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Generation of energetic electrons by an electron cyclotron wave through stochastic heating in a spherical tokamak

Published online by Cambridge University Press:  28 November 2023

Mingyuan Wang Open the ORCID record for Mingyuan Wang [Opens in a new window] ,
Shikui Cheng ,
Bing Liu ,
Shaodong Song ,
Dong Guo ,
Yunyang Song ,
Wenjun Liu ,
Debabrata Banerjee ,
Songjian Li  and
Tiantian Sun
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Mingyuan Wang
Affiliation:
School of Mathematics and Physics, Anqing Normal University, Anqing 246133, PR China Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Shikui Cheng
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Bing Liu
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Shaodong Song
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Dong Guo
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Yunyang Song
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Wenjun Liu
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Debabrata Banerjee
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Songjian Li
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Tiantian Sun
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Xiang Gu
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Yingying Li
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Jiaqi Dong
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Yuejiang Shi*
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Y.-K. Martin Peng
Affiliation:
Hebei Key Laboratory of Compact Fusion, Langfang 065001, PR China ENN Science and Technology Development Co., Ltd., Langfang 065001, PR China
Adi Liu*
Affiliation:
Department of Plasma Physics and Fusion Engineering, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
†Email addresses for correspondence: yjshi@ipp.ac.cn, lad@ustc.edu.cn
†Email addresses for correspondence: yjshi@ipp.ac.cn, lad@ustc.edu.cn
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Abstract

This study presents novel findings on stochastic electron heating via a random electron cyclotron wave (ECW) in a spherical tokamak. Hard x ray measurements demonstrate the time evolution of hard x ray counts at different energy bands, consistent with predictions from the stochastic heating model. The ECW heating rate shows a positive correlation with applied power, confirming the effectiveness of stochastic heating. Remarkably, the ECW-driven plasma current remains insensitive to ECW incidence angle, consistent with model predictions. The observed stochastic heating of electrons offers potential for exploring innovative non-inductive current drive modes in spherical tokamaks. This research contributes to the understanding of plasma behaviour and motivates the development of new models for non-inductive current drive in fusion devices.

Keywords

plasma heatingplasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 89 , Issue 6 , December 2023 , 905890603
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press

