Improvement of an MPD Thruster Performance with a Laval-type Magnetic Nozzle

Transcription

1 Improvmnt of an MPD Thrustr Prformanc wth a Laval-typ Magntc Nozzl IEPC-5-83 Prsntd at th 9 th Intrnatonal Elctrc Propulson Confrnc, Prncton Unvrsty, Octobr 3 Novmbr 4, 5 M.Inutak *, A.Ando, K.Hattor, H.Tobar, K.Harata **, and T.Komagom Dpartmnt of Elctrcal Engnrng, Graduat School of Engnrng, Tohoku Unvrsty 6-6-5, Aoba-yama, Snda, , Japan Abstract: A Laval-typ xtrnal magntc nozzl s appld to an MPD thrustr n ordr to mprov ts prformanc and th xhaustd plasma flow s nvstgatd spctroscopcally. By nstallng a magntc Laval nozzl nar th muzzl of an MPD thrustr, a subsonc flow s succssfully acclratd to a suprsonc on by convrtng on thrmal nrgy to flow nrgy. Howvr, flow vlocty s found to dcras suddnly n th dvrgng rgon of th Laval nozzl. By usng a magntc Laval nozzl wth a gntl gradnt n th dvrgng rgon, flow vlocty ncrass smoothly and a suprsonc flow s obtand n th unform magntc fld rgon. Nomnclatur I d = dscharg currnt Α = ffctv cross scton of plasma J r = radal componnt of currnt dnsty μ = magntc momnt BBz = axal componnt of magntc fld r p = plasma radus Bθ = azmuthal componnt of magntc fld ρ = Larmour radus of lctron U z = axal componnt of plasma flow vlocty ρ = Larmour radus of on U θ = azmuthal componnt of plasma flow vlocty U = total plasma flow vlocty M = on acoustc Mach numbr γ = spcfc hat rato of ons γ = spcfc hat rato of lctrons m = mass of on T = on tmpratur T = lctron tmpratur n = numbr dnsty of lctrons n = numbr dnsty of ons W thrmal = plasma thrmal nrgy W flow = plasma flow nrgy * Profssor, Dpartmnt of Elctrcal Engnrng, nutak@c.tohoku.ac.jp. Assocat Profssor, Dpartmnt of Elctrcal Engnrng, akra@c.tohoku.ac.jp. Rsarchr, Dpartmnt of Elctrcal Engnrng, hattor@c.tohoku.ac.jp.. Rsarchr, Dpartmnt of Elctrcal Engnrng, tobar@c.tohoku.ac.jp. ** Graduat studnt, Dpartmnt of Elctrcal Engnrng, harata@c.tohoku.ac.jp. Graduat studnt, Dpartmnt of Elctrcal Engnrng, komagom@c.tohoku.ac.jp Th 9 th Intrnatonal Elctrc Propulson Confrnc, Prncton Unvrsty, Octobr 3 Novmbr 4, 5

2 I. Introducton LECTRIC propulson (EP) s on of th most promsng spac propulsons wth a hgh spcfc mpuls I E sp whch s dfnd by a rato of a thrust to a propllant wght flow rat, rprsntng a propllant xhaust vlocty dvdd by th gravty acclraton. Ths systm utlzs th lctrc nrgy to onz a propllant gas that s acclratd by lctro-thrmal, lctrostatc or lctromagntc ffcts. Snc onzd propllant s xhaustd downstram of th thrustr wth a vlocty much hghr than that n a chmcal rockt, EP systm nabls a longtrm spac msson wth lss consumpton of th propllant. Rcntly, thy ar utlzd not only for an atttud or poston control for varous satllts but also for a man ngn n dp-spac xploratons. In an astrod-samplrturn projct of ISAS (JAXA), Japan launchd a spaccraft HAYABUSA n May, 3., Th man ngn conssts of 4 on ngns whch utlz an ECR(lctron cyclotron rsonanc) producd plasma nstad of a convntonal flamnt or hollow cathod dscharg plasma. Varous typs of advancd spac propulson dvcs hav bn proposd and undr dvlopmnt n ordr to b utlzd not only n a man ngn for a small spaccraft but for a larg-szd, long-trm spac mssons, such as a mannd Mars xploraton and an arth-mpact-astrod dorbtng. 