Time Evolution of the Bootstrap Current Profile in LHD Plasmas

Transcription

1 Time Evoluion of he Boosrap Curren Profile in LHD Plasmas Yuji Nakamura 1), K. Y. Waanabe 2), K. Kawaoo 1), K. Ida 2), Y. Narushima 2), M. Yoshinuma 2), S. Sakakibara 2), I. Yamada 2), T. Tokuzawa 2), M. Goo 2), K. Tanaka 2), N. Nakajima 2), K. Kawahaa 2), and LHD experimenal group 1) Graduae School of Energy Science, Kyoo Universiy, Uji, Kyoo , Japan 2) Naional Insiue for Fusion Science, Toki, Gifu 9-292, Japan conac of main auhor: Absrac. The direcion of he boosrap curren is invered in he ouward shifed plasmas of he Large Helical Device (LHD). In order o verify he reliabiliy of he heoreical models of he boosrap curren in helical plasmas, he roaional ransform profiles are observed by he Moional Sark Effec measuremen in he boosrap curren carrying plasmas of he LHD, and hey are compared wih he numerical simulaions of he oroidal curren profile including he boosrap curren. Since he oroidal curren profile is no in he seady sae in hese plasmas, aking care of he inversely induced componen of he oroidal curren and finie duraion of he resisive diffusion of he oroidal curren are imporan in he numerical simulaions. Reasonable agreemen can be obained beween he roaional ransform profiles measured in he experimens and hose calculaed in he numerical simulaions 1. Inroducion Since he roaional ransform profile, which has imporan roles on he magneohydrodynamics (MHD) sabiliy and ranspor, is sensiive o he ne plasma curren, i is indispensable o esimae he oroidal curren profile quaniaively. In he LHD, Ohmic curren is no driven acively by he exernal circui, and observed oal oroidal curren is mainly driven by he non-inducive curren, such as he boosrap curren and Ohkawa curren. Since he oal oroidal curren does no reach he seady sae in mos of he LHD experimens, he curren ramp-up due o he non-inducive curren induces he oroidal elecric field inversely in accordance wih Faraday s law. In addiion o ha, high elecric conduciviies of plasmas cause slow radial diffusion of he oroidal currens. In order o esimae he oroidal curren profile quaniaively, herefore, no only a heoreical model for he non-inducive curren bu also ha for he curren profile evoluion is required even in helical plasmas, in which he curren profile evoluions have no been sudied exensively. Oherwise, heoreical models of he non-inducive curren, such as he boosrap curren, in helical plasmas canno be verified properly by he experimens. I is prediced heoreically for LHD plasmas ha he configuraion dependence of he boosrap curren is srong in he ouward shifed plasmas and i affecs he MHD equilibrium limi [1]. In he previous sudies, oal amoun of he boosrap curren was esimaed experimenally in he LHD plasmas and compared wih ha obained from he heoreical calculaion [2]. Bu here had previously been no experimenal esimaion of he radial profile of he boosrap curren. The Moional Sark Effec (MSE) measuremen is now equipped in he LHD [3], and he roaional ransform profile can be measured. Moreover, a numerical simulaion code, TASK/EI+BSC [4, ], is available o calculae he ime evoluion of he boosrap curren profile consisenly wih he hree-dimensional (3D) MHD equilibrium. The TASK/EI+BSC code solves a ime evoluioquaion of he roaional ransform profile, which is equivalen o he oroidal curren profile, by he ieraive calculaion wih he 3D MHD equilibrium and he boosrap curren calculaions. In his paper, we compare he

