Journl of Nucler nd Prticle Physics 13, 3(4): 11-15 O: 1.593/j.jn.1334.9 Plsm nternl nductnce in Presence of Toroidl Field Rile of Tokmk A. Slr Elhi *, M. Ghornneviss Plsm Physics Reserch Center, Science nd Reserch Brnch, slmic Azd University, Tehrn, rn Astrct n this reserch we investigted the effects of toroidl field rile of tokmk on the lsm internl inductnce. For this urose, rry of mgnetic roes nd lso dimgnetic loo with its comenstion coil were designed, constructed, nd instlled on outer surfce of the R-T1 tokmk. Amlitude of the TF rile is otined.1, nd lso the effect of the TF rile on the lsm internl inductnce ws discussed. n the high field side region of tokmk chmer, the TF rile effect is incresing of the lsm internl inductnce, wheres the low field side hs inverse sitution. Keywords Tokmk, Toroidl Field Rile, Pls m nternl nductnce 1. ntroduction Usully tokmks lsm equiliri re investigted s two-dimensionl (xisymmetric) systems. Although this symmetry offers mny dvntges for its nlysis, ut relistic tokmks consists of finite numer of Toroidl Field (TF) coils. Then, this discreteness yields the toroidl field riles ( eriodic vrition of the toroidl mgnetic field). n other words, relistic tokmks could not e xisymmetric configurtions. Most of the TF rile studies hve een done on effects of the TF rile on confinement of the high energy lh rticles, formtion of internl trnsort rriers, lsm rottion, nd H-mode erformnce. n R-T1 Tokmk, which is smll, low Bet nd lrge sect rtio tokmk with circulr cross section (see Tle 1), the numer N of TF coils is 16, nd then the eriod of the TF rile ws.5. n this er we resent the effects of the TF rile on the ls m internl inductnce in R-T1 tokmk. etermintion of the internl inductnce is essentil for tokmk exeriments nd otimized oertion. Also some of the lsm informtion cn e deduced from this rmeter, such s lsm toroidl current rofile. Mgnetic dignostics, in rticulr dimgnetic loo (toroidl flux loo) re commonly used in tokmks to mesure the vrition of toroidl flux induced y the lsm nd then the oloidl Bet. On the other hnd, the mgnetic fields dis triution outs ide the ls m rovides the mesurement of the comintion of oloid l Bet nd internl inductnce, vi the Shfrnov rmeter ( ). Then mesurement of from the mgnetic roes nd oloidl * Corresonding uthor: Slri_hy@yhoo.com (A. Slr Elhi) Pulished online t htt://journl.su.org/jn Coyright 13 Scientific & Acdemic Pulishing. All Rights Reserved Bet from dimgnetic loo gives vlue of internl inductnce[1-65]. n this er we resent exerimentl investigtion of the TF rile on this rmeter. Becuse of deendence of the toroidl field on the TF rile mlitude, therefore we exect tht this rmeter is lso deending on TF rile mlitude. Brief roch for determintions of the TF rile nd Shfrnov rmeter using the discrete mgnetic roes will e resent in section. imgnetic loo method for mesurement of the oloidl Bet nd internl inductnce will resent in section 3. Exerimentl results of effects of TF rile on the lsm internl inductnce will discuss in section 4. Summry nd discussion will resent in section 5. Tle 1. Min Prmeters of the R-T1 Tokmk Prmeters Mjor Rdius Minor Rdius Toroidl Field Plsm Current ischrge urtion Vlue 45 cm 1.5 cm 1. T 4 ka 35 ms Electron ensity.7-1.5 1 13 cm 3 Toroidl Field Coils 16. etermintions of the TF Rile nd Shfrnov Prmeter Using the iscrete Mgnetic Proes A simle nlytic model of the toroidl mgnetic field strength widely used in the nlysis is[1]: B, B 1 cos - cos N, (1)