3 For a mannd ntrplantary spac thrustr, both a hghr spcfc mpuls and a largr thrust ar rqurd. Untl th ralzaton of a fuson-plasma thrustr, a magntoplasmadynamc thrustr (MPDT) drvn by a fsson ractor s on of th promsng canddats for a mannd Mars spaccraft. An MPDT plasma s acclratd axally by slf-nducd j B forc. 3 A pulsd MPDT of ISAS (JAXA), Japan drvn by a solar cll was tstd on board a spac laboratory SFU launchd by th H-II rockt of NASDA (JAXA), Japan n March, 995 and rtrvd by th spac shuttl Endavor of NASA, USA n January, 996. Th MPDT was succssfully opratd for 4, shots wth I sp of, sc. 4 An MPDT has hgh-thrust dnsty, whch s proportonal to th squar of th dscharg currnt, and so thrust ffcncy s mprovd n a hghr currnt opraton. Charactrstcs of an xpandng plasma from an appld-fld MPDT wr nvstgatd xprmntally 5,6 and thrust prformanc of an MPDT was found to b mprovd by applyng an xtrnal magntc nozzl nstad of a sold nozzl. 7-9 An appld-fld MPDT opraton wll hlp rduc roson of lctrods and dffus currnt attachmnt, whch ar crucal problms for a stady-stat and hgh-currnt opraton of an MPDT. Plasma acclraton mchansm, howvr, bcoms vry complcatd du to th addton of j r Bz rotatonal, j θ B r B Hall and magntc-nozzl acclratons. It s mportant to clarfy ffct of th magntc fld and to obtan an optmum magntc nozzl confguraton n th vcnty of an MPDT outlt for th mprovmnt of thrust ffcncy. In ordr to nvstgat ffcts of th xtrnal magntc fld on MPDT charactrstcs, w hav studd a plasma flow producd by an MPDT n dtal by us of a spctromtr and Mach probs n th HITOP dvc, Tohoku Unvrsty. -3 In our prvous xprmntal works, t was found that an on Mach numbr M of an MPDT plasma wth a unform magntc fld was lmtd blow unty vn n a hgh currnt opraton. Whn th dscharg currnt ncrass up to ka, a plasma flow vlocty ncrasd almost lnarly wth th currnt. Whras, an on tmpratur suddnly ncrasd whn th dscharg currnt bcoms mor than 8kA, rsultng n th lmtaton of M lss than unty n th vcnty of th MPDT. In such a hgh currnt rgon, an nput lctrc nrgy was convrtd to a thrmal nrgy rathr than a flow nrgy, ladng to undsrabl on hatng. Svral attmpts such as masurmnts of spatal profls of nducd magntc flds by a magntc prob array hav bn prformd to clarfy mchansms of th on hatng and th Mach numbr lmtaton. 4,5 It s vry mportant to dvlop an optmum magntc nozzl confguraton n th vcnty of an MPDT for convrtng a hgh on thrmal nrgy to an axal flow nrgy and for mprovng ts thrust ffcncy. In ordr to vrfy th magntc nozzl ffct on th MPDT plasma, w attachd a small-szd magntc col wth a shortr charactrstc lngth. A Laval-typ magntc nozzl confguraton s formd n th outlt rgon of th MPDT and ts ffcts on th spatal varaton of plasma paramtrs ar masurd by us of a spctromtr and Mach probs. It s xpctd that th subsonc flow nar th MPDT s convrtd to a suprsonc flow through th magntc Laval nozzl as n a convntonal comprssbl gas flow. In ths papr w prsnt charactrstcs of a plasma flow producd by an MPDT wth addtonal magntc nozzl confguratons. Spatal varatons of plasma paramtrs ar dscussd n comparson wth on-dmnsonal sntropc flud quatons n a comprssbl gas. Th 9 th Intrnatonal Elctrc Propulson Confrnc, Prncton Unvrsty, Octobr 3 Novmbr 4, 5

