn th thrustrs to b acclratd upstram toward th spaccraft on which th thrustrs ar mountd. Although this could rsult in an incrasd rosion rat in som aras du to incrasd ion impingmnt, th ffct is xpctd to b ngligibl sinc th impinging ions ar unlikly to xprinc acclrating potntials gratr than a fw volts in th rvrs dirction. Z(mm) Potntial (V): Y(mm) Figur 16: Plasma potntial profils downstram of thrustrs 3 and 4. Plasma Potntial (V) &4, Z=5 3&4, Z=6 3&4, Z=7 3&4, Z=8 3&4, Z=9 3&4, Z= 3&4, Z=1 3&4, Z= 3&4, Z=13 3&4, Z= Figur 17: Th volution of plasma potntial profils at various downstram locations. It has bn suggstd that th plasma potntial profils downstram of a clustr could b prdictd by simply intgrating th magntic fild data. 8 This is contradictd by th masurmnts prsntd in Figs. 18-, which show th plasma potntial downstram of thrustrs 3 and 4 at axial distancs of 6,, and 14 mm, rspctivly. Clarly, intgration along th magntic fild lins dpictd in Fig. 7 dos not rsult in th obsrvd potntial profils. Potntial (V) TH4 TH3 3&4 Calculatd Figur 18: Plasma potntial masurd 6 mm downstram of th clustr xit plan using a floating missiv prob. 7

8 Potntial (V) Potntial (V) TH4 TH3 3&4 Calculatd Figur 19: Plasma potntial profils mm downstram of thrustrs 3 and TH4 TH3 3&4 Calculatd Figur : Plasma potntial masurd 14 mm downstram. Not th agrmnt btwn masurd valus and thos calculatd using th Boltzmann quation. A mor convntional mthod for rlating th magntic fild architctur to th plasma potntial involvs considration of lctron dynamics in a plasma. Along a magntic fild lin, th motion of lctrons is govrnd purly by lctrostatic forcs and can b dscribd by th wll known Boltzmann rlation. 18 This lads naturally to th dfinition of a thrmalizd potntial, φ T, which is consrvd along a lin of forc. 19 Th thrmalizd potntial is dfind by Eqn. 5 whr φ rprsnts th plasma potntial and n is a rfrnc dnsity takn at som point along th fild lin. In th drivation of Eqn. 5, th lctron tmpratur has bn assumd constant along lins of forc. kbt φ T φ n ln n (5) Th concpt of thrmalizd potntial is usful in th dsign of Hall thrustrs sinc it shows that th magntic fild lins can b approximatd as quipotntial lins in situations whr th lctron tmpratur is ngligibl compard to th plasma potntial. In othr words, th thrmalizd potntial is a usful tool for prdicting plasma potntial in situations whr lctrons ar tightly bound to th magntic fild lins. This mthod, howvr, is lss usful in th thrustr plum sinc th corrction trm du to thrmal ffcts and dnsity gradints can b as larg as th plasma potntial. Comparing th plasma potntial data of Fig. 16 to th magntic fild profils shown in Fig. 7, it is clar that th lins of forc do not corrspond to quipotntial contours. This is not surprising, sinc th magntic fild strngth is gnrally lss than G and th lctrons ar only wakly magntizd throughout th aras whr th plasma potntial is prsntd. In this situation, thrmal ffcts and dnsity gradints ar dominant ovr th ffcts of th magntic fild, and th plasma potntial is dscribd by th Boltzmann quation givn by Eqn. 6. Th profils calculatd using Eqn. 6 ar shown in Figs. 18- and gnrally agr to within on volt of th masurd valus, xcpt in th most upstram locations of th sampld rgion. In utilizing Eqn. 6, th rfrnc dnsity (n =7x 17 m -3 in this cas) is chosn so as to mak th plasma potntial calculatd along th cntrlin of thrustr 3 at mm match th masurd valu. Whil th choic to match th valu at mm is arbitrary, this approach is xpctd to b valid in most practical clustr configurations