1 A. Slr Elhi et l.: Plsm nternl nductnce in Presence of Toroidl Field Rile of Tokmk where B is the toroidl mgnetic field t center of the tokmk chmer, nd re oloidl nd toroidl ngles resectively, is the inverse sect rtio, N is the numer of the toroidl field coils, nd is the mlitude of the TF rile where defined s: B Bmx Bmin. () B B B n the R-T1 the numer of TF coils is 16, then the eriod of the TF rile ws.5, nd the inverse sect rtio is.78. From the Eq. (1) we cn write: 1 B, / N B, 4 B (3) 1 B, / N B,, 4 B where these vlues of the toroidl mgnetic fields cn e determined using the mgnetic roes t ove oloidl nd toroidl ngles. Our mesurements show tht the mlitude of the TF rile in R-T1 is.1, s shown in Fig. (1). mx min where R is the mjo r rdius of the vcuum vessel, the Shfrnov shift, is s is the lsm current, nd re the minor lsm rdius nd minor chmer rdius resectively. These equtions ccurte for low lsm, lrge sect rtio, nd circulr cross section tokmks s R-T1, nd where: where nd where l B B ln i / 1 R B B ( B ( ) B ( ) B B ), ( ), 3 ( ), (6) (7) is the oloidl Bet nd l i is the ls m internl inductnce. We cn otin B nd B fter comensting nd integrting of outut signls of the mgnetic roes. The comenstion done y fields dischrge without lsm nd receives outut signls of the mgnetic roes nd sutrct those from totl outut signls. Exerimentl results will resent in the section 4. Figure (1). eendence of the Toroidl Mgnetic Field on the Poloidl nd Toroidl Angles, TF Rile is lso oservle Also the Shfrnov rmeter relte to the distriution of mgnetic fields round the lsm current. Therefore, those cn e written in terms of the tngentil nd norml comonents of the mgnetic field on the contour (see Fig. ()). istriutions of the tngentil nd norml mgnetic fields re lso cn e written in the first order of the inverse sect rtio s follows, resectively[,3,5]: B 4 R ln 1 1 B 4 R R 1 1 R ln 1 s sin s (4) cos, (5) 3. etermintion of the Plsm nternl nductnce Using the imgnetic Loo The toroidl flux tht roduced y the lsm is relted to the totl erendiculr therml energy of the lsm. This dimgnetic flux is usully mesured with the dimgnetic loo. n cses of the ohmiclly heted tokmks (low et) where the lsm energy density is smll comred to the energy density of the mgnetic field, the chnge in the totl toroidl mgnetic flux is smll. Therefore reference signl equl to the vcuum toroidl mgnetic flux is usully sutrcted from it, giving net toroidl flux equl to the dimgnetic flu x roduced y the circulr lsm. Reltion etween the dimgnetic flux nd the oloidl et derived from simlified equilirium reltion[-7]: totl vcuum 1, (8) 8 B y sustituting the Eq. (1) in the Eq. (8) we hve: 8 B (1 cos - cos N ) 1, (9) where vcuum T O V E, nd where B is the toroidl mgnetic field in the sence of the lsm wh ich cn e otined y the mgnetic roe, is the lsm current which cn e otined y the Rogowski coil, T is the toroidl flux ecuse of toroidl field coils,
Journl of Nucler nd Prticle Physics 13, 3(4): 11-15 13 O nd V re the ssing flux through loo due to ossile mislignment etween ohmic field nd verticl field nd the dimgnetic loo, nd is the toroidl field due E to eddy current on the vcuum chmer. These fluxes cn e comensted either with comenstion coil or fields dischrge without lsm. t must e noted tht comensting coil for dimgnetic loo is wred out of the lsm current, nd only the toroidl flux (which is induced y the chnge of toroidl field coil current when lsm dischrges) cn e received. So the dimgnetic flu x cused y lsm current cn e mesured from the dimgnetic nd comensting coil using sutrction. Therefore, ccording to ove two sections we cn find the internl inductnce. From Eq. (6) we hve: li 1 (1) By sustituting the Eq. (6) nd (9) in Eq. (1), we cn write: li ln 16 B R ( B 1 cos - cos N B ), (11) where the effect of the TF rile introduced in the Shfrnov rmeter. Exerimentl results of effects of the TF rile on the internl inductnce will resent in next section. 