3 Anod Fast Actng Valv mm Gas flow Gas Rsrvor. m 3mm Cathod Fgur. Schmatc vw of th HITOP dvc. Fgur. A sd vw of th MPD thrustr. II. Exprmntal apparatus A. HITOP dvc Exprmnts ar prformd n th HITOP (HIgh dnsty TOhoku Plasma) dvc of Tohoku unvrsty 5-7. Th HITOP dvc conssts of a larg cylndrcal vacuum chambr (damtr D =.8 m, lngth L = 3.3 m) and man and 6 auxlary xtrnal magntc cols, whch can gnrat a unform magntc fld up to kg, as shown n Fg.. Although varous typs of magntc fld confguratons can b formd by adjustng ths col currnts, a unform magntc fld B of.87t s appld by ths cols n th prsnt xprmnts. A hgh-powr, quas-stady MPDT s nstalld at on nd of th HITOP dvc. A schmatc vw of th MPDT s shown n Fg.. It has a coaxal structur wth a cntr tungstn rod cathod ( mm n outr damtr) and an annular molybdnum anod (3 mm n nnr damtr). A fast actng gas valv can njct hlum gas quas-stadly for 3ms. Aftr th gas valv s opn, dscharg currnt I d up to ka s suppld by a puls-formng ntwork (PFN) systm wth a quas-stady duraton of ms. Th currnt can b ncrasd to 5kA wth a shortr quas-stady duraton of.4ms. Th currnt I d can b controlld by varyng th chargng voltag of th PFN powr supply. Th coordnat drcton of X, Y and Z-axs ar shown n Fg. and. Th poston Z= s locatd at th cathod tp of th MPDT. B. Dagnostcs Spctroscopc dagnostcs ar usd to masur an on tmpratur T, axal and azmuthal (rotatonal) flow vlocts U z, U θ n th outlt rgon of th MPDT. Th on tmpratur and flow vlocts ar obtand from Dopplr broadnng and spctral shft of ln spctra. Emsson from th plasma s collctd by a quartz lns and s transfrrd to a spctromtr by a sngl fbr cabl. A ln spctrum s dtctd wth an mag ntnsfr tub coupld wth a CCD camra st at th xt plan of a Czrny-Turnr spctromtr wth a focal lngth of m and a gratng 4 groovs/mm. In cas of hlum gas, HII ln spctra (λ = nm) ar obtand n vry.msc tm ntrval durng a shot wth th spctral rsoluton of.nm and tm volutons of T, U z and U θ ar obtand. optcal fbr scan quarz lns MPDA Cathod Anod B to spctromtr B LN HITOP dvc Laval nozzl col typa Y X Z Laval nozzl col typb Fgur 3. Layout of altrnatvly usd two typs of Laval-nozzl cols. Axal profls of th magntc fld nar th MPDT ar shown n cas of typ-a col ( BLN) n addton to a unform fld (B B ). 3 Th 9 th Intrnatonal Elctrc Propulson Confrnc, Prncton Unvrsty, Octobr 3 Novmbr 4, 5

