Analytic stability boundaries for compressional and global Alfv\'en eigenmodes driven by fast ions. II. Interaction via Landau resonance

TL;DR

This paper derives analytical stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions via Landau resonance, validated by simulations and experimental data from NSTX.

Contribution

It introduces approximate analytical conditions for mode stability considering realistic beam distributions and mode characteristics, including mode coupling effects.

Findings

Analytical stability boundaries match numerical and experimental results.

Mode coupling influences the existence of GAE instability.

Good agreement with NSTX observations of co-CAEs.

Abstract

Conditions for net fast ion drive are derived for beam-driven, co-propagating, sub-cyclotron compressional (CAE) and global (GAE) Alfv\'en eigenmodes driven by the Landau resonance with super-Alfv\'enic fast ions. Approximations applicable to realistic neutral beam distributions and mode characteristics observed in spherical tokamaks enable the derivation of marginal stability conditions for these modes. Such conditions successfully reproduce the stability boundaries found from numerical integration of the exact expression for local fast ion drive/damping. Coupling between the CAE and GAE branches of the dispersion due to finite $\omega/\omega_{ci}$ and $k_\parallel/k_\perp$ is retained and found to be responsible for the existence of the GAE instability via this resonance. Encouraging agreement is demonstrated between the approximate stability criterion, simulation results, and a database of NSTX observations of co-CAEs.