Drift-Alfvén kinetic stability theory in the ballooning mode approximation

Abstract

The coupled drift-shear Alfvén mode including the complete Bessel function gyroradius effect and the ∇⊥B -curvature guiding center drift resonance of kinetic theory is solved for the toroidal ballooning mode eigenvalues and eigenfunctions. Comparisons between nonlocal (ballooning) and local kinetic theory and between nonlocal fluid and kinetic theory are made. The critical plasma pressure for kinetic ballooning mode instability is only the same as the magnetohydrodynamic (MHD) theory critical pressure βMHD for ηi=0. The critical kinetic theory plasma pressure βK(ηi) is well below βMHD and the kinetic theory growth rate is unstable for all k. The MHD second stability region is also unstable in the kinetic theory. The kinetic theory growth rate is a maximum around k≤0.3–0.5 for finite aspect ratio εn=rn/R. The effects of trapped electrons are found to be weakly stabilizing both analytically and numerically, and the instability is still significant outside the ideal MHD stable window from the ion magnetic drift resonances when ηi≳1. The kinetic growth rate is a function of the six dimensionless parameters k, q2β, εn, s, ηi, and τ=Te/Ti.