Semi-Implicit Continuum Kinetic Modeling of Weakly Collisional Parallel Transport in a Magnetic Mirror

TL;DR

This paper introduces an efficient IMEX kinetic simulation method for weakly collisional plasma transport in magnetic mirrors, significantly reducing computation time and enabling detailed kinetic studies.

Contribution

The work develops a Jacobian-free Newton--Krylov IMEX scheme with multigrid preconditioning for plasma transport, achieving large time-step improvements and incorporating a bounce-averaged model for validation.

Findings

IMEX scheme achieves 2500x speedup over explicit methods.

The bounce-averaged model effectively evaluates velocity-space discretization.

Comparison of collision operators reveals their impact on plasma behavior.

Abstract

We present implicit-explicit (IMEX) kinetic simulations of weakly collisional parallel plasma transport in magnetic mirror configurations using the continuum code \textsc{COGENT}. The numerical scheme employs a Jacobian-free Newton--Krylov method with algebraic multigrid preconditioning to overcome the severe time-step limitations imposed by strong mirror forces in fully explicit schemes. Applied to parameters relevant to the WHAM mirror experiment, the IMEX approach enables time steps up to $2.5 \times 10^4$ times larger than those permitted by explicit methods, resulting in a 2500x speedup in 1D--2V simulations of parallel transport with kinetic ions and Boltzmann electrons. Additionally, a reduced bounce-averaged model for a square mirror is implemented to support the computationally intensive fully kinetic simulations. The bounce-averaged formulation is used to evaluate the numerical convergence of the velocity-space discretization algorithms and to assess the role of the collision model by comparing simulations employing the nonlinear Fokker--Planck and the simplified Lenard--Bernstein--Dougherty collision operators.