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arXiv · 1806.10203

An integral transform technique for kinetic systems with collisions

Jeffrey M. Heninger·Philip J. Morrison
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Abstract

The linearized Vlasov-Poisson system can be exactly solved using the $G$-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 $G$-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 $G$-transformed equation. Since many gyro-/drift-kinetic codes use Hermite polynomials as basis elements, we include an explicit calculation of their $G$-transform.

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Jeffrey M. Heninger, Philip J. Morrison. 2018-08-25. An integral transform technique for kinetic systems with collisions. https://doi.org/10.1063/1.5046194

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