Semi-empirical Evaluation of the Plasma Internal Inductance in Tokamaks

Transcription

1 Jounl of Nucle nd Ptcle Physcs 14 4(3): DO: 1.593/j.jn Sem-emcl Evluton of the Plsm ntenl nductnce n Tokmks A. Pknezhd 1* A. Sl Elh M. Ghonnevss 1 Physcs Detment Shest nch-slmc Azd Unvesty Shest n Plsm Physcs esech Cente Scence nd esech nch slmc Azd Unvesty Tehn n Astct n ths e we esented n nlytcl nd exementl och fo mesuement of the lsm ntenl nductnce n -T1 tokmk. Fo ths uose dmgnetc loo wth ts comenston col nd lso n y of mgnetc oes wee desgned constucted nd nstlled on oute sufce of the -T1 tokmk chme nd the olodl et nd the Shfnov mete nd then the ntenl nductnce mesued. Moeove few oxmte vlues of the ntenl nductnce fo dffeent ossle ofles of the lsm cuent densty e lso clculted. Keywods Tokmk Plsm ntenl nductnce Dmgnetc Loo Mgnetc Poe 1. ntoducton ecuse of the elton etween the lsm ntenl nductnce nd lsm cuent ofle t s one of the mn metes of the tokmk lsm. Mgnetc dgnostcs n tcul toodl flux loo (dmgnetc loo) e commonly used n tokmks to mesue the vton of toodl flux nduced y the lsm. Fom ths mesuement the totl dmgnetc enegy content nd the confnement tme of the lsm cn e otned s well s the olodl et. On the othe hnd mesuements of the mgnetc felds dstuton outsde the lsm gve us the Shfnov mete (symmety fcto Λ β + l / 1 ). Theefoe the lsm ntenl nductnce s cn e otned usng sutcton. Also the vlue of l s detemned y the dl dstuton of toodl cuent ofle of the lsm [1-13]. n ths e we esented n exementl och sed on the dmgnetc loo nd mgnetc oe nd moeove n oxmte clcultons fo detemnton of the lsm ntenl nductnce n -T1 Tokmk whch s smll low β nd lge sect to tokmk wth ccul coss secton (see Tle 1) [14-67]. Detls of the exementl och fo mesuement of the lsm ntenl nductnce wll e esented n secton. Detls of oxmte clcultons fo detemnton of the ntenl nductnce wll e esented n secton 3. Exementl * Coesondng utho: A.Pknezhd@ush.c. (A. Pknezhd) Pulshed onlne t htt://jounl.su.og/jn Coyght 14 Scentfc & Acdemc Pulshng. All ghts eseved esults wll e dscussed n secton 4. Also summy wll e esented n secton 5. Tle 1. Mn metes of the -T1 tokmk Pmetes Mjo dus Mno dus Toodl Feld Plsm Cuent Dschge Tme Vlue 45 cm 1.5 cm 1. T 4 ka 35 ms Electon Densty cm 3. Exementl Aoch fo Mesuement of the Plsm ntenl nductnce Shfnov mete elte to the dstuton of mgnetc felds ound the lsm cuent. Theefoe t cn e wtten n tems of the tngentl nd noml comonents of the mgnetc feld ound the lsm. Dstutons of the olodl nd dl mgnetc felds e cn e wtten n the fst ode of the nvese sect to s follows esectvely [1]: ln π 4π Λ s (1) cos