4 Elctron tmpratur and dnsty profls ar masurd by a movabl trpl prob and a fast-voltag-scannng Langmur prob. An on Mach numbr M s also masurd by a movabl Mach prob 6 and an array of 3-channl Mach probs st at.7m downstram of th MPDT. Tm-varyng magntc flds n th plasma flow ar masurd drctly by a movabl magntc prob array. C. Laval nozzl cols In ordr to closly nvstgat a Laval nozzl ffct on a thrmal nrgy convrson to a flow nrgy, a short magntc Laval nozzl confguraton s formd nar th MPDT outlt. Small-szd addtonal cols, typ-a and B ar nstalld n th vcnty of th MPDT. Fg.3 shows an arrangmnt of th cols and axal profls of th rsultant magntc fld. Two typs of th cols (typ-a and typ-b wth th nnr damtrs of cm and 4cm, rspctvly) ar usd. As th locaton of th cols and col currnts can b changd, w can nvstgat ffcts of th nozzl shap on th xhaust plasma paramtrs n ordr to optmz th magntc Laval nozzl confguraton. III. Exprmntal rsults A. Effct of th magntc Laval nozzl Frstly, a magntc Laval nozzl confguraton s formd by usng only th typ-a col. W masurd axal varatons of T and U n both upstram and downstram rgons of th magntc throat n ordr to clarfy mchansm of th magntc Laval nozzl. Fgur 4 shows axal profls of a magntc fld, an ffctv cross scton of th plasma A, T, U z and M. Th ffctv cross scton s stmatd from a radal profl of th lght msson ntnsty. Th profl s almost Gaussan and a plasma radus s drvd from th - foldng lngth of th profl. Total flow vlocty U of th MPDT has two domnant componnts, that s, axal vlocty U z and azmuthal vlocty U θ. Ths vlocts ar masurd smultanously by th spctromtr. Th vlocty U s drvd as U U Z +. Axal flow vlocty Magntc fld, T cross scton, U z, 3 m/s cm Ion tmpratur T, V Mach numbr M (c) (d) () wth Laval w/o Laval B LN B LN =T B LN =.3T 3 Axal poston Z, cm 3 5 Fgur 4. Axal profls of flow charactrstcs wth (sold crcls) and wthout (opn crcls) th Laval nozzl. A subsonc flow s convrtd nto a suprsonc on passng through th magntc Laval nozzl. I d =7.kA. = U θ () An on Mach numbr of th plasma M s drvd by usng T and U and rlatd to th rato of a plasma flow nrgy to a thrmal nrgy, U U M = = C γ T + γ T / m = s ( ) ( n + n ) mu γ n T + γ n T = W W flow thrmal, Hr γ and γ ar th spcfc hat rato of ons and lctrons, rspctvly, and m s th mass of a hlum on. W assumd γ =5/3, γ =and T =5V n th calculaton of M n Fg.4. It s clarly shown n Fg.4 that th on tmpratur dcrass and th flow vlocty ncrass whn th plasma passs through th Laval nozzl. M also ncrass from a subsonc valu (M <) to a suprsonc on (M >). M 4 Th 9 th Intrnatonal Elctrc Propulson Confrnc, Prncton Unvrsty, Octobr 3 Novmbr 4, 5 Flow nrgy, V ()

5 attans unty at th nozzl throat, whch s th sam bhavor as n a comprssbl gas. In th upstram rgon of th nozzl, ths varatons of th flow paramtrs ar rvrsd: that s, T bcoms hghr and U z and M bcom lowr n th cas wth th nozzl. Ths shows that th subsonc flow upstram of th nozzl prcvs th xstnc of th nozzl and slf-adjusts so as to satsfy th sonc condton at th nozzl throat. Fgur 5 shows flow charactrstcs masurd at Z=3.5cm n th downstram rgon of th Laval nozzl as a functon of I d. As I d ncrass, U z and T ncrass n proporton to th currnt but T abruptly ncrass abov I d =8kA n th cas wthout th Laval nozzl. By applyng th Laval nozzl n th outlt rgon of th MPDT, th ncras of T s supprssd and U z ncrass addtonally and as a