The intermittent excitation of geodesic acoustic mode by resonant Instanton of electron drift wave envelope in L-mode discharge near tokamak edge

Zhao-Yang Liu(刘朝阳)^{1,†}, Yang-Zhong Zhang(章扬忠)^{2}, Swadesh Mitter Mahajan^{3}, A-Di Liu(刘阿娣)^{4}, Chu Zhou(周楚)^{4}, and Tao Xie(谢涛)^{5}

1 Institute for Fusion Theory and Simulation and Department of Physics, Zhejiang University, Hangzhou 310027, China; 2 Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230026, China; 3 Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712, USA; 4 School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China; 5 School of Science, Sichuan University of Science and Engineering, Zigong 643000, China

Abstract There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow. A long-lived standing wave phase, which we call the Caviton, and a short-lived traveling wave phase (in radial direction) we call the Instanton. Several abrupt phenomena observed in tokamaks, such as intermittent excitation of geodesic acoustic mode (GAM) shown in this paper, could be attributed to the sudden and fast radial motion of Instanton. The composite drift wave—zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale. The eigenmode equation of the model defines the zero-order (micro-scale) variation; it is solved by making use of the two-dimensional (2D) weakly asymmetric ballooning theory (WABT), a theory suitable for modes localized to rational surface like drift waves, and then refined by shifted inverse power method, an iterative finite difference method. The next order is the equation of electron drift wave (EDW) envelope (containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW. This equation is coupled to the zonal flow equation, and numerically solved in spatiotemporal representation; the results are displayed in self-explanatory graphs. One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW. The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition. Then, it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz. The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM. The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. U1967206, 11975231, 11805203, and 11775222), the National MCF Energy Research and Development Program, China (Grant Nos. 2018YFE0311200 and 2017YFE0301204), and the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDB-SSW-SYS004).

Corresponding Authors:
Zhao-Yang Liu
E-mail: lzy0928@mail.ustc.edu.cn

Cite this article:

Zhao-Yang Liu(刘朝阳), Yang-Zhong Zhang(章扬忠), Swadesh Mitter Mahajan, A-Di Liu(刘阿娣), Chu Zhou(周楚), and Tao Xie(谢涛) The intermittent excitation of geodesic acoustic mode by resonant Instanton of electron drift wave envelope in L-mode discharge near tokamak edge 2022 Chin. Phys. B 31 045202

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