INDUCTIVE PULSED THRUSTER WITH SUPERCONDUCTING ACCELERATING ELEMENTS
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1 DTVE PSED THRSTER WTH SPERODTG AEERATG EEMETS Vas Rashova¹, a Poomaova¹, Oma JRamez, Ae Dashov² ¹suo Poécco acoa e Méco, ESME-HAA,Av Saa Aa,, P, Méoco DFFAX:6-6--8, E-ma: vas@camecacesmecupm ²aoa Aeospace ves of ae (KhA), 7 haov See, Khaov, 67, ae, FAX: (8)7--- The ucve meho of magec boes acceeag b he supecoucg acceeag ssem s cosee O he base of he suggese moe s possbe o ceae a ew pe of huse fo he supepecse oeao of spacecaf The eecoamcs cacuao of he huse chaacescs s couce The pobem of he effecve asfomao of eecomagec eeg o he ec oe s cosee ouco The ucve meho s cosee o be oe of he mos effecve mehos of acceeag of magec boes The speca sese he meho maes whe supecoucg acceeag ssems ae appe 6 The ma avaage hs case s he absece of osses of ohm essace a he possb of use he hgh eves of eeg suppe o he acceeag ssem O he base of he suggese moe s possbe o ceae a ew pe of huse fo he supe pecse oeao of spacecaf mgh eaze he ehaus of sma so magec boes of a pecse mass o pasmos wh a hgh pecse veoc The cea scheme of he ucve Puse Thuse wh fuhe acceeao of he pasmo he fe of he supecoucg co he egme of o-ecag cue ccuao s cosee Eecoamcs cacuao of he huse chaacescs s couce eveae a umbe of avaages of hs scheme compaave o "wam" ssems The aass of powe epeses of cogec povece s cae o a he osses of he pese scheme ae esmae he puse egme of acceeao The pobem of he effecve asfomao of eecomagec eeg o he ec oe s cosee 7 Theoeca Pa Oe ca cose he scheme of he uco mpuse eecc oce huse wh eacceeao he magec fe of he supecoucg g he egme of he uampe cue ccuao The eecoamc cacuao of he huse cou evea he avaages of hs scheme compaso wh wam ssems Beses, oe ca aaze he powe epeses fo he cogec povece a osses he mpuse egme of he acceeag ssem The ccu of he uco mpuse eecc oce huse wh supecoucg acceeag eemes s pesee Fg The wog subsace s suppe o he mpuse quc-acg vave a ece he foe-pa of he acceeag chae Smuaeous wh he wog subsace supp sag he schage s aze he chae fom he capaco o he ucve eeg accumuao hough he phase shfe (s ecess s show beow) The ge ccu a he phase shfe ae ause so ha he schage cue he co-uco eaches mamum he mome of mamum gas es sbuo he acceeag chae foe-pa A ha sa he avaache ozao pocess begs a he suffce vaue of he fe uco vaao The uce cues appea he oze pasma These uce cues ae fome b movabe eecos, whch eac wh he oaoa magec fe of he schage cue a, heefoe, ae acceeae he eco of he supecoucg g A ha os ae cae awa b he sef-cooae eecc fe of he pasmo Fuhe he acceeao he magec fe of he supecoucg co beg he egme of he uampe cue ccuao occus The pasma veoc eaches mamum he supecoucg co pae Afe ha he pasmo appeas he zoe beh he she 6 Thus, oe ca oe he wo acceeao sages he suggese scheme: acceeao a he schage fom he accumuao hough he co-uco acceeao he magec fe of he supecoucg co The equvae eecc
2 ccu of he eecc oce huse s show Fg ( he case of he capaco use as he eeg accumuao) s equvae mechaca ccu s pesee Fg Fg The scheme of he mpuse huse wh supecoucg uco Fg The eecc scheme Fg The equvae mechaca ccu To cose he acceeag pocess oe ca obseve he agage fuco esgag he schage ccu poso as he a cooae: m & ()
