J. Plasa Fuso Res. SERIES, Vol. 8 (2009) A Novel Method fo Hgh Cuet Vacuu Ac Iteupto Usg Exteally Appled Ulta Hgh Axal Pulsed Magetc Feld Jouya JADIDIAN, Kaveh NIAYESH ad Ehsa HASHEMI School of Electcal ad Copute Egeeg, Uvesty of Teha, IR-14395 Teha, IRAN * (Receved: 4 Septebe 2008 / Accepted: 9 Febuay 2009) Axal Magetc Feld (AMF) s wdely used vacuu teuptes to keep the ac the dffused ode. Wth ceasg axal agetc feld, the ultple ac ode exteds to hghe ac cuets. I ths ode of ac, the fault cuet ca be easly teupted due to fast ecovey of the dffused vacuu ac. The agetc feld apltudes cosdeed the pecedg studes ae all less tha hudeds of T. I ths pape, the teacto of the vacuu acs wth uch oe tese agetc felds of seveal T ae cosdeed. Fo ths pupose, the MHD equatos descbg the behavo of the hgh cuet vacuu ac ae sulated pesece of a vey tese pulsed agetc feld that s geeated by a hgh cuet pulsed powe souce (Cascaded Flux Copesso Geeatos), ad posed to the teupto chabe exteally. It ca be possble by usg a cuet cayg ducto, whch fly suouds the chabe. Ths helcal ducto s placed as FCG load. The esults dcate that FCG ca ultply the seed cuet,.e., fault cuet (150-kA) up to 1-MA ad cosequetly geeate agetc flux desty ode of 10 T teo of the chabe. Accodg to the sulato esults, such a agetc flux desty, the hgh cuet vacuu ac (150-kA) ca ea dffused ode; ths ethod ca be appled to pove the teupto capablty of vacuu teuptes. Keywods: Axal agetc feld, agetc flux copesso, pulsed powe, cuet teupto vacuu. 1. Itoducto Ma egeeg applcatos of hgh-cuet vacuu acs (VA) ae lked to the use the vacuu swtchgea. Theefoe, the ost studes o hgh cuet VA ae the paaete age specfed by the tasks to be accoplshed by swtchg appaatus. The ost posg fo vacuu teuptes (VIs) sees to be the use of acs, stablzed by a axal agetc feld (AMF) [1,2]. The studes of hgh cuet VA AMF ae fa advaced ad udele the ceato of VI wth hgh pefoace [1-3]. I ecet yeas thee has bee a ceased teest the use of VIs fo hgh voltages [3, 4], ad also fo hgh cuets [1, 5]. Fo stace, a 168 kv two beak pocela type ad a100 ka oe beak vacuu swtchgea have aleady appeaed the Japaese aket ad they ae cuetly beg expoted to wold-wde akets [4]. Fo the quattatve pedcto of the plasa status hgh cuet VA, a ultphyscs appoach has bee appled ths pape. Thee qualfcatos have bee checked fo hgh cuet VA teupto usg a fte eleet sulato: the electo ad o cocetato the VA, electo tepeatue ad the ac voltage. Ths odel assues that a exteal ulta hgh AMF ode of seveal Teslas- has bee appled to the teupto chabe a pulsed ege. The agetc feld apltudes whch have bee cosdeed the pecedg studes ae all less tha hudeds of T. The stogest AMF whch s cosdeed fo hgh cuet VA cotol has bee epoted by Chaly et al. [1] s about 1.2 T whch has studes oly the depedece of ac voltage o the appled B AMF stegth. The a hbto to the applcato of the hghe AMF to the VI s the huge deso of the capacto sets whch poduce AMF. Ths pape deals wth up to 17-T stog AMFs. Such a tese agetc feld ca be poduced usg huge capacto-ducto sets whch ae ot appopate fo cuet teupto puposes. Ths pape has poposed a ovel appoach whch a cascaded Flux Copesso Geeatos (FCG) [6] has bee appled to poduce AMF sde the chabe wth lowe pce, weght ad volue [7]. Fo ths pupose, the ulta hgh agetc fled a pulsed ege (geeated by the FCG [6]) has bee eteed to the odel a te-depedet pocedue. Descptos ad esults of the poposed ethod ad detaled uecal sulatos have bee peseted sectos 2, ad 3 espectvely. Majo cocluso follows the esults s that the ethod of hgh cuet VA cotol by pulsed axal agetc felds s applcable ad effectve, whch keeps hgh cuet VAs up to 200 ka dffused ode. 2. Poposed Syste Fgue 1 llustates the echas of geeatg ulta hgh agetc flux desty teo of the teupto chabe. Oe of the ost advatages of the * E-al: jadda@eee.og 1496 2009 by The Japa Socety of Plasa Scece ad Nuclea Fuso Reseach
