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A simple model for internal transport barrier induced by fishbone in tokamak plasmas

Published online by Cambridge University Press:  28 December 2023

Zhaoyang Liu
Affiliation:
Institute for Fusion Theory and Simulation and School of Physics, Zhejiang University, Hangzhou 310027, PR China
Guoyong Fu*
Affiliation:
Institute for Fusion Theory and Simulation and School of Physics, Zhejiang University, Hangzhou 310027, PR China
*
Email address for correspondence: gyfu@zju.edu.cn

Abstract

Fishbone bursts have been observed to strongly correlate to internal transport barrier (ITB) formation in a number of tokamak devices. A simple model incorporating the fishbone dynamics and ion pressure gradient evolution is proposed in order to investigate the key physics parameters assisting the triggering of ITB. The time evolution of fishbone is described by the well-known predator–prey model. For each burst cycle, the energetic particles (EPs) resonantly interact with fishbone and are radially expelled from inner region leading to a radial current. A compensating bulk plasma return current and, hence, poloidal flow can be induced if the fishbone cycle frequency is greater than the poloidal flow damping rate. When the shear of the poloidal flow exceeds a critical value, the turbulent fluctuations are suppressed and the bulk ion pressure gradient transits to the high-confinement state. It is shown that this process is only sensitive to the deposition rate of the trapped EPs within the $q=1$ surface, but not sensitive to other parameters. A quantitative formula for the shearing rate of poloidal flow induced by fishbone bursts is derived and verified numerically.

