Beta-induced Alfvén-acoustic eigenmodes in stellarator plasmas with low shear

Abstract

The coupling of low-frequency Alfvénic modes with acoustic oscillations due to curvature of the background magnetic field is considered for stellarator plasmas with low shear. Magnetohydrodynamic ͑MHD͒ analysis demonstrates that the interaction between these branches can generate gaps in the continua with a width proportional to beta as well as the magnitude of the Fourier harmonics of the magnetic field strength which cause the coupling. The gaps can provide a habitat for beta-induced Alfvén-acoustic eigenmodes ͑BAAEs͒. Using the causality principle, a technique is developed to resolve the singular behavior of the MHD BAAE eigenmode equation at the points of resonance with the acoustic continuum. Alternatively, the singularities arising in the reduced MHD description can be resolved by accounting for the finite parallel electrical field. Both approaches yield consistent continuum damping rate, which proves to be small. Numerical calculations for analytically fitted experimental profiles of electron-dominated plasma in Helically Symmetric eXperiment ͑HSX͒ facility yield two weakly damped BAAE modes with different frequencies: one is close to the maximum of the lower-frequency Alfvén-acoustic continuum, and the other is located well within the BAAE gap. The numerically found BAAEs have frequencies in the same range as the experimentally observed electromagnetic modes in HSX, even when the finite diamagnetic frequency effects are considered.

Gyrokinetic particle simulation of beta-induced Alfven-acoustic eigenmode

“…The finite amplitude of the m ¼ 5 and m ¼ 7 harmonics in a wide radial range also indicates that the local theory may be invalid to describe the dispersion relation of the BAAE. [7][8][9][10][11][12] Figure 3(g) shows the Alfven continuum and the BAAE frequencies. Compared with Fig.…”

“…Therefore, it has been debated whether the BAAE as predicted by the MHD theory could exist in the collisionless plasmas of fusion interest where BAAE is expected to be heavily damped by ion kinetic effects. [10][11][12] A kinetic approach is thus required for the accurate simulation of the BAAE. In this work, the BAAE is verified and studied through global gyrokinetic particle simulations for the first time using the gyrokinetic toroidal code (GTC).…”

Nonlinear co-existence of beta-induced Alfvén eigenmodes and beta-induced Alfvén-acoustic eigenmodes

“…33,34 The frequency of BAAE is lower than the frequency of BAE, since the BAAE spectral gap is below the BAE spectral gap in the Alfv en continuum. Due to BAAE's low frequency, it is heavily damped by ion kinetic effects, [35][36][37] especially when ion temperature (T i ) and electron temperature (T e ) are comparable, which has been verified by simulations. 33 With a strong drive of fast particles, the non-perturbative effect 38,39 of fast particles should be considered, which will modify radially local dispersion relation 34 and thus build up a new wave-particle energy exchange channel.…”

Energetic‐Particle‐Driven Instabilities in General Toroidal Configurations

“…2(b) generally agree with the frequency minima measured experimentally. Alfvén-sound couplings can introduce new eigenmodes near the minima of these continua, such as the BAAE [10,11] (beta-induced Alfvén-acoustic eigenmode) and EGAM [13] (energetic-particle-induced geodesic acoustic mode).…”

“…A number of models have been developed for the calculation of such continua in stellarators [6][7][8] and generally provide reasonable agreement with frequency lines that are measured in experiments, to within uncertainties related to imprecise knowledge of the i --and density profiles, average ion mass and Doppler shifts related to plasma flows. A topic of recent interest both for tokamaks [9,10] and stellarators [4,6,8,11] has been the inclusion of sound wave couplings to the shear Alfvén continua. In a three-dimensional system these couplings might be expected to become of importance when k …”