J. Jadda et al., A Novel Method fo Hgh Cuet Vacuu Ac Iteupto Usg Exteally Appled Ulta Hgh Axal Pulsed Magetc Feld ethod s that o seed souces lke, chaged capactos s eeded. The fault cuet whch passes the VA s adequate fo flowg pay cuet though the FCG. Fo sepaatg the ccut of FCG fo powe ccut, two hgh cuet tasfoes have bee used. A exaple of a eadly avalable tghtly coupled tasfoes s cuet tasfoes (CT) used by utltes to easue lage AC cuets [8]. Such a tasfoe s oally opeated wth a shot ccut place wth a lage tus-ato fo utlty applcatos. I the ccut of Fg.1, cuet ultplcato of CTs s ot equed ad tus-ato ca be chose as 1. The a duty of these CTs s segegato of ccuts. Also fo pevetg CT coes fo satuato, segeted coe tasfoes ca be used stead of oday CT coes wthout ay a gaps. The output cuet of CTs, s ultpled by a cascaded helcal FCG [7] ad appled to the suoudg wdg of teupto chabe. Ivestgato of FCG behavo wth such a hghly ductve load has bee pefoed by a fte eleet soluto whch the acto of FCG s odeled a sultaeous 3-D theodyac ad electoagetc ethod [6,9]. Fo the cascaded FCG of [7] ad wdg wth3-tus, 14-c coss-secto daete ad 4-c alttude as the FCG load, the cuet eaches 8-T fo oe tha 15-ll secods. Futhe, uecal sulatos ae pefoed fo physcal behavo ad heat flux to the aode of hgh-cuet dffuse of acs as foud vacuu teuptes. The agetohydodyac (MHD) appoach s appled. Heat flux destes to the aode ae pedcted the ght ode of agtude ad essetal physcal detals of the hgh-cuet vacuu ac ( ode of 100-kA) ae dsclosed the pesece of stog pulsed AMF whch s ceated by suoudg wdg of teupto chabe. 3. Plasa odel descpto I ths secto, the atheatcal foulato of the plasa expaso pheoea ad cuet flow the dvdual jets ad the coo cuet chael has bee peseted. I the te-electode plasa ego, whee the jets fo the dvdual cathode spots the case of the ult-cathode-spot VA ae aveaged ad theefoe all plasa paaetes wll be assued to be ufo [5]. The hgh-cuet dffuse ac ode s bedded by the ultple acs at lowe cuets, by dffuse colua acs at hghe cuets ad by colua acs at hgh cuet ad low o o AMF [5, 9]. The ac plasa ca be egaded as a flud that flows fo cathode to aode [9-11]. A 2-D cyldcal hybd odel has bee developed ode to bette pedct the VI behavo the pesece of tese AMF. Ths hybd odel cossts of (1): ass ad (2): oetu cosevato equatos fo electo, o, (3): The heat balace equatos that detee the tepeatues of os ad electos, ad (4) detaled Maxwell equato Plasa behavo ad heat flux desty to the aode ae pedcted fo steady-state codtos, whch appoxate well those dug acg wth susodal 50-Hz cuets (ac). Ths s because the te scales of elaxato ae uch faste tha paaete vaatos (e.g., vaatos of cuet o cotact dstace). u + ( u. ) u + ( u ) = 0 = q ( E + u B) P γ u (1) (2) 3 2 T T + v. z z + T ( v T + v. e e ) + Q = τ e ( T D B H = j +, E =, D = ρ, E = 0 e T ) (3) (4) Fg.1 The echas of geeato of the AMF: Seed cuet of the cascaded helcal FCG s povded fo powe dstbuto syste by eas of hgh cuet segeted coe cuet tasfoe. Ths FCG ultples ths cuet ad jects t to the exteal col to geeate the tese pulsed AMF teo the teupto pocess. whee, sybol epesets electo, os ad o-chaged patcles dexes sepaately (e, dcate electo ad os dexes espectvely). Othe paaetes ca be defed as follows: 1497
