Gyrokinetic particle simulations of reversed shear Alfvén eigenmode excited by antenna and fast ions

Abstract

Global gyrokinetic particle simulations of reversed shear Alfvén eigenmode ͑RSAE͒ have been successfully performed and verified. We have excited the RSAE by initial perturbation, by external antenna, and by energetic ions. The RSAE excitation by antenna provides verifications of the mode structure, the frequency, and the damping rate. When the kinetic effects of the background plasma are artificially suppressed, the mode amplitude shows a near-linear growth. With kinetic thermal ions, the mode amplitude eventually saturates due to the thermal ion damping. The damping rates measured from the antenna excitation and from the initial perturbation simulation agree very well. The RSAE excited by fast ions shows an exponential growth. The finite Larmor radius effects of the fast ions are found to significantly reduce the growth rate. With kinetic thermal ions and electron pressure, the mode frequency increases due to the elevation of the Alfvén continuum by the geodesic compressibility. The nonperturbative contributions from the fast ions and kinetic thermal ions modify the mode structure relative to the ideal magnetohydrodynamic ͑MHD͒ theory. The gyrokinetic simulations have been benchmarked with extended hybrid MHD-gyrokinetic simulations.

The complex mixed Wentzel–Kramers–Brillouin-full-wave approach and its application to the two dimensional mode structure analysis of ion temperature gradient/collisionless trapped electron mode drift waves

“…18) and is thought to be relevant to the toroidal momentum transport due to up-down (along poloidal angle h) symmetry breaking of residual stress. 18 Similar observations of symmetry breaking of the mode structure have been noticed in the simulation 19,20 and experiment 21 of energetic particle driven Alfv enic fluctuations, and explained in terms of the non-Hermitian properties of wave operator. 22 Although heuristic analyses have been discussed on the "tilting" structure, 23 more rigorous derivation based on the mixed WKB-full-wave approach remains to be done, for a better estimate of asymmetric component of the parallel mode structure and momentum transport due to radial equilibrium variation.…”

Verification and validation of linear gyrokinetic simulation of Alfvén eigenmodes in the DIII-D tokamak

“…In the current problem, the fast ion pressure gradient is the dominant source for the radial symmetry breaking, which ultimately determines the radial mode structure. 25,[49][50][51][52][53][54] Therefore, fully self-consistent, non-perturbative simulation is needed to determine the eigenmode structure in order to accurately calculate the damping and growth rate.…”

“…The electromagnetic field is solved using the gyrokinetic Poisson's equation 45 and Ampère's law. GTC was originally developed for simulations of micro-turbulence 46,47 and has recently been extended for simulation of energetic particle physics [48][49][50][51] and kinetic magnetohydrodynamic (MHD) processes with equilibrium current. 52 The gyrokinetic formulation in GTC has been proven to recover all the linear ideal MHD physics including kinetic ballooning modes, shear Alfv en waves, current-driven modes, and pressure-driven modes.…”

Validation of electron temperature gradient turbulence in the Columbia Linear Machine

“…9) is a sophisticated massively parallel gyrokinetic particle simulation code, which has been successful in simulating toroidal ion temperature gradient (ITG) mode, collisionless trapped electron mode (CTEM), toroidal ETG, Alfvén eigenmodes, and other plasma phenomena. [10][11][12][13] We adapt the toroidal GTC code to study the cylindrical plasmas by taking the limit of infinite constant q and setting the equivalent major radius R 0 & 1=k jj . In this section, we will first focus on results for the set of parameters listed in Table I and later do a parametric scan of the T e gradient and parallel wave number k k .…”