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

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.

arXiv commentJoint Varenna--Lausanne International Workshop on Theory of Fusion Plasmas, October 12--16th, 2020

References in corpus (16)

• GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
• Variational formulation of particle algorithms for kinetic plasma simulations
• Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
• Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
• Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov-Maxwell system
• Structure-Preserving Geometric Particle-in-Cell Methods for Vlasov-Maxwell Systems
• Hamiltonian integration methods for Vlasov-Maxwell equations
• Metriplectic Integrators for the Landau Collision Operator
• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• Conservative discretization of the Landau collision integral
• Energetically-consistent collisional gyrokinetics
• Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures
• Structure-preserving strategy for conservative simulation of relativistic nonlinear Landau--Fokker--Planck equation
• A fully implicit, scalable, conservative nonlinear relativistic Fokker-Planck 0D-2P solver for runaway electron
• Subcycling of particle orbits in variational, geometric electromagnetic particle-in-cell methods
• Collisional Gyrokinetics Teases the Existence of Metriplectic Reduction

Cited by in corpus (5)

• Multispecies structure-preserving particle discretization of the Landau collision operator
• Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory
• Energy-momentum-conserving stochastic differential equations and algorithms for nonlinear Landau-Fokker-Planck equation
• A metriplectic formulation of polarized radiative transfer
• Fully discrete energy-dissipative and conservative discrete gradient particle methods for a class of continuity equations