consqunc, M kps th valu abov unty n th downstram rgon. It s also confrmd that th total nrgy, sum of th flow nrgy and th thrmal nrgy, n th cass wth and wthout th Laval nozzl agrs wll wth ach othr wthn an xprmntal rror. Ths ndcats that thrmal nrgy succssfully s convrtd to th flow nrgy by th magntc Laval nozzl. B. Bhavor as a plasma flud Whn a plasma s collsonlss and hghly magntzd, ons and lctrons gyrat n th Larmour moton many tms btwn collsons. Th kntc nrgy of th chargd partcls paralll and prpndcular to th magntc fld changs accordng to th magntc fld strngth so as to kp th magntc momnt, μ =(/)mv /B, constant. As a consqunc, thr should not occur any chang n th plasma flow vlocty upstram and downstram of th magntc Laval nozzl, snc thr s no dffrnc n th magntc fld strngth. Undr th prsnt xprmntal condtons, howvr, th xhaustd plasma dnsty s mor than m -3 and th magntc fld strngth s rlatvly wak around.t. Th Hall paramtrs of lctrons and ons, ω c τ and ω c τ, ar calculatd along th Z-axs as shown n Fg.6. Ratos of th Larmour radus to th plasma radus r p drvd by spctroscopy for lctrons and ons, ρ /r p and ρ /r p, ar also shown n th fgur. Snc th Hall paramtr of ons s lss than unty, th ons do not magntzd n th rgon of th Laval nozzl. Ions colld wth ach othr so frquntly that thy bhav as an on flud. Whras, th lctrons ar magntzd n th nozzl rgon and th lctron Larmour radus s much lss than th plasma radus. Thn th moton of lctrons n th plasma flow s constrand by a magntc fld ln. Although th ons bhav as a flud, ts boundary n radal drcton s affctd by th bhavor of th lctrons, whch ar constrand by th magntc fld, du to th ambpolar radal lctrc fld. Thrfor, ons act as a contnuum mdum boundd by th magntc fld confguraton. Ths mchansm plays an mportant roll for makng th magntc Laval nozzl ffctv. Axal flow vlocty U z, 3 m/s Ion tmpratur T, V Mach numbr M Total Enrgy, V (c) wth Laval w/o Laval (d) 4 8 Dscharg currnt I d, ka 3 5 Flow nrgy, V Fgur 5. Flow charactrstcs wth (sold crcls) and wthout (opn crcls) th Laval nozzl an a functon of dscharg currnt of th MPDT masurd n th downstram rgon of th Laval nozzl (Z-3.5cm). ρ / r p ω c τ lctron on 3 Axal poston Z, cm ρ / r p ω c τ Fgur 6. Axal profls of ratos of a Larmour radus to a plasma radus, ρ /r p and ρ /r p, and Hall paramtrs, ω c τ and ω c τ, for lctrons and ons. 5 Th 9 th Intrnatonal Elctrc Propulson Confrnc, Prncton Unvrsty, Octobr 3 Novmbr 4, 5

6 Magntc fld, T Axal flow vlocty cross scton, U, 3 m/s z cm Ion tmpratur T, V Mach numbr M wth Laval (B =.3T) LN w/o Laval (c) wth Laval w/o Laval.5.5 (d) () Axal poston Z, cm Fgur 7. Axal profls of BBZ, plasma cross scton masurd by spctroscopy A, (c)u Z, (d)t, and ()M, wth and wthout th typ-a magntc Laval nozzl col. I d =7.kA, B =.87T. Magntc fld, T Axal flow vlocty cross scton, U, 3 m/s z cm Ion tmpratur T, V Mach numbr M Isntropc modl Exp. (c) (d).5 () Axal poston Z, cm Fgur 8. Sam as n Fg.7 usng th typ-a and B Laval nozzl cols. Dottd lns corrsponds to prdctd valu by -D sntropc flow modl. In trms of a