2 Jounl of Nucle nd Ptcle Physcs 14 4(3): ln 4π 1 + Λ s sn whee s the mjo dus of the vcuum vessel the Shfnov shft () s s s the lsm cuent nd e the mno lsm dus nd mno chme dus esectvely nd Λ s the Shfnov mete. These equtons ccute fo low β lsm nd ccul coss secton tokmks s -T1 nd whee: Λ β + l / 1 (3) whee β s the olodl et nd l s the lsm ntenl nductnce. engng of the Eq. (3) gve us the fst elton fo l : l ( Λ β 1). (4) 1 + Also y engng nd comnton of the Eq. (1) nd Eq. () the Shfnov mete cn e mesued: π Λ ln + ( + n ) whee (5) ( ) ( π ) π 3π n n( ) n( ) whch cn e mesued usng the mgnetc oes. Also the olodl et s cn e mesued usng the dmgnetc loo. Theefoe wth comnton of the mgnetc oes nd dmgnetc loo mesuements the ntenl nductnce cn e mesued fom the Eq. (4). Mgnetc oes consst of col n solenodl fom whch whose dmensons e smll comed to the gdent scle length of the mgnetc feld. A totl mgnetc flux ssed though such col s Φ na whee n s the nume of tuns of col A s the vege e of coss secton of col nd s the locl mgnetc feld llel to the col xs. The nduced voltge n the mgnetc oe nd then mgnetc feld s: dφ d V na naω dt dt (6) 1 V dt na whee ω s the fequency of the fluctutons of the mgnetc feld. Theefoe n ode to mesuement of the mgnetc feld dstuton we must e ntegtng the outut sgnls of the mgnetc oe. On the othe hnd dmgnetc loo mesues the toodl dmgnetc flux fo the uose of mesuement of the olodl et nd theml enegy of the lsm. t s usully sngle we whch cclng the lsm column ethe nsde o outsde of the lsm vcuum chme. ntnsclly ths loo wll lso cku the toodl mgnetc flux fom the toodl feld col nd ny cuent ccultng n the olodl lne n tcul toodl feld col cuent eddy cuents n the conductng vcuum chme nduced dung tnsent chnges n the lsm enegy nd lsm cuent. n othe wods the dmgnetc loo consst of smle loo tht lnks the lsm column delly locted n olodl decton n ode to mnmze detectng the olodl feld. elton etween the dmgnetc flux nd the olodl et deved fom smlfed equlum elton [-4] s: 8π φ β 1 Φ D (7) whee Φ D Φ totl Φ vcuum nd whee Φ vcuum ΦT + Φ O + ΦV + Φ E whee φ s the toodl mgnetc feld n the sence of the lsm whch cn e otned y the mgnetc oe o dmgnetc loo s the lsm cuent whch cn e otned y the ogowsk col T s the toodl flux ecuse of toodl feld cols Φ O nd Φ V e the ssng flux though loo due to ossle mslgnment etween ohmc feld nd vetcl feld nd the dmgnetc loo nd Φ E s the toodl feld due to eddy cuent on the vcuum chme. These fluxes cn e comensted ethe wth comenston col o dy uns technque. t must e noted tht comenstng col fo dmgnetc loo s wed out of the lsm cuent nd only the toodl flux (whch s nduced y the chnge of toodl feld col cuent when lsm dschges) cn e eceved. Accodng to ove dscusson we desgned constucted nd nstlled fou mgnetc oes nd lso dmgnetc loo wth ts comenston col on oute sufce of the -T1 n ode to mesuements of the Shfnov mete nd olodl et esectvely. Plsm cuent s lso mesued wth ogowsk col. Exementl esults wll e esented n the secton Aoxmte Clcultons of the Plsm ntenl nductnce The ntenl nductnce of the lsm e unt length nomlzed to / 4π cn e detemned fom the consevton of zeoth ode mgnetc enegy: Φ

3 96 A. Pknezhd et l.: Sem-emcl Evluton of the Plsm ntenl nductnce n Tokmks l L / π / 4π Plsm ( ) Fo tycl ofle of the olodl feld whch coesond to flt cuent densty ofle J (usully ccute fo low et tokmk) s: J J < J < whee. π Then fst oxmte vlue fo the ntenl nductnce cn e esly otned y susttutng Eq. (9) n Eq. (8): l d 3 V (8) (9) 1 ln (1) whee ths elton fo -T1 tokmk metes equl to vlue of.994. Second oxmte vlue fo the ntenl nductnce cn e detemned fom the well-known ennett cuent densty ofle s: J π ( + ) J < < (11) theefoe the olodl mgnetc feld ofle cn e otned: π + < < 4 π (1) nd then second oxmte vlue fo ntenl nductnce cn e otned: 1 4 l 3 ln 1 (13) whee ths elton fo -T1 tokmk metes equl to vlue of.33. n genel cse fo the lge sect to nd ccul lsm the cuent densty dstuton s []: J J J 1 ( ) υ < < (14) The olodl mgnetc feld ofle cn e otned: whee J ( ) ( υ + 1) J ( ) ( υ + 1) 1 1 q q ( ) ( ) π 1 P J υ+ 1 ( ) < < 1 (15) υ (16) f we ssume moe eked cuent ofle wth centl sfety fcto q ( ) 1 then the fouth oxmte vlues of the ntenl nductnces cn e detemned fom susttutng the Eq. (15) n Eq. (8) s functon of the υ. esults esent n tle nd Fgue (1). Tle. Deendence of the ntenl nductnce to the vlues of υ fo -T1 tokmk metes υ ntenl nductnce ( l 4 ) υ ntenl nductnce ( l 4 ) Fgue (1). Deendence of the ntenl nductnce to the vlues of υ fo -T1 tokmk metes Ou exements show tht the vlue of υ whch ootonl to the edge sfety fcto educed fom 8 to 1 long tme ntevl of lsm cuent (see Fgue ()). Theefoe ccodng to ecent clcultons fo the -T1 tokmk lsm the vlues of ntenl nductnce educed fom.5 to 1. long the tme ntevl of lsm cuent.