3 he ecpoca uco vaues of he gs,, he uco vaues of he gs he cue vaues of he gs coespog The chages he gs q, q q, a he pasma fame cooae X ca be esgae as he geeaze cooaes oseg he Rea s fuco w R w Q R R Q & Q& () a ffeeag () wh espec o he geeaze cooaes a veoces, oe ca oba he equaos, whch escbe he equvae ccu of he huse Fg m ( ) ( ) R () ( ) ( ) ( ) ( ) ( ) he ssem () he fs s he equao of moo, he hee ohes ae Khgoff s equaos, whch escbe he vaao of he eecc paamees he ccus,, Oe ca ouce he foowg esgaos: K E K E [ ] K ( ) E( ), [ ] ( ) ( ), [ ] ( ) ( ), ( ) ( ) ( ), () ( ) whee s he sace bewee he gs a he pasmo cooae (Fg) hs case he pasma ucaces ae we as: µ [ ], µ [ ], µ [ ] () To eoe he evaves of he ecpoca ucaces oe ca ouce he esgaos: { } K ( ) E( ), ( ) ( ) { } ( ) ( ) ( ), ( ) ( ) ( ) ( ) K E (6) K( ) E( ) ( ) {} ( ) The ucaces of he h gs ae epesse b he epeeces 8 : 8 7 b 8 7 b 8 b 7 µ µ µ, (7) whee he g wh, he auses of he gs,, coespog b,
4 Theefoe { } µ { } µ (8) Fo he umeca cacuaos s covee o cove he ssem of equaos () o he mesoess fom Fo hs oe ca ouce he foowg mesoess vaabes: Dmesoess cues: Dmesoess cooaes: Dmesoess me : (9) Dmesoess voage : Dmesoess auses of gs: Oe ca oba he mesoess ssem of equaos: { } { } q q { } [ ] [ ] v α { } [ ] [ ] { } () [ ] [ ] { } he ssem of equaos () he paamee m q µ s he aaogous of he Asmovsh s paamee epeses he eao of eecomagec a ea quaes of he ssem The vaue R α s he sspaoa paamee of he co-uco 7 8 b - The a aa fo he ssem (79) ae as foows: () he pese case o evauae he acceeao paamees s covee o pescbe he a cue coespog o he equao of he a soe eeges he capaco a he supecoucg co:
5 Ψ ε, () whee Ψ he magec fow hough he supecoucg g Theefoe, he a cue s efe b he fomua: ε () Thus, he ma paamees chaacezg he cosee eecc oce huse ae: q he eao of he accumuae eeg a he ea foces ε he eao, whch eemes he eeg sbuo he ssem bewee he capaco a he supecoucg co α he paamee, whch eemes he vaue of eeg osses fo he essace The smpe evauaos of hese paamees fo pasma cae, ha 7 q α Due o he umeca cacuaos he foowg esus ae obae: he epessos fo he schage a uce cues he pasma he epesso fo he cue he supecoucg co As he esu of he umeca epemes oe geea pecua s eveae w be cosee fs of a ue ou ha he scheme of he uco acceeao ca pove wo egmes he fs oe whe he acceeao sas a he phase, he egee of he soe eeg coveso o he buch ec eeg s sma a he acceeao effcec oes o ecee few pece he seco egme whe he acceeao begs a he mome of mamum cue sbuo ma, he effcec ses coseab a ca each ozes of pece To caf he epeece of he acceeao o he a phase he equao s cacuae fo he eeg coveso effcec he cosee pe of huses: η mv e () o he mesoess fom: ηe () q The eomao of he fomua () oes o coa he coseao of he eeg ouce o he supecoucg g ca be epae ha he cosa eeg cosevao s coec a a eea fe chages he ccuao egme of he uampe cue fo he supecoucg co Thus, he supecouco eeg s o cosume bu coseve accog o he aw of he magec fow cosac (sce he supecoucg g eeg ) s cea ha he supecoucg co w have he osses whe fucog he mpuse egme Fg The epeeces of he movabe eeme veoc o he sace a ffee vaues of he Asmvch s paamee q