sinc th data prsntd hr shows th plasma potntial dirctly downstram of on thrustr in a clustr to b largly unaffctd by th surrounding dvics. Implmntation of Eqn. 6 along with Eqns. 3 and 4 thus allows th plasma proprtis downstram of a clustr of idntical Hall thrustrs to b prdictd basd solly on masurmnts or simulations of a singl unit. Rsults obtaind in this way appar to b accurat to within th margin of rror of typical plasma diagnostics. kbt φ = n ln n (6) As Figs. 16- show, th plasma potntial profils downstram of a clustr ar fundamntally diffrnt than thos of a singl thrustr. Whn ions xit a singl Hall thrustr, thy xprinc a continuous dclin in plasma potntial as thy procd away from th dvic. In othr words, th lctric fild vctor is vrywhr dirctd away 8

9 from th thrustr. Whn multipl thrustrs ar opratd togthr, howvr, a minimum in th plasma potntial occurs in th rgion btwn th thrustrs. This lads to a situation whr sufficintly slow ions, such as thos cratd by charg xchang (CEX), could b trappd in th potntial wll nar th cntr of th clustr and rflctd back upstram as mntiond prviously. This situation is dpictd in Fig. 1, blow, whr dashd blu lins rprsnt quipotntial contours in th rvrsd fild rgion, i.. in aras whr th plasma potntial incrass with incrasing downstram distanc. Th curvd magnta lin rprsnts th path travrsd by a low-nrgy, CEX ion cratd in th plum with insufficint kintic nrgy to ovrcom th rvrsd lctric fild. Fast ions, which compris th majority of th discharg, would not b rflctd by th rlativly wak rvrsd lctric fild btwn th thrustrs. Thy may, howvr, b dflctd downstram by th plasma potntial hill cratd by adjacnt thrustrs. This phnomnon is illustratd in Fig. 1, in which th blu lins rprsnt contours of constant plasma potntial and th rd lins rprsnt th trajctoris of sampl ions. Th phnomnon illustratd in Fig. 1 may constitut an ion focusing mchanism by which ions initially dirctd toward th clustr cntr ar dflctd to marginally lowr angls with rspct to th clustr cntrlin. This ffct may b rsponsibl for th slightly rducd bam divrgnc rportd by Hargus t al. for two oprating thrustrs compard to that prdictd by linar suprposition of th ion flux from individual thrustrs. 8 Figur 1: Ion focusing as a rsult of th plasma potntial structur downstram of a clustr. A B Dtctor In addition to a possibl rduction in ovrall bam divrgnc, th focusing mchanism discussd abov may affct th ion nrgy spctra of Hall thrustr clustrs by prfrntially dflcting low nrgy ions. On can gain insight into this mchanism by rsorting to a simpl phnomnological discussion. Considr two ions, A and B, xiting a thrustr and travling in an idntical dirction toward th cntr of th clustr, but with diffrnt initial kintic nrgis. In this situation, th slowr moving ion, B, would b dflctd by a givn potntial ris to a gratr dgr than its high nrgy countrpart, ion A, as dpictd in Fig. 1. Considring this, a dtctor swpt through th plum would dtct ion A at a highr angl off cntrlin, whil ion B with its lowr nrgy would b dflctd furthr downstram and dtctd at a rlativly low angl. This mchanism may b rsponsibl for th lownrgy structurs visibl in rcntly publishd ion nrgy data. 7 Conclusion A combination of tripl Langmuir probs and floating missiv probs is usd to charactriz th plasma proprtis in th plum of a low-powr Hall thrustr clustr. Th masurmnts show that th plasma dnsity in th clustr plum can b prdictd to a high lvl of accuracy by linar suprposition of th dnsity du to individual thrustrs. Th lctron tmpratur downstram of a clustr of thrustrs