Study of kinetic effects on MHD instabilities in cylindrical geometry using a spectral hybrid kinetic-MHD code

Machine-scale instabilities in fusion devices are commonly described using magnetohydrodynamics (MHD), however kinetic effects can significantly affect MHD instabilities through kinetic compression and wave-particle interaction. We propose a new code that solves the drift-kinetic-MHD equations using a spectral method, formulated using a Case-Van Kampen approach (N. G. Van Kampen, Physica 21 , 949 (1955)). The eigenvectors of the standardised eigenvalue problem are composed of the perpendicular MHD-like displacement, a potential that describes the parallel electric field, as well as the kinetic correction to the perturbed distribution function. The new code, which can solve for generalised kinetic equilibria in axisymmetric toroidal geometry, is benchmarked favourably against exact analytic solutions for kinetic-MHD in a cylindrical screw pinch. In this configuration, kinetic effects are driven by the particles in the long free path limit subject to angular drifts associated with the radial curvature of the configuration. The kinetic effect of highly energetic particles is shown to be stabilising via exact cancellation of ideal MHD interchange (Suydam), while for moderately energetic particles, their effective guiding centre velocity resonates with the wave frequency, causing novel kinetic instabilities in the cylinder.