Type
Research Article
Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press

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References

Biglari, H., Diamond, P.H. & Terry, P.W. 1990 Influence of sheared poloidal rotation on edge turbulence. Phys. Fluids B 2 (1), 14.CrossRefGoogle Scholar
Brochard, G., Liu, C., Wei, X., Heidbrink, W., Lin, Z., Gorelenkov, N., Chrystal, C., Du, X., Bao, J., Polevoi, A.R., et al. 2023 Saturation of fishbone instability by self-generated zonal flows in tokamak plasmas. arXiv:2301.01792. Accepted by Phys. Rev. Lett. on 9 November 2023.Google Scholar
Burrell, K.H. 1997 Effects of $E\times B$ velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices. Phys. Plasmas 4 (5, 2), 14991518, 38th Annual Meeting of the Division of Plasma Physics of the American Physical Society, Denver, CO, Nov, 11–15, 1996.CrossRefGoogle Scholar
Chen, L., White, R.B. & Rosenbluth, M.N. 1984 Excitation of internal kink modes by trapped energetic beam ions. Phys. Rev. Lett. 52 (13), 11221125.CrossRefGoogle Scholar
Chu, Y.Q., Liu, H.Q., Zhang, S.B., Jie, Y.X., Lian, H., Wu, M.Q., Zhu, X., Wu, C.B., Xu, L.Q., Wang, Y.F., et al. 2021 Study of the mechanism of ITB formation and sustainment with optimized $q$ profiles in ELMy H mode discharges on the EAST. Plasma Phys. Control. Fusion 63, 105003.CrossRefGoogle Scholar
Chu, Y., Liu, H., Zhang, S., Xu, L., Li, E., Jie, Y., Lian, H., Zhou, T., Feng, X., Zhang, X., et al. 2022 Magnetohydrodynamic effect of internal transport barrier on EAST tokamak. Plasma Sci. Technol. 24, 035102.CrossRefGoogle Scholar
Clive, M., Crocker, N. & Hillesheim, J. 2019 Influence of fishbone-induced fast-ion losses on rotation and transport barrier formation in MAST. In 16th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems - Theory of Plasma Instabilities.Google Scholar
Connor, J.W., Fukuda, T., Garbet, X., Gormezano, C., Mukhovatov, V., Wakatani, M., ITB Database Grp & ITPA Topical Grp Transport Intern 2004 A review of internal transport barrier physics for steady-state operation of tokamaks. Nucl. Fusion 44 (4), R1R49.CrossRefGoogle Scholar
Deng, W., Liu, Y., Ge, W.L., Jiang, M., Shi, Z.B., Li, D., Ji, X.Q., Dong, Y.B., Wang, F., Cao, J.Y., et al. 2022 Investigation of the role of fishbone activity in the formation of internal transport barrier in HL-2A plasma. Phys. Plasmas 29, 102106.CrossRefGoogle Scholar
Diamond, P.H., Lebedev, V.B., Newman, D.E. & Carreras, B.A. 1995 Dynamics of spatiotemporally propagating transport barriers. Phys. Plasmas 2 (10), 36853695.CrossRefGoogle Scholar
Diamond, P.H., Lebedev, V.B., Newman, D.E., Carreras, B.A., Hahm, T.S., Tang, W.M., Rewoldt, G. & Avinash, K. 1997 Dynamics of transition to enhanced confinement in reversed magnetic shear discharges. Phys. Rev. Lett. 78 (8), 14721475.CrossRefGoogle Scholar
Field, A.R., Michael, C., Akers, R.J., Candy, J., Colyer, G., Guttenfelder, W., Ghim, Y.C., Roach, C.M., Saarelma, S. & MAST Team 2011 Plasma rotation and transport in MAST spherical tokamak. Nucl. Fusion 51, 063006.CrossRefGoogle Scholar
Fu, G.Y., Park, W., Strauss, H.R., Breslau, J., Chen, J., Jardin, S. & Sugiyama, L.E. 2006 Global hybrid simulations of energetic particle effects on the $n=1$ mode in tokamaks: internal kink and fishbone instability. Phys. Plasmas 13, 052517.CrossRefGoogle Scholar
Ge, W., Wang, Z.-X., Wang, F., Liu, Z. & Xu, L. 2023 Multiple interactions between fishbone instabilities and internal transport barriers in EAST plasmas. Nucl. Fusion 63, 016007.CrossRefGoogle Scholar
Gruber, O., Wolf, R., Bosch, H.S., Dux, R., Gunther, S., McCarthy, P.J., Lackner, K., Maraschek, M., Meister, H., Pereverzev, G., et al. 2000 Steady state H mode and $T_e \approx T_i$ operation with internal transport barriers in ASDEX upgrade. Nucl. Fusion 40 (6), 11451155, 2nd IAEA Technical Committee Meeting on Steady State Operation of Magnetic Fusion Devices, Plasma Control and Plasma Facing Components, Fukuoka, Japan, Oct 25–29, 1999.CrossRefGoogle Scholar
Gunter, S., Gude, A., Hobirk, J., Maraschek, M., Saarelma, S., Schade, S., Wolf, R.C. & ASDEX Upgrade Team 2001 MHD phenomena in advanced scenarios on ASDEX upgrade and the influence of localized electron heating and current drive. Nucl. Fusion 41 (9), 12831290.CrossRefGoogle Scholar
He, X.X., Yan, L.W., Yu, D.L., Chen, W., Yu, L.M., Ma, Q., Liu, L., Wei, Y.L., He, X.F., Zhang, N., et al. 2022 The ITB dynamics controlled by internal kink modes on HL-2A tokamak. Plasma Phys. Control. Fusion 64, 015007.CrossRefGoogle Scholar
Heidbrink, W.W., Duong, H.H., Manson, J., Wilfrid, E., Oberman, C. & Strait, E.J. 1993 The nonlinear saturation of beam-driven instabilities – theory and experiment. Phys. Fluids B 5 (7, 1), 21762186.CrossRefGoogle Scholar
Ida, K. & Fujita, T. 2018 Internal transport barrier in tokamak and helical plasmas. Plasma Phys. Control. Fusion 60, 033001.CrossRefGoogle Scholar