2 roaional ransform profile obained by he MSE measuremen and ha calculaed by he numerical simulaion of he oroidal curren including he boosrap curren componen and he inducive curren componen. 2. Numerical Simulaion of he Toroidal Curren Evoluion In he BSC code [6], he boosrap curren is esimaed based on he momenum mehod for asymmeric devices proposed by K.C. Shaing e al. [7, 8], where he linearized drif kineic equaion is solved analyically, and connecion formula from 1/ν o Pfirsch-Schüler collisional regime is applied. A conservaioquaion of he roaional ransform ι is derived from he conravarian componen of Faraday s law: ι 1 φ ι V = η ( NI ) φ + s s j B j B φ, s φ =Φ /2π Φ T Φ / edge T ΦT where, is he oroidal magneic flux, s is he oroidal flux T 2 normalized by is value a he plasma boundary, V=V /( 2 π), V is volume inside he flux surface. Primes denoes derivaive wih respec o s, η is he neoclassical parallel resisiviy, j B and jni B correspond o he flux averaged parallel curren densiy and non-inducive curren densiy, respecively. When we use he relaion beween j B and ι, we can obain, 2 φ φ 1 B ι a a ι = η ( S ι S 11 12) { ( ι S ) η 2 2 }. + + s V + + η p S j B s φ s μ s s V V NI a edge 2 where =Φ /2π, B is flux surface average of he square of magneic field srengh, φ a T p is pressure, S and S are he suscepance marix defined in Ref.[9]. This equaion is solved in he TASK/EI code wih he MHD equilibrium quaniies obained by he VMEC code [1] and non-inducive curren (he boosrap curren in he presen case) calculaed by he BSC code. The equilibrium and boosrap curren daa are supplied o he TASK/EI and he roaional ransform is evolved during some ime inerval, which is ypically 1ms for LHD plasmas. In he equaion of he roaional ransform evoluion, we assumed ha MHD equilibrium quaniies such as suscepance marix are consisen wih evolved ι (in his sense, he equaion is inrinsically non-linear), bu we also assumed ha change of ι and he resulan change of MHD quaniies are negligibly small during he ime inerval. Then, he updaed roaional ransform profile along wih he experimenally obained densiy and emperaure profiles are used as inpu of he equilibrium code, and boosrap curren is re-esimaed by he BSC again. These procedures are ieraed during he simulaion. 3. Dependence of he Boosrap Curren on he Plasma Posiion In order o verify he capabiliy of he boosrap curren calculaion code, BSC code, he oal amoun of he oroidal curren calculaed by he BSC code is compared wih ha esimaed experimenally. We esimae he non-inducive curren by aking ino accoun of he muual coupling due o he srucure surrounding he plasma, such as coils, vacuum vessel and so on. Figure 1 shows he dependence of he non-inducive curren obained experimenally on he magneic configuraions wih differen magneic axis. The volume averaged bea values are

3 4 3 Experimen Theo. Pred. 1.. #61863, 1.48T <β dia > (%) I p /B (ka/t) R (m) ax Fig.1 The magneic axis posiion dependence of he non-inducive curren obained experimenally and he comparison beweexperimenal resuls and he heoreical predicion. almos same, <β dia >=.33~.41%. The daa are obained under he same condiion of NB injecion; co NB has he por hrough power of 2MW wih beam energy of 1keV, and wo couner NBs have.6mw wih 12keV and 1MW wih 1keV, respecively. Circles denoe he experimenal daa and a line denoes he heoreical predicion of he boosrap curren by he BSC code. We find ha he boosrap curren is he mos probable candidae as a driving mechanism of he non-inducive curren in LHD experimens under he balanced NB injecion. The roaional ransform profile is measured by he MSE in LHD plasmas of which vacuum magneic axis posiion are R axis =3.9m. Time evoluion of his discharge is shown in Fig.2. In his NB balanced injecion discharge, <β dia >~.% and he oal oroidal curren reaches around 1kA. Figure 3 shows ime evoluion of he elecron densiy and emperaure profiles of his discharge obained from he experimen. In 1/2 Fig.3, he radial variable s corresponds o he represenaive normalized minor radius. The elecron densiy has a raher fla or hollow profile. The elecron emperaure has a bell-shaped profile and is profile is almos consan in ime. Figure 3 also shows a pressure profile when we (1 19 m -3 ) ime (s) Fig.2 Time evoluion of experimenally observed elecron densiies, volume averaged bea, and he oal plasma curren for R axis =3.9m case. p 3 [m ] 2 1 T e [kev] [arb. unis] Fig.3 Time evoluions of elecron densiy profile, elecromperaure profile, and pressure profile measured in he experimen for R axis =3.9m case shown in Fig.2.

