Analytic stability boundaries for compressional and global Alfv\'en eigenmodes driven by fast ions. I. Interaction via ordinary and anomalous cyclotron resonances

TL;DR

This paper derives analytic conditions for the stability of compressional and global Alfvén eigenmodes driven by fast ions in spherical tokamaks, extending previous narrow-distribution models to realistic broad distributions and validating with simulations and observations.

Contribution

It provides a generalized analytic framework for fast ion drive of Alfvén eigenmodes applicable to realistic beam distributions, correcting and extending prior narrow-distribution results.

Findings

Analytic stability conditions match numerical evaluations.

Conditions agree with NSTX observations of counter-propagating GAE.

Extended models include all relevant terms in frequency and wavenumber ratios.

Abstract

Conditions for net fast ion drive are derived for beam-driven, sub-cyclotron compressional (CAE) and global (GAE) Alfv\'en eigenmodes, such as those routinely observed in spherical tokamaks such as NSTX(-U) and MAST. Both co- and counter-propagating CAEs and GAEs are investigated, driven by the ordinary and anomalous Doppler-shifted cyclotron resonance with fast ions. Whereas prior results were restricted to vanishingly narrow distributions in velocity space, broad parameter regimes are identified in this work which enable an analytic treatment for realistic fast ion distributions generated by neutral beam injection. The simple, approximate conditions derived in these regimes for beam distributions of realistic width compare well to the numerical evaluation of the full analytic expressions for fast ion drive. Moreover, previous results in the very narrow beam case are corrected and generalized to retain all terms in $\omega/\omega_{ci}$ and $k_\parallel/k_\perp$, which are often assumed to be small parameters but can significantly modify the conditions of drive and damping when they are non-negligible. Favorable agreement is demonstrated between the approximate stability criterion, simulation results, and a large database of NSTX observations of cntr-GAEs.