Analysis of kinetic-diffusion Monte Carlo simulation and source term estimation scheme in nuclear fusion applications

TL;DR

This paper analyzes a kinetic-diffusion Monte Carlo method for plasma edge simulations in nuclear fusion, demonstrating its accuracy and efficiency improvements over traditional fluid-based and kinetic methods.

Contribution

It provides a theoretical convergence analysis and numerical validation of the KDMC method combined with fluid estimation, showing superior accuracy and speed in fusion-relevant scenarios.

Findings

KDMC achieves lower error than fluid-based methods.

The algorithm is significantly faster than fully kinetic MC.

Error bounds are theoretically established and numerically verified.

Abstract

In plasma edge simulations, the behavior of neutral particles is often described by a Boltzmann--BGK equation. Solving this kinetic equation and estimating the moments of its solution are essential tasks, typically carried out using Monte Carlo (MC) methods. However, for large-sized reactors, like ITER and DEMO, high collision rates lead to a substantial computational cost. To accelerate the calculation, an asymptotic-preserving kinetic-diffusion Monte Carlo (KDMC) simulation method (Mortier et al., SIAM J. Sci. Comput., 2022) and a corresponding fluid estimation technique (Mortier et al., Contrib. Plasma Phys., 2022) have recently been proposed. In this work, we present a comprehensive analysis of the convergence of KDMC combined with the associated fluid estimation. The analysis consists of proving theoretical upper bounds for both KDMC and the fluid estimation, and numerical verifications of these bounds. In addition, we compare the analyzed algorithm with a purely fluid-based method using the fully kinetic MC method as a reference. The algorithm consistently achieves lower error than the fluid-based method, and even one order of magnitude lower in a fusion-relevant test case. Moreover, the algorithm exhibits a significant speedup compared to the reference kinetic MC method. Overall, our analysis confirms the effectiveness of KDMC with the associated fluid estimation in nuclear fusion applications.