4 .8 # =.6s =2.9s =3.9 1 = 3.1s j B ( = 3.1s) bs j B.6 2 [ATm ].4 = 2.1s =.6 s Fig.4 Time evoluion of he roaional ransform profile obained by he MSE measuremen for R axis =3.9m case. # =.6s.8 =2.1s =3.1s.6 Fig. Time evoluion of he flux averaged parallel curren profile obained by he numerical simulaion for R axis =3.9m case. ι = 3.1 wihou inducive curren wih inducive curren.4 currenless Fig.6 Time evoluion of he roaional ransform profile obained by he numerical simulaion for R axis =3.9m case. Fig.7 Dependence of he roaional ransform profile a =3.1s on he assumed curren profile for R axis =3.9m case. assume ha he iomperaure is equal o he elecromperaure. These profiles obained from he experimen are used in he numerical simulaion of he plasma curren. In Fig.4, he roaional ransform profiles obained by he MSE measuremen for he R axis =3.9m case corresponding o Figs.3 and 4 are shown. I can be seen from Fig.4 ha he cenral value of he roaional ransform is around.6, and is minimum is abou. and locaed around =.4~.. Time evoluion of he roaional ransform profile is calculaed by he TASK/EI+BSC wih he VMEC. In his calculaion, experimenally esimaed ime evoluion of densiy and emperaure profiles in Fig.3 is used. Measured oal curren in Fig.2 is also used as a boundary condiion of he roaional ransform evoluion. Figure 4 shows ime evoluion of he flux averaged parallel curren profiles obained by he numerical simulaion. The curren densiy is almos zero around he half radial posiion and slighly posiive near he edge, and i is increased wih ime near he plasma cener. Toal curren a = 3.1s is abou 1kA. On he oher hand, he boosrap curren calculaed by he BSC is posiive in he enire region, and oal boosrap curren is abou 3kA. Corresponding roaional ransform profile is shown in Fig.6. This profile does no change in ime excep for he cenral region, as same as ha in Fig.4 esimaed by he MSE measuremen. Finally, he

5 1.. #8282, 2.44T (1 19 m -3 ). <β dia > (%) I p /B (ka/t) ime (s) 1-3 [m ] 2 1 Fig.8 Time evoluion of experimenally observed elecron densiies, volume averaged bea, and he oal plasma curren for R axis =4.m case. T e [kev] roaional ransform esimaed by he simulaion is compared in Fig.7 wih hose calculaed by using wo differen curren profiles. One is ha calculaed by he VMEC code wih he currenless consrain. Anoher is ha obained from he VMEC equilibrium calculaion by aking he boosrap curren ino accoun bu neglecing he inverse inducive curren. The currenless equilibrium gives he similar roaional ransform near he edge, bu increase of ha near he plasma cener canno be reproduced. If we neglec he inducive curren, we canno explain he small oal curren and obain larger roaional ransform near he edge. From hese resuls, we can conclude ha he numerical resul is consisen quaniaively wih he measured one for his case. Since he configuraion dependence of he boosrap curren around R axis =4.m is more sensiive han ha around R axis =3.9m, as is shown in Fig.1, dependence of he heoreical model is more pronounced in he R axis =4.m case. Therefore, his configuraion is more suiable o verify he heoreical model for he boosrap curren calculaion. Time evoluion of his discharge is shown in Fig.8. In his discharge, <β dia >~.4% and he oal oroidal curren flows inverse direcion compared o he case of R axis =3.9m and reaches around 14kA. Figure 9 shows ime evoluions of he elecron densiy profile, emperaure profile, and pressure p [arb. unis] Fig.9 Time evoluions of elecron densiy profile, elecromperaure profile, and pressure profile measured in he experimen for R axis =4.m case shown in Fig # 8282 =.9s =2.7s =3.9s Fig.1 Time evoluion of he roaional ransform profile obained by he MSE measuremen for R axis = 4.m case.