4 Jounl of Nucle nd Ptcle Physcs 14 4(3): detect the noml comonent of the mgnetc feld ρ. Also dmgnetc loo wth ts comenston col wee constucted nd nstlled on oute sufce of the -T1 tokmk chme nd then the olodl et mesued fom them. Afte mesuements of nd ρ nd then the Shfnov mete fom mgnetc oes fom ogowsk col olodl et fom dmgnetc loo nd susttutng them n to Eq. (4) the ntenl nductnce ws mesued. esults esented n the Fg. (3). Desgn metes of the mgnetc cku cols esented n Tle 3. Dmgnetc loo nd ts comenstng col lso wee constucted nd nstlled on the -T1 tokmk. ts chctestcs e lso shown n Tle 3. As shown n Fgue (3) the vlues of the ntenl nductnce educed fom to.61 long the tme ntenl of the lsm cuent. Fgue (). Comnton of the Dmgnetc Loo nd Mgnetc Poe esults: () Plsm Cuent () Effectve Edge Sfety Fcto (c) Toodl Mgnetc Feld nd (d) Shfnov Pmete 4. Exementl esult fo Mesuement of the Plsm ntenl nductnce Tle 3. Desgn metes of the mgnetc oe nd dmgnetc loo Pmetes Mgnetc Poe Dmgnetc Loo (esstvty) 33 Ω 1 Ω L (nductnce) 1.5mH mh n (Tuns) 5 17 S (Senstvty).7mV/G.5V/G f (Fequency esonse) khz 5kHz Effectve na. m 16 m d (We Dmete).1mm.mm Fgue (3). Comnton of the Dmgnetc Loo nd Mgnetc Poe esults: () Plsm Cuent () ntenl nductnce otned y Sutcton of Polodl et (c) fom Shfnov Pmete (d). As osevle the ntenl nductnce educes fom to.61 d m (Col Avege dus) 3mm 175mm Accodng to exementl och n secton n the -T1 tokmk n y of fou mgnetc oes wee desgned two mgnetc oes wee nstlled on the ccul contou Γ of the dus 16. 5cm n ngles of nd π to detect the tngentl comonent of the mgnetc feld nd two mgnetc oes e lso nstlled ove π / nd elow 3π / to 5. Summy Ay of mgnetc oes nd lso dmgnetc loo wth ts comenston col hve een desgned constucted nd nstlled on oute sufce of the -T1 tokmk chme. The olodl nd dl comonents of the mgnetc felds nd lso dmgnetc flux sgnl mesued nd theefoe the Shfnov mete nd olodl et nd then the lsm ntenl nductnce wee mesued fom them. Also few oxmte vlues of the ntenl nductnce clculted.

