Low-frequency shear Alfv\'en waves at DIII-D: theoretical interpretation of experimental observations

TL;DR

This paper provides a theoretical analysis of low-frequency shear Alfvén waves observed in DIII-D, demonstrating the predictive power of the GFLDR framework in interpreting experimental data and distinguishing between different unstable modes.

Contribution

It applies the GFLDR to interpret experimental observations of BAEs and LFAMs, clarifying their instability mechanisms and polarization characteristics.

Findings

BAEs are dissipative-type unstable modes with maximum drive near $q_{min}$ deviations.

LFAMs are reactive-type unstable modes with peaks at energetic particle pressure gradients.

Theoretical frequency spectra match experimental observations by varying $q_{min}$.

Abstract

The linear properties of the low-frequency shear Alfv\'en waves such as those associated with the beta-induced Alfv\'en eigenmodes (BAEs) and the low-frequency modes observed in reversed-magnetic-shear DIII-D discharges (W. Heidbrink, et al 2021 Nucl. Fusion 61 066031) are theoretically investigated and delineated based on the theoretical framework of the general fishbone-like dispersion relation (GFLDR). By adopting representative experimental equilibrium profiles, it is found that the low-frequency modes and BAEs are, respectively, the reactive-type and dissipative-type unstable modes with dominant Alfv\'enic polarization, thus the former being more precisely called low-frequency Alfv\'en modes (LFAMs). More specifically, due to different instability mechanisms, the maximal drive of BAEs occurs, in comparison to LFAMs, when the minimum of the safety factor ($q_{min}$) deviates from a rational number. Meanwhile, the BAE eigenfunction peaks at the radial position of the maximum energetic particle pressure gradient, resulting in a large deviation from the $q_{min}$ surface. Moreover, the ascending frequency spectrum patterns of the experimentally observed BAEs and LFAMs can be theoretically reproduced by varying $q_{min}$ and also be well interpreted based on the GFLDR. The present analysis illustrates the solid predictive capability of the GFLDR and its practical usefulness in enhancing the interpretative capability of both experimental and numerical simulation results.