J. Jadda et al., A Novel Method fo Hgh Cuet Vacuu Ac Iteupto Usg Exteally Appled Ulta Hgh Axal Pulsed Magetc Feld u T j Q σ P ΔT γ B E ρ patcle desty; patcle dft velocty; patcle tepeatue; ac cuet desty; patcle theal flux; coductvty; pessue; tepeatue dffeeces betwee patcle types Bagsk coeffcets; agetc feld; electc feld, volue chage desty; patcle ass; As bouday codtos, the odel assues o futhe fucto of cathode ad aode othe tha to host the cathode spots ad to be a pefect sk, espectvely [5]. Fgue 2 shows sply the sketch of the VI geoety ad odel of the VA plasa expaso. teupto chabe cosdeg effect of duced cuet electodes ad plasa. Fgue 4 deostates the dstbuto of agetc feld sde the chabe ad both electodes dffeet te steps. Afte seveal co secods afte detoato of FCG, the ducto cuets the cotacts pevet fo sg of the agetc flux desty sde the te-electode aea [Fg. 4, pat (a)], howeve afte elapsg seveal llsecods, whe the tal ducto cuets have dshed, tese agetc flux desty coes to the te-electode space whee hgh cuet vacuu ac has bee appeaed at ths peod [Fg. 4, pat (b)]. Ievtable esstve chaactestcs of the AMF col (load of the FCG) esults a expoetal decease ts cuet ad the geeated AMF cosequetly. Thee s a blateal elatoshp betwee plasa sulatos (Eq. (1-3)) ad electoaget feld calculatos (Eq. 4). It ca be feed fo Fg. 4 that the coductvty of plasa has a o effect o the B AMF dstbuto. It s because of the electcal coductvty of VA s appoxately oe ode of agtude lowe tha coppe (substace of the electodes). The te vayg dstbuto of B AMF has bee eteed to the plasa sulatos each te step of soluto. Fgue 5 lets the sulato esults fo poposed syste ad a covetoal VI to be copaed. Accodg to dstbuto of electo ad o desty these fgues, whch have bee expessed as ol/ 3, t s easoable to thk that the appled B AMF the poposed syste could dffuse the vacuu ac. Aothe esult of the sulato,.e., electo tepeatue these cases, suppots ths dea. Based o Fg. 6, whch shows the dstbuto of electo tepeatue cases of covetoal ad poposed VI, at the te whe each of the each of the eaches the peak of the electo tepeatue. As t ca be see fo ths fgue, the covetoal VI, fo a 150-kA ac, the electo eaches 8.41-eV, whch s hghe tha the theshold [12] of dffused ac. Ths paaete fo the poposed syste, about 6.3-eV, s lowe tha ctcal age. The shape of ths weak AMF dstbuto has bee eteed fo a AMF cotact geeated feld [12]. Fg.2: Sketch of the vacuu ac geoety ad odel of the vacuu ac plasa expaso. 4. Nuecal sulatos esults Fgues 3, 4, 5 ad 6 show sulato esults fo a 150-kA cuet whch s to be teupted. The effect of pulsed AMF has bee vestgated by applyg the wave fo of Fg.3 whch s calculated a sepaate sulato of FCG [6]. Fg.3 shows the te vaatos of pulsed AMF at the cete of the teupto chabe. It ca be see ths fgue that AFM eas hghe tha 8-T fo oe tha 8-s afte detoato of the FCG. The dstbuto of B AMF has bee calculated the Fg.3: Vaato of the pulsed AMF at the cete of the teupto chabe tes of te. 1498
