An integral transform technique for kinetic systems with collisions
Abstract
The linearized Vlasov-Poisson system can be exactly solved using the -transform, an integral transform introduced in Refs. 1-3 that removes the electric field term, leaving a simple advection equation. We investigate how this integral transform interacts with the Fokker-Planck collision operator. The commutator of this collision operator with the -transform (the "shielding term") is shown to be negligible. We exactly solve the advection-diffusion equation without the shielding term. This solution determines when collisions dominate and when advection (i.e. Landau damping) dominates. This integral transform can also be used to simplify gyro-/drift-kinetic equations. We present new gyrofluid equations formed by taking moments of the -transformed equation. Since many gyro-/drift-kinetic codes use Hermite polynomials as basis elements, we include an explicit calculation of their -transform.
Cite
@article{arxiv.1806.10203,
title = {An integral transform technique for kinetic systems with collisions},
author = {Jeffrey M. Heninger and Philip J. Morrison},
journal= {arXiv preprint arXiv:1806.10203},
year = {2018}
}