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References

Amano, T., Katou, T., Kitamura, N., Oka, M., Matsumoto, Y., Hoshino, M., Saito, Y., Yokota, S., Giles, B.L., Paterson, W.R., et al. 2020 Observational evidence for stochastic shock drift acceleration of electrons at the Earth's bow shock. Phys. Rev. Lett. 124 (6), 065101.CrossRefGoogle ScholarPubMed
Bernhardi, K. & Wiesemann, K. 1982 X-ray bremsstrahlung measurements on an ECR-discharge in a magnetic mirror. Plasma Phys. 24 (8), 867.CrossRefGoogle Scholar
Cheng, S.K., Zhu, Y.B., Chen, Z.Y., Li, Y.X., Bai, R.H., Chen, B., Huang, X.L., Dai, L.L. & Liu, M.S. 2021 Tangential hard x-ray diagnostic array on the EXL-50 spherical tokamak. Rev. Sci. Instrum. 92 (4), 043513.CrossRefGoogle ScholarPubMed
Citrin, J., Jenko, F., Mantica, P., Told, D., Bourdelle, C., Garcia, J., Haverkort, J.W., Hogeweij, G.M.D., Johnson, T. & Pueschel, M.J. 2013 Nonlinear stabilization of tokamak microturbulence by fast ions. Phys. Rev. Lett. 111 (15), 155001.CrossRefGoogle ScholarPubMed
Gary, S.P. & Wang, J. 1996 Whistler instability: electron anisotropy upper bound. J. Geophys. Res.: Space 101 (A5), 10749–10754.CrossRefGoogle Scholar
Guo, D., Shi, Y., Liu, W., Song, Y., Sun, T., Liu, B., Li, Y., Tian, X., Zhang, G., Xie, H., et al. 2022 Experimental study of the characteristics of energetic electrons outside LCFS in EXL-50 spherical torus. Plasma Phys. Control. Fusion 64 (5), 055009.CrossRefGoogle Scholar
Han, H., Park, S.J., Sung, C., Kang, J., Lee, Y.H., Chung, J., Hahm, T.S., Kim, B., Park, J.-K., Bak, J.G., et al. 2022 A sustained high-temperature fusion plasma regime facilitated by fast ions. Nature 609 (7926), 269–275.CrossRefGoogle ScholarPubMed
Idei, H., Kariya, T., Imai, T., Mishra, K., Onchi, T., Watanabe, O., Zushi, H., Hanada, K., Qian, J., Ejiri, A., et al. 2017 Fully non-inductive second harmonic electron cyclotron plasma ramp-up in the quest spherical tokamak. Nucl. Fusion 57 (12), 126045.CrossRefGoogle Scholar
Ikegami, H., Aihara, S., Hosokawa, M. & Aikawa, H. 1973 Generation of energetic electrons by electron cyclotron heating in a magnetic mirror field. Nucl. Fusion 13 (3), 351.CrossRefGoogle Scholar
Ishida, A., Peng, Y.-K.M. & Liu, W. 2021 Four-fluid axisymmetric plasma equilibrium model including relativistic electrons and computational method and results. Phys. Plasmas 28 (3), 032503.CrossRefGoogle Scholar
Ishiguro, M., Hanada, K., Liu, H., Zushi, H., Nakamura, K., Fujisawa, A., Idei, H., Nagashima, Y., Hasegawa, M., Tashima, S., et al. 2012 Non-inductive current start-up assisted by energetic electrons in Q-shu university experiment with steady-state spherical tokamak. Phys. Plasmas 19 (6), 062508.CrossRefGoogle Scholar
Jaeger, F., Lichtenberg, A.J. & Lieberman, M.A. 1972 Theory of electron cyclotron resonance heating. I. Short time and adiabatic effects. Plasma Phys. 14 (12), 1073.CrossRefGoogle Scholar
Karney, C.F.F. 1978 Stochastic ion heating by a lower hybrid wave. Phys. Fluids 21 (9), 1584–1599.CrossRefGoogle Scholar
Karney, C.F.F. & Bers, A. 1977 Stochastic ion heating by a perpendicularly propagating electrostatic wave. Phys. Rev. Lett. 39 (9), 550.CrossRefGoogle Scholar
Kawamura, T., Momota, H., Namba, C. & Terashima, Y. 1971 Stochastic model of electron-cyclotron heating in a magnetic mirror. Nucl. Fusion 11 (4), 339.CrossRefGoogle Scholar
Kuckes, A.F. 1968 Limit of the plasma temperature attainable by cyclotron resonance heating in a magnetic mirror. Phys. Lett. A 26 (12), 599–600.CrossRefGoogle Scholar
Li, H.Y., Li, S.J., Xie, Q.F., Liu, J.H., Bai, R.H., Tao, R.Y., Lun, X.C., Li, N., Bo, X.K., Liu, C.Q., et al. 2022 Thomson scattering diagnostic system for the XuanLong-50 experiment. Rev. Sci. Instrum. 93 (5), 053504.CrossRefGoogle ScholarPubMed
Li, S.J., Bai, R.H., Tao, R.Y., Li, N., Lun, X.C., Liu, L.C., Liu, Y., Liu, M.S. & Deng, B.H. 2021 A quasi-optical microwave interferometer for the XuanLong-50 experiment. J. Instrum. 16 (08), T08011.CrossRefGoogle Scholar
Lieberman, M.A. & Lichtenberg, A.J. 1973 Theory of electron cyclotron resonance heating. II. Long time and stochastic effects. Plasma Phys. 15 (2), 125.CrossRefGoogle Scholar
Lvovskiy, A., Heidbrink, W.W., Paz-Soldan, C., Spong, D.A., Dal Molin, A., Eidietis, N.W., Nocente, M., Shiraki, D. & Thome, K.E. 2019 Observation of rapid frequency chirping instabilities driven by runaway electrons in a tokamak. Nucl. Fusion 59 (12), 124004.CrossRefGoogle Scholar
Ma, C.-y. & Summers, D. 1998 Formation of power-law energy spectra in space plasmas by stochastic acceleration due to whistler-mode waves. Geophys. Res. Lett. 25 (21), 4099–4102.CrossRefGoogle Scholar
