Kinetic Simulation of Collisional Magnetized Plasmas with Semi-Implicit Time Integration

TL;DR

This paper introduces a semi-implicit time integration algorithm for kinetic plasma simulations that efficiently handles highly-collisional regimes by combining implicit and explicit methods, improving computational performance.

Contribution

The paper develops and tests a semi-implicit additive Runge-Kutta method for gyrokinetic plasma simulations, enabling larger time steps in highly-collisional conditions.

Findings

The semi-implicit method achieves accurate results in highly-collisional plasma tests.

It allows larger time steps compared to explicit methods, reducing computational cost.

The implementation demonstrates improved efficiency in the COGENT code.

Abstract

Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for weakly-collisional high-temperature plasmas, high collisionality in colder regions render the equations numerically stiff due to disparate time scales. In this paper, we propose an implicit-explicit algorithm for such cases, where the collisional term is integrated implicitly in time, while the advective term is integrated explicitly in time, thus allowing time step sizes that are comparable to the advective time scales. This partitioning results in a more efficient algorithm than those using explicit time integrators, where the time step sizes are constrained by the stiff collisional time scales. We implement semi-implicit additive Runge-Kutta methods in COGENT, a finite-volume gyrokinetic code for mapped, multiblock grids and test the accuracy, convergence, and computational cost of these semi-implicit methods for test cases with highly-collisional plasmas.