A Multiscale Eulerian Vlasov-Rosenbluth-Fokker-Planck Algorithm for Thermonuclear Burning Plasmas

TL;DR

This paper introduces a multiscale Eulerian algorithm for kinetic plasma modeling that effectively captures alpha particle slowing-down in thermonuclear fusion, improving numerical accuracy and efficiency.

Contribution

The paper presents a novel two-grid method that separates energetic and thermal alpha particles, with a mass-conserving transfer scheme that does not rely on strict velocity scale separation.

Findings

Robustness demonstrated on challenging multiscale fusion problems

Accurate energy and mass conservation in alpha particle modeling

Effective handling of sharp velocity-space features

Abstract

Accurate treatment of energetic fusion byproducts in laboratory plasmas often requires a kinetic description, owing to their large birth kinetic energy and long mean-free-paths compared with the characteristic system scale lengths. For example, alpha particles produced by deuterium--tritium fusion reactions are born at high energies (\SI{3.5}{MeV}) and predominantly slow down through interactions with electrons traveling at comparable speeds. As an alpha particle slows, its distribution collapses near the background ion-thermal speed, forming a sharp structure in velocity space. Such sharp features pose numerical challenges in grid-based Eulerian methods: capturing the full alpha-particle energies demands a large velocity domain, while resolving the near-thermal region requires a sufficiently fine mesh. Inspired by the work of Peigney et al.[J. Comput. Phys. 278 (2014)], we present a two-grid approach that splits the alpha-particle distribution into energetic (suprathermal) and ash (thermal) components. A Gaussian-based sink term transfers particles from the energetic population to the ash population as they slow to the thermal regime, and a conservative projection scheme ensures that mass, momentum, and energy of the alpha and ash interactions are preserved. Unlike the formulation of Peigney, our method does not require a strict asymptotic separation of velocity scales, which can, in principle, be arbitrary. We demonstrate the robustness of this approach on challenging multiscale problems, including a surrogate for an igniting inertial confinement fusion capsule.