4. Exerimentl Results According to ove discussion, we determined the lsm internl inductnce nd the effects of TF rile on it. Results resent in Figs. () nd (3). As shown, the difference etween the internl inductnce in resence of the TF rile nd in sence of the TF rile is in order of the 1, nd in the high field side region of tokmk chmer, the TF rile effect is incresing of the lsm internl inductnce, wheres the low field side hs inverse sitution. 5. Summry nd iscussion n this reserch we investigted the effects of TF rile on the lsm internl inductnce in R-T1 Tokmk. For this urose, rry of mgnetic roes nd lso dimgnetic loo with its comenstion coil were designed, constructed, nd instlled on the outer surfce of the R-T1. Amlitude of the TF rile is otined.1, nd lso the effects of the TF rile on the ls m internl inductnce resented. One of the results is tht the difference etween the internl inductnce in resence of the TF rile nd in sence of the TF rile is in order of the 1, nd lso in the high field side region the difference is ositive, wheres in low field side the difference is negtive. n other words, in the high field side region of tokmk chmer, the TF ri le effect is incresing of the ls m internl inductnce, wheres the low field side hs inverse sitution. Figure (). Prmeters in sence of the TF rile, () lsm current, () oloidl Bet, (c) internl inductnce, nd (d) Horizontl islcement (H..)
14 A. Slr Elhi et l.: Plsm nternl nductnce in Presence of Toroidl Field Rile of Tokmk Figure (3). Effects of the TF rile mlitude on the difference of internl inductnce with nd without TF rile (li) t different oloidl ngles. As shown, difference etween the internl inductnce in resent of the TF rile nd in sent of the TF rile is in order of the1. Also in the high field o side region ( 18 ) the difference is ositive, ut in low field side ( ) the difference is negtive o REFERENCES [1] K. Nkmur nd M. Ghornneviss, Fusion Eng. es. 66-68 (3) 771-777. [] V. S. Mukhovtov nd V.. Shfrnov, Nucl. Fusion 11, (1971), 65 [3]. P. Shkrofsky, Phys. Fluids 5 (1) 89-96, (198). [4] G.S. Lee nd nd M. Ghornneviss, Nucl. Fusion 41, 1515 (1) [5] S.H. Seo, Phys. Plsms 16, 351 (9) [6] A. Slr Elhi nd M. Ghornneviss, EEE Trns. Plsm Science 38 (), 181-185, (1) [7] A. Slr Elhi nd M. Ghornneviss, EEE Trns. Plsm Science 38 (9), 3163-3167, (1) [8] A. Slr Elhi nd M. Ghornneviss, J. Plsm Physics 76 (1), 1-8, (9) [9] A. Slr Elhi nd M. Ghornneviss, Fusion Engineering nd esign 85, 74 77, (1) [1] A. Slr Elhi nd M. Ghornneviss, Phys. Scrit 8, 4551, (9) [11] A. Slr Elhi nd M. Ghornneviss, Phys. Scrit 8, 555, (9) [1] A. Slr Elhi nd M. Ghornneviss, Phys. Scrit 81 (5), 5551, (1) [13] A. Slr Elhi nd M. Ghornneviss, Phys. Scrit 8, 55, (1) [14] M. Ghornneviss, A. Slr Elhi, Phys. Scrit 8 (3), 355, (1) [15] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 8 (4), 346-349, (9) [16] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 8 (4), 416-419, (9) [17] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 8 (4), 48-411, (9) [18] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 8 (4), 41-415, (9) [19] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 8 (4), 394-397, (9) [] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 8 (4), 44-47, (9) [1] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 8 (4), 39-393, (9) [] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 8 (4), 385-389, (9) [3] A. Rhimi Rd, M. Ghornneviss, M. Emmi, nd A. Slr Elhi, J. Fusion Energy 8 (4), 4-46, (9) [4] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), 1-4, (1) [5] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), -5, (1)
