Resonant theory of kinetic ballooning modes in general toroidal geometry

TL;DR

This paper extends the linear kinetic-ballooning-mode theory to include weakly-driven resonant regimes in general toroidal geometry, revealing new destabilization mechanisms and their impact on plasma turbulence.

Contribution

It introduces an analytical model for resonant KBMs in general toroidal geometry, validated by gyrokinetic simulations, enhancing understanding of sub-threshold instabilities.

Findings

Resonant KBMs have broad eigenfunctions and near-marginal growth rates.

Good agreement between analytical model and gyrokinetic simulations.

Resonant KBMs can significantly influence turbulent transport.

Abstract

The linear theory of the kinetic-ballooning-mode (KBM) instability is extended to capture a weakly-driven regime in general toroidal geometry where the destabilization is caused by the magnetic-drift resonance of the ions. Such resonantly-destabilized KBMs are characterized by broad eigenfunctions along the magnetic field line and near-marginal positive growth rates, even well below the beta threshold of their non-resonant counterparts. This unconventional (or sub-threshold) KBM, when destabilized, has been shown to catalyze an enhancement of turbulent transport in the Wendelstein 7-X (W7-X) stellarator [1, 2]. Simplifying the energy dependence of key resonant quantities allows for an analytical treatment of this KBM using the physics-based ordering from the more general equations of Tang, Connor, and Hastie [3]. Results are then compared with high-fidelity gyrokinetic simulations for the (st)KBM in W7-X and the conventional KBM in a circular tokamak at both high and low magnetic shear, where good agreement is obtained in all cases. This reduced KBM model provides deeper insight into (sub-threshold) KBMs and their relationship with geometry, and shows promise for aiding in transport model development and geometry-based turbulence optimization efforts going forward.