Geodesic Acoustic Mode
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2021 ◽  
Liu Zhao-Yang ◽  
Zhang Yang-Zhong ◽  
Swadesh Mitter Mahajan ◽  
Liu A-Di ◽  
Zhou Chu ◽  

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 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.

Yahui Wang ◽  
Tao Wang ◽  
Shizhao Wei ◽  
Zhiyong Qiu

Abstract The parametric decay process of a reversed shear Alfv\'{e}n eigenmeode (RSAE) into a geodesic acoustic mode (GAM) and a kinetic reversed shear Alfv\'{e}n eigenmode (KRSAE) is investigated using nonlinear gyrokinetic theory. The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold, which could be readily satisfied in burning plasmas operated in steady-state advanced scenario. This decay process can contribute to thermal plasma heating and confinement improvement.

Ningfei Chen ◽  
Shizhao Wei ◽  
Guangyu Wei ◽  
Zhiyong Qiu

Abstract The two-field equations governing fully nonlinear dynamics of the drift wave (DW) and geodesic acoustic mode (GAM) interaction in toroidal geometry are derived in the nonlinear gyrokinetic framework. Two stages with distinctive features are identified and analyzed by both analytical and numerical approaches. In the linear growth stage, the derived set of nonlinear equations can be reduced to the intensively studied parametric decay instability (PDI), accounting for the spontaneous resonant excitation of GAM by DW. The main results of previous works on spontaneous GAM excitation, e.g., the much enhanced GAM group velocity and the nonlinear growth rate of GAM, are reproduced from the numerical solution of the two-field equations. In the fully nonlinear stage, soliton structures are observed to form due to the balancing of the self-trapping effect by the spontaneously excited GAM and kinetic dispersiveness of DW. The soliton structures enhance turbulence spreading from DW linearly unstable to stable region, exhibiting convective propagation instead of typical linear dispersive process, and is thus, expected to induce core-edge interaction and nonlocal transport.

2021 ◽  
Vol 28 (11) ◽  
pp. 112505
E. Poli ◽  
A. Bottino ◽  
O. Maj ◽  
F. Palermo ◽  
H. Weber

2021 ◽  
Vol 23 (3) ◽  
pp. 035101
Zhaoyang LIU ◽  
Yangzhong ZHANG ◽  
Swadesh Mitter MAHAJAN ◽  
Adi LIU ◽  
Tao XIE ◽  

2020 ◽  
Vol 37 (9) ◽  
pp. 095201
Yang Chen ◽  
Wenlu Zhang ◽  
Jian Bao ◽  
Zhihong Lin ◽  
Chao Dong ◽  

2020 ◽  
Vol 60 (11) ◽  
pp. 112007
Hao Wang (王 灏) ◽  
Yasushi Todo (藤堂 泰) ◽  
Masaki Osakabe (長壁 正 ◽  
Takeshi Ido (井戸 毅) ◽  
Yasuhiro Suzuki (鈴木 康

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