Gyrokinetic particle simulation of beta-induced Alfvén eigenmode

Abstract

The beta-induced Alfvén eigenmode ͑BAE͒ in toroidal plasmas is studied using global gyrokinetic particle simulations. The BAE real frequency and damping rate measured in the initial perturbation simulation and in the antenna excitation simulation agree well with each other. The real frequency is slightly higher than the ideal magnetohydrodynamic ͑MHD͒ accumulation point frequency due to the kinetic effects of thermal ions. Simulations with energetic particle density gradient show exponential growth of BAE with a growth rate sensitive to the energetic particle temperature and density. The nonperturbative contributions by energetic particles modify the mode structure and reduce the frequency relative to the MHD theory. The finite Larmor radius effects of energetic particles reduce the BAE growth rate. Benchmarks between gyrokinetic particle simulation and hybrid MHD-gyrokinetic simulation show good agreement in BAE real frequency and mode structure.

Linear dispersion relation of beta-induced Alfvén eigenmodes in presence of anisotropic energetic ions

“…Subsequently, BAEs have been observed in Ohmically heated plasmas in absence of energetic ions [20,21], as well as plasmas heated by ion cyclotron [16,22] and electron cyclotron resonant heating [23]. Recent numerical simulations have also shown BAE excitation by EPs [24][25][26]. A general theoretical framework, the so-called generalized fishbone-like dispersion relation (GFLDR) [2,[5][6][7][27][28][29][30], has been developed to describe the various Alfvénic fluctuations in tokamak plasmas observed in experiments and numerical simulations.…”

“…The simulations of BAEs excited by EPs have been limited to isotropic slowing down or Maxwellian distribution functions [24,25]. However, EPs generated by neutral beam injection (NBI) heating are better described by anisotropic slowing down distribution function.…”

NBI-driven Alfvénic modes at ASDEX Upgrade

“…Finally, also the non-linear interaction with other Alfvénic instabilities, such as TAEs has been investigated [10]. In this paper, we aim to describe and model another, closely connected Alfvénic mode in the same frequency regime as the RSAE, the beam-driven beta induced Alfvén eigenmode (BAE) [11,12,13,16,17,18,19]. Although a lot of literature is available for BAE modes they have so far not been investigated in the current ramp-up phase of a tokamak discharge.…”

A comparison of Vlasov with drift kinetic and gyrokinetic theories

“…7 which have been employed to a variety of applications (see, for example, the recent Refs. [12][13][14]. Equation (1) remains identical in form where f ðR; v k ; l; tÞ is now the gyrocenter distribution function for ions.…”

“…In addition, the temporary and probably future computational efficiency puts a limitation on numerical solutions of the Maxwell-Vlasov equations. For this reason, approximate kinetic theories in a reduced phase space, as the drift kinetic 1-6 and gyrokinetic ones, [7][8][9][10][11][12][13][14][15] have been developed and applied to numerous simulations, e.g., on turbulence in connection with the creation of zonal flows. In both theories, the reduced phase space is five dimensional with three spatial components associated with the guiding center position, R (or the gyrocenter position in the framework of gyrokinetic theory), and a velocity component parallel to the magnetic field, v k .…”