Journl of Nucler nd Prticle Physics 13, 3(4): 11-15 15 [6] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), 9-31, (1) [7] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), 6-8, (1) [8] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), 3-35, (1) [9] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), 36-4, (1) [3] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), 6-64, (1) [31] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), 76-8, (1) [3] A. Rhimi Rd, M. Emmi, M. Ghornneviss, A. Slr Elhi, J. Fusion Energy 9 (1), 73-75, (1) [33] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), 83-87, (1) [34] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (1), 88-93, (1) [35] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (3), 9-14, (1) [36] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (3), 3-36, (1) [37] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (3), 51-55, (1) [38] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (3), 79-84, (1) [39] M. Ghornneviss, A. Slr Elhi, J. Fusion Energy 9 (5), 467-47, (1) [4] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 9 (5), 461-465, (1) [41] A. Slr Elhi nd M. Ghornneviss, Brzilin J. Physics 4 (3), 33-36, (1) [4] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 3 (), 116-1, (11) [43] M.R. Ghnri, M. Ghornneviss, A. Slr Elhi, Phys. Scrit 83, 5551, (11) [44] A. Slr Elhi, J. Fusion Energy 3 (6), 477-48, (11), 477-48 [45] A. Slr Elhi nd M. Ghornneviss, Fusion Engineering nd esign 86, 44 445, (11) [46] A. Slr Elhi nd M. Ghornneviss, J. Fusion Energy 31 (), 191-194, (1) [47] M.R. Ghnri, M. Ghornneviss, A. Slr Elhi, R. Arvin nd S. Mohmmdi, Rdition Effects & efects in Solids 166 (1), 789 794, (11) [48] A. Slr Elhi nd M. Ghornneviss, EEE Trns. Plsm Science 4 (3), 89-897, (1) [49] Z. Goodrzi, M. Ghornneviss nd A. Slr Elhi, J. Fusion Energy 3 (1), 13-16, (13) [5] M.R. Ghnri, M. Ghornneviss, A. Slr Elhi, Phys. Scrit 85 (5), 555, (1) [51] A. Slr Elhi nd M. Ghornneviss, Rdition Effects nd efects in Solids 168(1), 4-47, (13) [5] K. Mikili Agh, M. Ghornneviss, A. Slr Elhi, J. Fusion Energy 3 (), 68-7, (13) [53] A. Slr Elhi nd M. Ghornneviss, Fusion Engineering nd esign 88 (), 94-99, (13) [54] A. Slr Elhi nd M. Ghornneviss, EEE Trnsctions on Plsm Science 41 (), 334-34, (13) [55] A. Slr Elhi nd M. Ghornneviss, J. of Fusion Energy 3, 496-5, (13) [56] A. Slr Elhi nd M. Ghornneviss, Review of Scientific nstruments 84 (5), 5354 (13) [57] A. Slr Elhi nd M. Ghornneviss, J. Nucler nd Prticle Physics 1(1), 1-15, (11) [58] A. Slr Elhi nd M. Ghornneviss, J. Nucler nd Prticle Physics (), 1-5, (1) [59] A. Slr Elhi nd M. Ghornneviss, J. Nucler nd Prticle Physics (), -5, (1) [6] A. Slr Elhi nd M. Ghornneviss, J. Nucler nd Prticle Physics (4), 91-97, (1) [61] A. Slr Elhi nd M. Ghornneviss, J. Nucler nd Prticle Physics (4), 11-16, (1) [6] A. Slr Elhi nd M. Ghornneviss, J. Nucler nd Prticle Physics (5), 11-118, (1) [63] A. Slr Elhi nd M. Ghornneviss, J. Nucler nd Prticle Physics (6), 14-146, (1) [64] A. Slr Elhi nd M. Ghornneviss, J. Nucler nd Prticle Physics 3(1), 1-7, (13) [65] A. Slr Elhi nd M. Ghornneviss, J. Nucler nd Prticle Physics 3(1), 14-19, (13)