Joffrin, E., Gorini, G., Challis, C.D., Hawkes, N.C., Hender, T.C., Howell, D.F., Maget, P., Mantica, P., Mazon, D., Sharapov, S.E., et al. 2002 Triggering of internal transport barrier in jet. Plasma Phys. Control. Fusion 44 (8), 17391752.CrossRefGoogle Scholar
Liu, Z.X., Ge, W.L., Wang, F., Liu, Y.J., Yang, Y., Wu, M.Q., Wang, Z.X., Zhang, X.X., Li, H., Xie, J.L., et al. 2020 Experimental observation and simulation analysis of the relationship between the fishbone and ITB formation on EAST tokamak. Nucl. Fusion 60, 122001.CrossRefGoogle Scholar
McClements, K.G. & Thyagaraja, A. 2006 Collective electric field effects on the confinement of fast ions in tokamaks. Phys. Plasmas 13, 042503.CrossRefGoogle Scholar
McGuire, K., Goldston, R., Bell, M., Bitter, M., Bol, K., Brau, K., Buchenauer, D., Crowley, T., Davis, S., Dylla, F., et al. 1983 Study of high-beta magnetohydrodynamic modes and fast-ion losses in PDX. Phys. Rev. Lett. 50 (12), 891895.CrossRefGoogle Scholar
Newman, D.E., Carreras, B.A., Lopez-Bruna, D., Diamond, P.H. & Lebedev, V.B. 1998 Dynamics and control of internal transport barriers in reversed shear discharges. Phys. Plasmas 5 (4), 938952.CrossRefGoogle Scholar
Peeters, A.G. 1998 Equations for the evolution of the radial electric field and poloidal rotation in toroidally symmetric geometry. Phys. Plasmas 5 (3), 763767.CrossRefGoogle Scholar
Pinches, S.D., Günter, S., Peeters, A.G., the ASDEX Upgrade Team 2001 Fishbone generation of sheared flows in the creation of transport barriers. In 28th EPS Conference on Controlled Fusion and Plasma Physics, pp. 57–60.Google Scholar
Ren, Z., Shen, W., Li, G., Wu, M., Yang, J. & Wang, W. 2022 Numerical investigation of the fishbone instability effect on thermal pressure in EAST tokamak. AIP Adv. 12, 075318.CrossRefGoogle Scholar
Rosenbluth, M.N. & Hinton, F.L. 1996 Plasma rotation driven by alpha particles in a tokamak reactor. Nucl. Fusion 36 (1), 5567.CrossRefGoogle Scholar
Shaing, K.C., Ida, K. & Sabbagh, S.A. 2015 Neoclassical plasma viscosity and transport processes in non-axisymmetric tori. Nucl. Fusion 55 (12), 125001.CrossRefGoogle Scholar
Thyagaraja, A., Schwander, F. & McClements, K.G. 2007 Rotation driven by fast ions in tokamaks. Phys. Plasmas 14 (11), 112504.CrossRefGoogle Scholar
White, R.B., Goldston, R.J., McGuire, K., Boozer, A.H., Monticello, D.A. & Park, W. 1983 Theory of mode-induced beam particle loss in tokamaks. Phys. Fluids 26 (10), 29582965.CrossRefGoogle Scholar
Wolf, R.C. 2003 Internal transport barriers in tokamak plasmas. Plasma Phys. Control. Fusion 45 (1), R1R91.CrossRefGoogle Scholar
Wolf, R.C., Gruber, O., Maraschek, M., Dux, R., Fuchs, C., Gunter, S., Herrmann, A., Kallenbach, A., Lackner, K., McCarthy, P.J., et al. 1999 Stationary advanced scenarios with internal transport barrier on ASDEX upgrade. Plasma Phys. Control. Fusion 41 (12B), B93B107, 26th European-Physical-Society Conference on Controlled Fusion and Plasma Physics, Maastricht, Netherlands, Jun 14–18, 1999.CrossRefGoogle Scholar
Xu, L., Zhang, J., Chen, K., Hu, L., Li, E., Lin, S., Shi, T., Duan, Y. & Zhu, Y. 2015 Fishbone activity in experimental advanced superconducting tokamak neutral beam injection plasma. Phys. Plasmas 22 (12), 122510.CrossRefGoogle Scholar
Yang, Y., Gao, X., Liu, H.Q., Li, G.Q., Zhang, T., Zeng, L., Liu, Y.K., Wu, M.Q., Kong, D.F., Ming, T.F., et al. 2017 Observation of internal transport barrier in ELMy H-mode plasmas on the EAST tokamak. Plasma Phys. Control. Fusion 59 (8), 085003.CrossRefGoogle Scholar
Yu, D.L., Wei, Y.L., Liu, L., Dong, J.Q., Ida, K., Itoh, K., Sun, A.P., Cao, J.Y., Shi, Z.B., Wang, Z.X., et al. 2016 Ion internal transport barrier in neutral beam heated plasmas on HL-2A. Nucl. Fusion 56 (5), 056003.CrossRefGoogle Scholar
Zhang, B., Gong, X., Qian, J., Zeng, L., Xu, L.Q., Duan, Y.M., Zhang, J.Y., Hu, Y.C., Jia, T.Q., Li, P., et al. 2022 Progress on physics understanding of improved confinement with fishbone instability at low $q$ (95) < 3.5 operation regime in EAST. Nucl. Fusion 62 (12), 126064.CrossRefGoogle Scholar
Zhang, X., Wu, M.Q., Li, G., Li, G., Tang, T., Yang, Y., Zhong, F.B., Long, F.F., Wu, M.F., Zhang, T., et al. 2023 Investigation of key factors for ITB formation and maintenance in EAST high $\beta$ discharges. Phys. Lett. A 462, 128646.CrossRefGoogle Scholar
Zhang, Y.Z. & Mahajan, S.M. 1992 Edge turbulence scaling with shear-flow. Phys. Fluids B 4 (6), 13851387.CrossRefGoogle Scholar
Zhu, X., Zeng, L., Qiu, Z., Hao, B., Shen, W., Gu, X., Wu, M., Tang, T., Qian, J., Liu, H., et al. 2020 Dependence of fishbone cycle on energetic particle intensity in EAST low-magnetic-shear plasmas. J. Plasma Phys. 86 (6), 905860610.CrossRefGoogle Scholar
Zonca, F., Buratti, P., Cardinali, A., Chen, L., Dong, J.Q., Long, Y.X., Milovanov, A.V., Romanelli, F., Smeulders, P., Wang, L., et al. 2007 Electron fishbones: theory and experimental evidence. Nucl. Fusion 47 (11), 15881597.CrossRefGoogle Scholar