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

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.