6 profile of his discharge obained from he experimen. The elecron densiy profile is quie fla and increases wih ime. In Fig.1, he roaional ransform profiles obained by he MSE measuremen for he R axis =4.m case corresponding o Figs.8 and 9 are shown. I can be seen from Fig.1 ha he roaional ransform is almos uniform and is value is around.68. I is found from Fig.1 ha he roaional ransform a he edge decreases in ime slighly. This is consisen o he behavior of he oal currevoluion. Figure 11 shows ime evoluion of he flux averaged parallel curren profiles obained by he numerical simulaion. The ne curren is negaive excep for he cenral region. The boosrap curren profile shown in Fig.11 has similar profile bu oal amoun of he boosrap curren is abou. ka a = 3.9s, while he oal curren observed in he experimen is around 14kA. The resul of he ime evoluion calculaion of he roaional ransform profile for he configuraion wih R axis =4.m, which corresponds o Fig.1, is shown in Fig.12. Boh he numerical resul and he measured one show fla roaional ransform profiles around.68. Bu here is a small difference a he plasma cener. As we can see in Fig.13, neglecing he plasma curren, i.e. currenless equilibrium, gives larger roaional ransform han he MSE measuremen on he overall region. Neglecing he inducive curren, i.e. considering only he boosrap curren in he MHD equilibrium calculaion, gives oo large roaional ransform a he cener. In hose sense, he numerical simulaion by considering he inducive curren shows reasonable agreemen wih he experimenal observaion. Bu more accurae boosrap curren calculaion, such as ha using he DKES code, is expeced o improve he agreemen since he heoreical model used in he BSC is no sufficienly accurae when he boosrap curren is nearly zero. 4. Conclusion The MSE measuremen and numerical 1 j B 2 [ATm ] = 3.9 s = 2.7 s j B ( = 3.9s) bs =.9 s Fig.11 Time evoluion of he flux averaged parallel curren profile obained by he numerical simulaion for R axis =4.m case. ι # = 3.9 wihou inducive curren currenless wih inducive curren Fig.13 Dependence of he roaional ransform profile a =3.9s on he assumed curren profile for R axis =4.m case. =.9s =2.7s =3.9s Fig.12 Time evoluion of he roaional ransform profile obained by he calculaion for R axis = 4.m case.

7 simulaion of he roaional ransform profile are performed in he boosrap curren flowing ouward-shifed LHD plasmas. The boosrap currens esimaed by he BSC code increase he roaional ransform in LHD plasmas of which vacuum magneic axis posiion are R axis =3.9m. Observed ne oroidal currens (1kA) are well below he boosrap currens (3kA), and can be explained by he exisence of he inverse inducive currens, which are aken ino accoun in he numerical simulaion. If we neglec he ne plasma curren or inverse inducive curren in he equilibrium calculaion, he roaional ransform profile measured by he MSE canno be reproduced. Numerical resul which is consisen wih he experimenal observaion can be obained quaniaively. For he case of R axis =4.m, negaive or subracive oal oroidal currens are observed in he experimen. The direcion of he subracive boosrap curren is opposie o ha of he boosrap currens in okamaks and corresponds wih ha in he sraigh helical plasmas. Theoreical predicion showed ha, in L=2 helioron, he boosrap curren flows opposie direcion when he plasma is shifed ouward. Therefore, he observaion can be explained qualiaively by he boosrap curren calculaion by he BSC code. However, he amoun of he calculaed boosrap curren (.ka) is differen from he observed oal curren ( 14kA). This can be also explained by he exisence of he inducive curren. Since boosrap curren flows in he posiive or addiive direcion a he plasma cener bu does in he subracive direciolsewhere han he plasma cener in he case of R axis =4.m, accurae esimaions of he boosrap curren are required. In his paper, we found ha he numerical simulaion preformed by considering boosrap curresimaed by he BSC code and he inducive curren shows reasonable agreemen wih he experimenal observaion. Bu more accurae boosrap curren calculaion, such as ha using he DKES code, is expeced o improve he agreemen since he heoreical model used in he BSC is no sufficienly accurae when he boosrap curren is nearly zero. Tha is a fuure problem we should resolve. References [1] K.Y. Waanabe and N. Nakajima, Effec of boosrap curren on MHD equilibrium bea limi in helioron plasmas, Nuclear Fusion 41 (21) 63. [2] K.Y. Waanabe e al, J. Plasma Fusion Res. Ser. (22) 124. [3] K. Ida, e al., Rev. Sci. Insrum. 76, 3 (2). [4] Yuji Nakamura e al., Proc. of 21h IAEA Fusion Energy Conf. (Chengdu, China, 26) IAEA-CN-149/TH/P [] Yuji Nakamura e al., Plasma Fusion Res. 3, S18 (28). [6] K. Y. WATANABE, e al., Nuclear Fusion 3 (199) 33. [7] K. C. Shaing, e al., Phys. Fluids 29 (1986) 21. [8] K. C. Shaing, e al., Phys. Fluids B1 (1989) [9] P. I. Srand and W. A. Houlberg, Phys. Plasma 8 (2) [1] S. P. Hirshman, W. I. Rij, and P. Merkel, Compu. Phys. Commun. 43 (1986) 143.