on-dmnsonal sntropc flow modl n a comprssbl gas, th Mach numbr s rlatd to varaton of th cross-sctonal ara A of th flow channl, dm + ( γ ) M da =. (3) M ( M ) A Also, th flow vlocty U, th tmpratur T and th mass dnsty ρ vary as follows, du da =, (4) U ( M ) A dt ( γ ) M da =, (5) T ( M ) A dρ M da =. (6) ρ ( M ) A Assumng that th flow-channl ara A vars accordng to th magntc flux consrvaton n vacuum BA = const., th axal profls of U, T and M ar calculatd from th abov Hugonot quatons. Th masurd varatons of U, T and M through th Laval nozzl ar compard wth thos prdctd by th -D sntropc flow modl and ar n agrmnt wth ach othr. Quanttatvly, M masurd downstram of th nozzl throat s lowr than th prdctd on. Ths would b du to an undr-xpanson xpctd from th obsrvaton that th cross scton of th 6 Th 9 th Intrnatonal Elctrc Propulson Confrnc, Prncton Unvrsty, Octobr 3 Novmbr 4, 5

7 plasma flow downstram of th throat dos not concd wth that of th vacuum magntc channl. In addton, rcnt xprmnts show that ffcts of th strong damagntsm and th hgh dynamc prssur of th hgh dnsty MPDT plasma dform th xtrnal magntc fld. Ths dformaton ffcts of th nozzl confguraton should b takn nto consdraton for a bttr prdcton. C. Shapng of th nozzl Th magntc Laval nozzl can mprov th xhaust plasma paramtrs as mntond abov. It s obsrvd, howvr, that th flow vlocty bgns to dcras abruptly at som pont n th dvrgng rgon of th Laval nozzl as shown n Fg.6. Ths phnomnon s prsumably rlatd to a shockwav n th dvrgng rgon of th nozzl as was obsrvd n th prvous rsarchs. 5,6 In ordr to avod ths phnomnon, a magntc fld wth a mor gntl gradnt n th dvrgng rgon s formd by usng typ-a and B nozzl cols. Whn ths nozzl s usd, th abrupt dcras of M n th downstram rgon tnds to dsappar. Th flow vlocty ncrass smoothly and M gradually ncrass mor than unty, and thn a suprsonc flow s obtand n th unform magntc fld rgon as shown n Fg.7. As shown also n th fgur, spatal varatons of plasma paramtrs ar smlar to thos prdctd by th -D sntropc flow modl, as far as th masurd cross sctonal ara s usd nstad of th ara prdctd by a vacuum flux tub. Ths xprmnt ndcats that prcs control of th Laval-typ magntc nozzl s ncssary n ordr to mprov th thrust prformanc. It s also notd that th magntc nozzl rato should b optmzd n both th convrgng and th dvrgng rgon by takng nto account ffcts of a hgh plasma prssur and a hgh dynamc prssur of a fast flow. IV. Concluson A magntoplasmadynamc thrustr (MPDT) wth an xtrnally-appld magntc Laval nozzl s nvstgatd to mprov th plasma flow xhaustd from an MPDT. Small-szd cols wth a shortr charactrstc lngth ar attachd nar th outlt of an MPDT to form a Laval-typ magntc nozzl. A plasma flow vlocty ncrass and an on tmpratur dcrass as th plasma passs through th magntc Laval nozzl. An on Mach numbr ncrass from a valu blow unty to abov unty. Incrmnt of th plasma xhaust vlocty s rlatd to th ncras n thrust and spcfc mpuls and rsults n th mprovmnt of th MPDT prformanc. A subsonc flow nar th outlt s succssfully acclratd to a suprsonc flow by convrtng