Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes

TL;DR

This paper introduces deterministic, structure-preserving discretization schemes for Coulomb collisions in kinetic plasma models, ensuring energy, positivity, and entropy properties are maintained in particle-in-cell simulations.

Contribution

It extends previous structure-preserving discretizations to discrete time, preserving key physical invariants for Landau and gyrokinetic Landau operators.

Findings

Schemes preserve energy, positivity, and entropy dissipation.

Standard Landau scheme also preserves discrete kinetic momentum.

Extensions enable more accurate and stable plasma collision simulations.

Abstract

This paper contributes new insights into discretizing Coulomb collisions in kinetic plasma models. Building on the previous works [Carrillo et al. J. Comp. Phys. X 7:100066 (2020), Hirvijoki and Burby Phys. Plasmas 27(8):082307 (2020)], I propose deterministic discrete-time energy- and positivity-preserving, entropy-dissipating marker-particle schemes for the standard Landau collision operator and the electrostatic gyrokinetic Landau operator. In case of the standard Landau operator, the scheme preserves also the discrete-time kinetic momentum. The improvements, the extensions of the structure-preserving discretizations in [Carrillo et al. J. Comp. Phys. X 7:100066 (2020), Hirvijoki and Burby Phys. Plasmas 27(8):082307 (2020)] to discrete time, are made possible by exploiting the underlying metriplectic structure of the collision operators involved and the so-called discrete-gradient integrators.