An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

TL;DR

This paper introduces an asymptotic-preserving numerical scheme for the relativistic collisional Drift-Kinetic Equation, enabling accurate runaway electron simulations in tokamak geometries across different plasma collisionalities.

Contribution

The paper presents a novel, simple two-step operator-split algorithm derived from Green's function solutions, ensuring uniform convergence and accuracy in relativistic runaway electron modeling.

Findings

Algorithm accurately simulates runaway electrons in tokamaks.

Method remains effective across various plasma collisionalities.

Demonstrates convergence and robustness through numerical experiments.

Abstract

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.