on thrmal nrgy to flow nrgy as s n a convntonal comprssbl gas flow. Ths rsults ar consstnt wth th prdcton from th -D sntropc flow modl. Howvr, flow vlocty s found to dcras abruptly aftr attanng a pak of th Mach numbr n th downstram rgon of th nozzl throat. By usng a magntc Laval nozzl wth a gntl gradnt n th dvrgng rgon, th flow vlocty ncrass smoothly, ladng to a suprsonc flow. Acknowldgmnts Ths work was supportd n part by Grant-n-Ad for Scntfc Rsarchs from Japan Socty for th Promoton of Scnc. Rfrncs Kunnaka H., t al., "Flght Rport Durng Two Yars on HAYABUSA Explorr Proplld by Mcrowav Dscharg Ion Engns, " Procdngs of 4st Jont Propulson Confrnc and Exhbt, AIAA , 5. Funak I., Kunnaka H., and Tok K., "Plasma Charactrzaton of a -cm Damtr Mcrowav Dscharg Ion Thrustr," J. of Propulson and Powr, Vol., No.4, 4, pp Jahn R.G., Physcs of Elctrc Propulson, McGRAW-HILL, Tok K., Shmzu Y., and Kurk K., "On-Orbt Dmonstraton of a Pulsd Slf-Fld Magntoplasmadynamc Thrustr Systm," J. of Propulson and Powr, Vol.6, No.5,, pp Kurk K. and Okada O., Exprmntal Study of a Plasma flow n a Magntc Nozzl, Phys. Fluds, Vol.3, No.9, 97, pp Kurk K. and Inutak M., Supr-Alfvénc Flow and Collson-fr Shock-wav n a Plasma Wnd-tunnl, Phys. Fluds, Vol.7, No., 974, pp Sasoh A., and Arakawa Y.," Elctromagntc ffcts n an appld-fld magntoplasmadynamc thrustr," J. of Propulson and Powr, Vol.8, No., 99, pp Tahara H., Kagaya Y., and Yoshkawa T., "Prformanc and Acclraton Procss of Quasstady Magntoplasmadynamc Arcjts wth Appld Magntc Flds," J. of Propulson and Powr, Vol.3, No.5, 997, pp Th 9 th Intrnatonal Elctrc Propulson Confrnc, Prncton Unvrsty, Octobr 3 Novmbr 4, 5

8 9 Krüll G., Auwtr-Kurtz M., and Sasoh A.,"Tchnology and Applcaton Aspcts of Appld Fld Magntoplasmadynamc Propulson," J. of Propulson and Powr, Vol. 4, No. 5, 998, pp Sasoh A., and Arakawa Y.," Thrust Formula for Appld-Fld Magntoplasmadynamc Thrustrs Drvd from Enrgy Consrvaton Equaton," J. of Propulson and Powr, Vol., No., 995, pp Ando A., t al., Spctroscopc Studs of a Hgh Mach-Numbr Rotatng Plasma Flow, Journal of Plasma Fuson Rsarch, SERIES, Vol.4,, pp Inutak M., t al., Charactrstcs of a Suprsonc Plasma Flow n a Magntc Nozzl, Journal of Plasma Fuson Rsarch, Vol.78,, pp URL: 35.pdf [ctd 3 Octobr 5]. 3 Inutak M., t al., Magntc-Nozzl Acclraton and Ion Hatng of a Suprsonc Plasma Flow, Transactons of Fuson Tchnology, Vol.43, No.T, FUSTE8,, pp Tobar, H., Inutak, M., Ando, A. and Hattor, K., Spatal Dstrbuton of Lorntz Forcs n an Appld-Fld Magnto- Plasma-Dynamc Arcjt Plasma, Journal of Plasma Fuson Rsarch, Vol.8, 4, pp URL: [ctd 3 Octobr 5]. 5 Tobar, H., Ando, A., Inutak, M., and Hattor, K.,, Drct Masurmnt of Lorntz Forcs n an Appld-Fld MPD Thrustr, Procdngs of th 9th Intrnatonal Elctrc Propulson Confrnc, IEPC-5-65, 5. 6 Ando, A. t al., Evaluaton of Para-Prp Typ Mach Prob by Usng a Fast Flowng Plasma Journal of Plasma Fuson Rsarch, Vol. 8, 5, pp URL: [ctd 3 Octobr 5]. 8 Th 9 th Intrnatonal Elctrc Propulson Confrnc, Prncton Unvrsty, Octobr 3 Novmbr 4, 5