J. Jadda et al., A Novel Method fo Hgh Cuet Vacuu Ac Iteupto Usg Exteally Appled Ulta Hgh Axal Pulsed Magetc Feld Fg. 4: Te vaatos of agetc flux desty teo of the vacuu teupto chabe, (a): 5µs, (b): 5s, (c): 10s afte detoato of the HFCG. It ca be deduced fo educto of electo ad o cocetato fo 4, ad 3 ol/ 3 to 1.2 ad 1 ol/ 3 espectvely that the poposed syste, the VA ea dffused. Also the copaso of the VA voltage dcates the tasto of VA state fo dffused to colua VA [3]. Fgue 7 shows the vaatos of ac voltage tes of B AMF stegth. It should be oted ths fgue deostates the peak value of the voltage. I the age B AMF s lowe tha 5-T at hghest value the pulsed shape (Fg. 3), the ac voltage shows soe spoadc oscllatos (oe of the costcted ac sgs), howeve, these fluctuatos have bee eoved by ceasg the B AMF peak. Futheoe, fo B AMF peaks hghe tha 10-T, ac voltage shows eglgble pple whch s aothe sg of dffused ode of the ac. I ths study, all the appled B AMF s assued to be sla the shape wth Fg. 3 ad oly dffe agetc flux desty apltude. The qualtatve easos of voltage ad cocetato loweg of the vacuu plasa by ceasg of B AMF ca be explaed by the cocept of expadg cathode spot plasa jets. The te-electode plasa s geeated by a ube of cathode spots at the cathode suface, as show qualtatvely Fg.8. I ths fgue, uppe electode s cathode, ad the othe oe s aode. Each dvdual cathode spot poduces a dvdual cuet chael. Due to ts teal pessue gadet, each plasa jet expads adally [11]. Because of the adal expaso, the jets x at soe axal dstace ad fo a coo cuet chael whch cocetato of patcles ae ceases [2]. Ths coo chael ca lead to dffuse-colua ac ad eve colua VA soe extee cases at low B AMF. Two paaetes cotol the state of the ovelapped plasa jets. Fst s the gap dstace, ad the secod s the stegth of B AMF. Loge gap dstace let the jets have oe oo to ovelap ad poduce colua ac. The stoge AMF pches plasa jets ad pevet the fo xg togethe ad poduce colua VA cosequetly (Fg. 8). Fg.5: Sulato esults fo VA the pesece of AMF, (a): electo cocetato fo pulsed AMF: 12 T, (b) Io cocetato fo pulsed AMF: 12 T, (c): electo cocetato fo AMF: 0.35 T, (d) Io cocetato fo AMF: 0.35 T. 1499
J. Jadda et al., A Novel Method fo Hgh Cuet Vacuu Ac Iteupto Usg Exteally Appled Ulta Hgh Axal Pulsed Magetc Feld 5. Cocluso The study of hgh cuet vacuu ac, stablzed by the tese pulsed AMF, have evealed the capablty of cotollg vacuu ac effcetly ad allowed developg the pcples of costucto of optal AMF. The effectveess of usg pulsed ulta hgh AMF has bee vestgated ths pape by odelg MHD equatos of vacuu ac. The esults dcate that the applcato of FCG fo poducg tese agetc feld sde the teupto chabe ca be a posg tool fo hgh cuet teupto. The sulato esults stogly eed futue expeetal valdato. Fg.6: Tepeatue of the electo (Top): fo covetoal AMF: (botto): fo the poposed syste. 6. Refeeces [1] A. M. Chaly et al., IEEE Tas. Plasa Sc. 16, 939 (2007) [2] P. G. Slade, The Vacuu Iteupte: Theoy, Desg ad Applcato (CRC Pess, Boca Rato, FL, 2008). [3] A. M. Chaly et al., IEEE Tas. Plasa Sc. 31, 884 (2003) [4] M. Hoa, IEEE Tas. Delec. Elec. Is., 13, (2006) [5] E. Schade, IEEE Tas. Plasa Sc. 33, 1564 (2005) [6] J. Jadda et al., Poceedg of 16 th ICEE, 720 (2007) [7] J. Jadda et al., IEEE Tas. Plasa Sc. 36, 1116 (2008). [8] L. L. Altglbes et al., Magetocuulatve Geeatos (Spge-Velag, New Yok, 2000). [9] A. Neube, Explosvely Dve Pulsed Powe, Helcal Magetc Flux Copesso Geeatos (Spge-Velag, New Yok, 2005), p 226. [10] J. Jadda et al., Poceedg of IEEE PPPS, 1159 (2007) [11] E. Schade, D. L. Shelev, IEEE Tas. Plasa Sc. 31, 1564 (2003) [12] M. Keda, I. Bels, R. L. Boxa, S. Foldsth, J. Phys. D: Appl. Phys. 29 (1996) [13] M. Keda, B. Schula, IEEE Tas. Plasa Sc., 28, 347 (2000) Fg.7: Depedece of voltage apltude of the ac voltage (peak) o the stegth of B AMF Fg.8: Scheatc vew of expadg plasa jets tes of AMF stegth. (Left): Weak o o AMF: costcted ac. (Mddle): Stog AMF: dffused ac, (Rght): Vey stog AMF: ultple vacuu ac. 1500