Hole-Clump Pair Creation in the Evolution of Energetic-Particle-Driven Geodesic Acoustic Modes

Abstract

Nonlinear frequency chirping of the energetic-particle-driven geodesic acoustic mode (EGAM) is investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic fluid. It is demonstrated in the simulation result that both frequency chirping up and chirping down take place in the nonlinear evolution of the EGAM. It is found that two hole-clump pairs are formed in the energetic particle distribution function in two-dimensional velocity space of pitch angle variable and energy. One pair is formed in the phase space region that destabilizes the instability, while the other is formed in the stabilizing region. The transit frequency of the hole (clump) in the destabilizing region chirps up (down), while in the stabilizing region the hole (clump) chirps down (up). The transit frequencies of particles in the holes and clumps are in good agreement with the chirping EGAM frequency indicating that the particles are kept resonant with the EGAM during the nonlinear frequency chirping. Continuous energy transfer takes place from the destabilizing phase space region to the stabilizing region during the spontaneous frequency chirping of the wave.

Effects of passing energetic particles on geodesic acoustic mode

“…While recent simulation results show that k 0 ' 0 can also excite instabilities. 24,25 After considering the poloidal dependence effect, the EPs with zero pitch-angle can destabilize the GAM and induce instabilities. Assuming v ¼ 2 and thereby, D 0 ¼ 1 and v 0 ¼ 1, the dispersion relation is written as…”

Implementation of energy transfer technique in ORB5 to study collisionless wave-particle interactions in phase-space

“…Other interesting effects, associated with the EGAM nonlinear evolution, are the EGAM frequency chirping, which consists in a fast modification of the mode frequency, and the saturation mechanisms. Since the frequency shift during the chirping is considered to occur as a result of the wave-particle interaction [60][61][62][63][64][65] , the MPR diagnostic can be used to investigate this phenomenon as well. The saturation mechanisms (wave-particle or wave-wave interactions) are important to investigate in order to build a theoretical model capable of predicting the saturation levels in experimentally relevant conditions, and as a consequence, the EP redistribution in phase space.…”

Linear properties of global energetic particle induced geodesic acoustic mode with bump-on-tail distribution in tokamak plasmas

“…Since then EGAM has been observed in other tokamaks [7][8][9] as well as in the Large Helical Device (LHD) [10][11]. Extensive theoretical and numerical work has been done on the linear physics of EGAM in the past decade [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. The research on EGAM has been reviewed recently in several papers [26][27][28].…”