Minisymposium Presentation

Magnetohydrodynamics (MHD) is widely used to study the stability of a given magnetic configuration with respect to potentially problematic machine-scale instabilities. The basic mechanism of these macroscopic modes are well described by this theory. Kinetic effects, through wave-particle interactions, can however significantly affect their stability. Some current kinetic-MHD studies estimating these effects rely on a number of assumptions, typically solving a drift-kinetic equation semi-analytically, which implies strong limitations on the type of orbits that can be reproduced by the model. Other codes integrate guiding-center orbits numerically in the framework of a Lagrangian approach, which requires less assumptions but strongly increases the computational requirements. We present a new spectral linear kinetic-MHD code which solves the MHD momentum equation along with an Eulerian discretization of the drift-kinetic equation. Following the Van Kampen approach, the problem is expressed as a standard linear generalized eigenvalue problem for the MHD displacement as well as the kinetic correction to the perturbed distribution function. The equations are discretized on an effective five-dimensional phase space and result in sparse matrices of very large dimension. The challenges associated with solving this eigenvalue problem on a parallel platform are presented as well as first benchmarks in simplified cylindrical geometry.