6 Fg shows he epeeces of he movabe eeme veoc as he fuco of he sace a ffee vaues q (a e 8 a 8 ) The po coespos o he co-uco poso he po 8 coespos o he supecoucg co poso Obvous, ha he sg of q coespos o he eeg coe cease he ssem ha poves he veoc gowh The eseach showe ha he fee magec bo (pasmo) acceeao ca be eaze he ssem of he coaa supecoucg cos hs case he agage fuco s we as foows: M& (6), whee he summazg, coespo o he umbe of he gs The geeaze cooaes ae, q q a he veoces &, Oe ca oba he equao of he fee pasmo moo: M (7) B he ffeeag o he coespoe cues oe ca efe fve moo egas, whch efec he coos of he magec fow cosac aw: Ψ,,, (8) The equaos fo he muua ucaces of he ssem ca be we he fom: µ K ( ) E( ),,,, (9) whee K ( ) a E( ) - he compee epc egas of he moue ( ) ( ) The evave of he muua ucaces wh espec o s: ( ) ( ) ( ) µ K ( ) E( ) () ( ) ( ) Tag o accou he equao () he moo equao ca be we as: ( ) ( ) ( ) M ( ) ( ) µ K E () ( ) ( ) Oe ca ouce he mesoess paamees: he mesoess cooae () he gs auses ao () Ψ, he magec fows ao () Ψ Ψ π µ M η he ucaces ao () he mesoess me (6) 6
7 he mesoess cooae of he supecoucg g Oe ca ouce he ew esgaos: β µ q π β β,,, (7) ( ) { } K ( ) ( ) ( ) ( ) ( ) ( E (8) ) g β ( ) ( ), K E,,, (9) g β ( ) ( ) K E, ( ) beg ow ha g g he coo a he paamee s he sace bewee he gs a coespog, epesse hough he paamees a Afe he subsuo oe ca we he ssem of equaos he mesoess vaabes escbg he g moo he ssem of he supecoucg gs { } q Ψ g,,,) Ψ The ssem () s he a fo he umeca egao The Aass of he umeca egao Resus The epemea esus ae show Fg Oe ca see he sequea gowh of he g veoc whe passes hough he mupe-u supecoucg ssem fo vaous aos a () Fg The epeeces of he g veoc gowh o he ao of he magec fows 7
8 The aass shows ha hs ssem he movabe g veoc ceases hee mes compaave o he case whe he movabe g s acceeae he fe of he supecoucve g Obvous ha he veoc gowh euces b s passg hough eve subseque g eve occus because of he moo veoc gowh a he euco of he eaco me wh eve subseque eeme oe o coseve he cosa veoc gowh oe ca chage he ssem geome so ha he sace bewee he gs ceases he eco of he moo The same esu ca be obae b he acceeao he g ssem of uequa auses o uequa magec fows The obae esus ae evece of he effecve acceeao possb of so boes o pasma he ssem of coaa gs To avo acceeao osses s suggese o aus he eave poso of he fe cos o o va he sbuo of he a magec fows aog he soeo egh The equao fo he eegec effcec he mesoess fom s: η ( e ) () π Ψ Ψ Ψ σ Ψ Ψ, 8 7 whee b K( ) E( ) The effcec fo vaous vaues of fow aos σ (a ) cacuae b fomua () s show Fg6 Fg6 The epeece of he effcec fo vaous vaues of he fow aos s cea ha whe he eeg ouce o he acceeag pasmo ceases he effcec ses a Fg7 The veoc gowh epeg o he soe eeg 8
9 9 ca each coseabe vaues (7) The obae veoc of he acceeae mass g he 6 cosee huse ca each he eve m/s a he foowg paamee vaues: he supecoucg co ucace H he soe eegj (Fg7) ocusos The eseach cofme ha he use of he supecoucg acceeag eemes pems o eaboae he popuso ssems of he magec boes a pasmos wh hgh effcec of he magec eeg asfomao o he ec eeg Acowegmes Fug fo hs eseach was pove b he ooaco Geea e Posgao e vesgaco e STTTO POTEO AOA e MEXO hough he Poec GP 7 Refeeces Asmovch A, uaov SYu, Pogo M, huva SA, Eecoamcs acceeao of he pasma bue, JETPh, Vo,o, 97 Koesov PM, Eecoamcs pasma acceeao, M Aomza, 97 Mchaevch VS, Kozoez VV, Rashova VM, a ohes, Magec poea we effec of he supecoucg amcs ssem sabzao, -Kev, auova Duma, 99 Sma V Eecosac a Eecoamcs, M zaesvo osao eaua, 9 Rashova VM, Eecoamcs of he eeco oces acceeaos, Khaov, ae, Bue B Supecoucv, -M, M, 97 7 Wa D, a Wuso G Eeco mechacs asfomao of eeg, -M-, -Eega, 96 8 Kaaaov P, Thse A acuao of ucaces, M: Goseegoza, 9 9
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