is slightly lvatd compard to that masurd downstram of a singl thrustr, although th chang is modst and is within th lvl of uncrtainty typical of th tripl prob diagnostic. A rasonabl stimat of th lctron tmpratur profil in a clustr plum is obtaind by calculating th dnsity wightd avrag of th lctron tmpratur du to ach thrustr oprating individually. Th plasma potntial downstram of a clustr of Hall thrustrs is shown to closly oby th Boltzmann rlation. Emissiv prob masurmnts show a rgion btwn thrustrs whr th plasma potntial incrass with downstram distanc. Th uniqu potntial profils downstram of a clustr lad to a situation whr low-nrgy charg xchang ions can b acclratd upstram by th wak, rvrsd lctric filds that xist btwn thrustrs. Fast ions initially dirctd toward th clustr cntrlin may b dflctd downstram by various dgrs dpnding on thir nrgy to charg ratios. This ion focusing mchanism is hypothsizd to b rsponsibl for ffcts obsrvd 9

10 in rcntly publishd ion flux and nrgy spctrum masurmnts. Rfrncs 1. Spanjrs, G.G., t al., Th USAF Elctric Propulsion Rsarch Program, AIAA , 36 th Joint Propulsion Confrnc & Exhibit, Huntsvill, AL,.. Spors, R.A., t al., Ovrviw of th USAF Elctric Propulsion Program, AIAA-1-35, 37 th Joint Propulsion Confrnc & Exhibit, Salt Lak City, UT, Dunning Jr., J., t al., NASA s Elctric Propulsion Program, IEPC-1-, 7 th Intrnational Elctric Propulsion Confrnc, Pasadna, CA, Dunning Jr., J., t al., NASA s Elctric Propulsion Program, AIAA--3557, 38 th Joint Propulsion Confrnc & Exhibit, Indianapolis, IN, mthus.htm 6. Bal, B.E., t al., Prliminary Plum Charactrization of a Low-Powr Hall Thrustr Clustr, AIAA--451, 38 th Joint Propulsion Confrnc & Exhibit, Indianapolis, IN,. 7. Bal, B.E., t al., Enrgy Analysis of a Hall Thrustr Clustr, IEPC-3-35, 8 th Intrnational Elctric Propulsion Confrnc, Toulous, Franc, Hargus Jr., W.A., t al., Th Air Forc Clustrd Hall Thrustr Program, AIAA , 38 th Joint Propulsion Confrnc & Exhibit, Indianapolis, IN,. 9. Hruby, V., t al., Dvlopmnt of Low Powr Hall Thrustrs, AIAA , 3 th Plasmadynamics and Lasrs Confrnc, Norfolk, VA, Haas, J.M., t al., Prformanc Charactristics of a 5 kw Laboratory Hall Thrustr, AIAA , 34 th Joint Propulsion Confrnc & Exhibit, Clvland, OH, Haas, J.M., t al., Hall Thrustr Discharg Charactrization Using a High- Spd Axial Rciprocating Elctrostatic Prob, AIAA-99-43, 35 th Joint Propulsion Confrnc & Exhibit, Los Angls, CA, Chn, S. and Skiguchi, T., Instantanous Dirct-Display Systm of Plasma Paramtrs by Mans of Tripl Prob, Journal of Applid Physics, 36, 363, Tilly, D.L., t al., Th Application of th Tripl Prob Mthod to MPD Thrustr Plums, AIAA-9-667, 1 st Intrnational Elctric Propulsion Confrnc, Orlando, FL, Haas, J.M., t al., Charactrization of th Intrnal Plasma Structur of a 5 kw Hall Thrustr, IEPC-99-78, 6 th Intrnational Elctric Propulsion Confrnc, Kitakyushu, Japan, Kmp, R.F. and Slln Jr., J.M., Plasma Potntial Masurmnts by Elctron Emissiv Probs, Rviw of Scintific Instrumnts, 37, 455, Ptrson, P.Y., t al., An Exprimntal Invstigation of th Intrnal Magntic Fild Topography of an Oprating Hall Thrustr, Physics of Plasmas, 9, 4354,. 17. Manzlla, D.H., Stationary Plasma Thrustr Ion Vlocity Distribution, AIAA , 3 th Joint Propulsion Confrnc & Exhibit, Indianapolis, IN Kidar M. and Boyd, I.D., Effct of a Magntic Fild on th Plasma Plum from Hall Thrustrs, Journal of Applid Physics, 86, 4786, Morozov, A.I., t al., Plasma Acclrator with Closd Elctron Drift and Extndd Acclration Zon, Sovit Physics Tchnical Physics, 17, 38, 197.