5 98 A. Pknezhd et l.: Sem-emcl Evluton of the Plsm ntenl nductnce n Tokmks ACKNOWLEDGEMENTS Ths wok ws suoted y Shest-nch slmc Azd Unvesty unde contct nume [5] A. Sl Elh et l. J. Fuson Enegy 8 (4) (9). [6] A. Sl Elh et l. J. Fuson Enegy 8 (4) (9). [7] A. Sl Elh et l. J. Fuson Enegy 8 (4) (9). [8] A. Sl Elh et l. J. Fuson Enegy 8 (4) (9). EFEENCES [1] V. S. Mukhovtov nd V. D. Shfnov: Nucl. Fuson 11 (1971) 65. [] J. Wesson Tokmks Clendon Oxfod [3] E. J. Stt nd et l. 6 Fuson Scence nd Technology [4] M. Soloe et l. Czech. J. Phys. 55 (1) (5). [5] P. Devynck et l. Physcs of Plsms 13 (1) (6). [6] A. Sl Elh et l. EEE Tns. Plsm Scence (1). [7]. Vtcheslv et l. J. Plsm Fuson es (). [8] E. Y. Wng et l. Nucl. Fuson (1995). [9] Ch. P. tz et l. ev. Sc. nstum (1998). [1] V. V. ulnn et l. Plsm Phys. Contol. Fuson 48 A11 (6). [11] J. A. C. Cl et l. Plsm Phys. Contol. Fuson 4 11 (1998). [1] C. Slv et l. 17th AEA Fuson Enegy Confeence EX/P1-1 Lyon Fnce () [13] A. Sl Elh et l. EEE Tns. Plsm Scence 38 () (1). [14] A. Sl Elh et l. EEE Tns. Plsm Scence 38 (9) (1). [15] M. Emm M. Ghonnevss A. Sl Elh nd A. hm d J. Plsm Phys. 76 (1) 1-8 (9). [16] A. Sl Elh et l. Fuson Engneeng nd Desgn (1). [17] A. Sl Elh et l. Phys. Sct (9). [18] A. Sl Elh et l. Phys. Sct (9). [19] A. Sl Elh et l. Phys. Sct 81 (5) 5551 (1). [] A. Sl Elh et l. Phys. Sct 8 55 (1). [1] M. Ghonnevss A. Sl Elh et l. Phys. Sct 8 (3) 355 (1). [] A. Sl Elh et l. J. Fuson Enegy 8 (4) (9). [3] A. Sl Elh et l. J. Fuson Enegy 8 (4) (9). [4] A. Sl Elh et l. J. Fuson Enegy 8 (4) (9). [9] A. Sl Elh et l. J. Fuson Enegy 8 (4) (9). [3] A. hm d M. Ghonnevss M. Emm nd A. Sl Elh J. Fuson Enegy 8 (4) 4-46 (9). [31] A. Sl Elh et l. J. Fuson Enegy 9 (1) 1-4 (1). [3] A. Sl Elh et l. J. Fuson Enegy 9 (1) -5 (1). [33] A. Sl Elh et l. J. Fuson Enegy 9 (1) 9-31 (1). [34] A. Sl Elh et l. J. Fuson Enegy 9 (1) 6-8 (1). [35] A. Sl Elh et l. J. Fuson Enegy 9 (1) 3-35 (1). [36] A. Sl Elh et l. J. Fuson Enegy 9 (1) 36-4 (1). [37] A. Sl Elh et l. J. Fuson Enegy 9 (1) 6-64 (1). [38] A. Sl Elh et l. J. Fuson Enegy 9 (1) 76-8 (1). [39] A. hm d M. Emm M. Ghonnevss A. Sl Elh J. Fuson Enegy 9 (1) (1). [4] A. Sl Elh et l. J. Fuson Enegy 9 (1) (1). [41] A. Sl Elh et l. J. Fuson Enegy 9 (1) (1). [4] A. Sl Elh et l. J. Fuson Enegy 9 (3) 9-14 (1). [43] A. Sl Elh et l. J. Fuson Enegy 9 (3) 3-36 (1). [44] A. Sl Elh et l. J. Fuson Enegy 9 (3) (1). [45] A. Sl Elh et l. J. Fuson Enegy 9 (3) (1). [46] M. Ghonnevss A. Sl Elh et l. J. Fuson Enegy 9 (5) (1). [47] A. Sl Elh et l. J. Fuson Enegy 9 (5) (1). [48] A. Sl Elh et l. zln J. Physcs 4 (3) (1). [49] A. Sl Elh et l. J. Fuson Enegy 3 () (11). [5] M.. Ghn M. Ghonnevss A. Sl Elh et l. Phys. Sct (11). [51] A. Sl Elh J. Fuson Enegy 3 (6) (11). [5] A. Sl Elh et l. Fuson Engneeng nd Desgn (11). [53] A. Sl Elh et l. J. Fuson Enegy 31 () (1). [54] M.. Ghn M. Ghonnevss A. Sl Elh nd S. Mohmmd dton Effects & Defects n Solds 166 (1) (11). [55] A. Sl Elh et l. EEE Tns. Plsm Scence (Jnuy 13 n ess) DO: 1.119/TPS [56] A. Sl Elh et l. Acceted fo ulcton n dton Effects & Defects n Solds (Jnuy 1 n ess) DO: 1.18/

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