Maekawa, T., Peng, Y.-K.M. & Liu, W. 2023 Particle orbit description of cyclotron-driven current-carrying energetic electrons in the EXL-50 spherical torus. Nucl. Fusion 63 (7), 076014.CrossRefGoogle Scholar
Maekawa, T., Yoshinaga, T., Uchida, M., Watanabe, F. & Tanaka, H. 2012 Open field equilibrium current and cross-field passing electrons as an initiator of a closed flux surface in EC-heated toroidal plasmas. Nucl. Fusion 52 (8), 083008.CrossRefGoogle Scholar
McChesney, J.M., Stern, R.A. & Bellan, P.M. 1987 Observation of fast stochastic ion heating by drift waves. Phys. Rev. Lett. 59 (13), 1436.CrossRefGoogle ScholarPubMed
McClements, K.G., Dieckmann, M.E., Ynnerman, A., Chapman, S.C. & Dendy, R.O. 2001 Surfatron and stochastic acceleration of electrons at supernova remnant shocks. Phys. Rev. Lett. 87 (25), 255002.CrossRefGoogle ScholarPubMed
Puri, S. 1968 Statistical particle acceleration in random fields. Phys. Fluids 11 (8), 1745–1753.CrossRefGoogle Scholar
Puri, S. 1974 Stochastic heating of plasma electrons using microwave noise. Plasma Phys. 16 (6), 517.CrossRefGoogle Scholar
Putvinski, S.V., Ryutov, D.D. & Yushmanov, P.N. 2019 Fusion reactivity of the pB11 plasma revisited. Nucl. Fusion 59 (7), 076018.CrossRefGoogle Scholar
Seo, E.-S. & Ptuskin, V.S. 1994 Stochastic reacceleration of cosmic rays in the interstellar medium. Astrophys. J. 431, 705–714.CrossRefGoogle Scholar
Shi, Y., Liu, B., Song, S., Song, Y., Song, X., Tong, B., Cheng, S., Liu, W., Wang, M., Sun, T., et al. 2022 Solenoid-free current drive via ECRH in EXL-50 spherical torus plasmas. Nucl. Fusion 62 (8), 086047.CrossRefGoogle Scholar
Smirnov, A.P. & Harvey, R.W. 2001 The genray ray tracing code. CompX Report CompX-2000-01. Available at: https://www.compxco.com/Genray_manual.pdf.Google Scholar
Smith, G.R., Cohen, R.H. & Mau, T.K. 1987 Harmonic overlap in electron-cyclotron current drive at high $T_e$. Phys. Fluids 30 (11), 3633–3635.CrossRefGoogle Scholar
Smith, G.R. & Kaufman, A.N. 1975 Stochastic acceleration by a single wave in a magnetic field. Phys. Rev. Lett. 34 (26), 1613.CrossRefGoogle Scholar
Sturrock, P.A. 1966 Stochastic acceleration. Phys. Rev. 141 (1), 186.CrossRefGoogle Scholar
Sun, J., Gao, X., Lu, Q. & Wang, S. 2014 The efficiency of ion stochastic heating by a monochromatic obliquely propagating low-frequency alfven wave. Plasma Sci. Technol. 16 (10), 919.CrossRefGoogle Scholar
Takase, Y., Ejiri, A., Kakuda, H., Oosako, T., Shinya, T., Wakatsuki, T., Ambo, T., Furui, H., Hashimoto, T., Hiratsuka, J., et al. 2013 Non-inductive plasma initiation and plasma current ramp-up on the TST-2 spherical tokamak. Nucl. Fusion 53 (6), 063006.CrossRefGoogle Scholar
Tanaka, H., Uchida, M., Maekawa, T., Bae, Y.-S., Joung, M., Jeong, J.H. & KSTAR team 2016 Non-inductive initiation of closed flux surfaces by ECH/ECCD on KSTAR using an oblique fundamental O-mode injection from the low-field side. Nucl. Fusion 56 (4), 046003.CrossRefGoogle Scholar
Uchida, M., Yoshinaga, T., Tanaka, H. & Maekawa, T. 2010 Rapid current ramp-up by cyclotron-driving electrons beyond runaway velocity. Phys. Rev. Lett. 104 (6), 065001.CrossRefGoogle ScholarPubMed
Wang, M., Guo, D., Shi, Y., Chen, B., Liu, B., Song, S., Zhao, X., Song, Y., Liu, W., Guan, Y., et al. 2022 Experimental study of non-inductive current start-up using electron cyclotron wave on EXL-50 spherical torus. Plasma Phys. Control. Fusion 64 (7), 075006.CrossRefGoogle Scholar
Wang, M., Li, J., Bai, Y., Dong, J., Shi, Y., Zou, X., Liu, A., Zhuang, G., Li, H., Li, S., et al. 2023 a Particle pump-out induced by trapped electron mode turbulence in electron cyclotron heated plasmas on XuanLong-50 spherical torus. Nucl. Fusion 63 (7), 076024.CrossRefGoogle Scholar
Wang, M., Shi, Y., Dong, J., Gao, X., Lu, Q., Wang, Z., Chen, W., Liu, A., Zhang, G., Wang, Y., et al. 2023 b Observation of whistler wave instability driven by temperature anisotropy of energetic electrons on EXL-50 spherical torus. https://doi.org/10.48550/arXiv.2307.06497.CrossRefGoogle Scholar
Wang, M., Tan, M., Shi, Y., Wang, Z., Dong, J., Liu, A., Zhuang, G., Li, S., Song, S., Yuan, B., et al. 2023 c Experimental investigation of kinetic instabilities driven by runaway electrons in the EXL-50 spherical torus. https://doi.org/10.48550/arXiv.2307.06498.CrossRefGoogle Scholar
Wang, M., Xiuchun, L., Xiaokun, B., Bing, L., Adi, L. & Yuejiang, S. 2023 d Radio-frequency measurements of energetic-electron-driven emissions using high-frequency magnetic probe on XuanLong-50 spherical torus. Plasma Sci. Technol. 25 (4), 045104.CrossRefGoogle Scholar
Yoshinaga, T., Uchida, M., Tanaka, H. & Maekawa, T. 2006 Spontaneous formation of closed-field torus equilibrium via current jump observed in an electron-cyclotron-heated plasma. Phys. Rev. Lett. 96 (12), 125005.CrossRefGoogle Scholar