A Kinetic Model for Ions in the Solar Corona Including Wave‐Particle Interactions and Coulomb Collisions

Abstract

A model for the kinetics of ions in the solar corona is presented. The model includes wave-particle interactions within the framework of quasi-linear theory and Coulomb collisions calculated by using the Landau collision integral. The integration of the ion velocity distribution functions (VDFs) over the velocity components perpendicular to the background magnetic field yields so-called reduced VDFs. Coupled Vlasov equations for these reduced VDFs are derived. Since they depend only on the coordinate s, speed v∥, and time t, they can be solved numerically with reasonable effort. The model equations guarantee conservation of energy between waves and particles. The Vlasov equations are solved using a temporal relaxation scheme. Tests of the numerical method concerning conservation of momentum and energy, relaxation into thermal equilibrium, and the reproduction of the shape of the known VDF in the case of a temperature gradient have been performed successfully. Kinetic results for ions in a coronal funnel are presented. They show a preferred heating of the heavy ions in agreement with solar observations and strong deviations of their reduced VDFs from a Maxwellian distribution function. An extensive discussion of the model results for the solar corona is presented in a companion paper.