NORSE: A solver for the relativistic non-linear Fokker-Planck equation for electrons in a homogeneous plasma

TL;DR

This paper introduces NORSE, a novel solver for the relativistic non-linear Fokker-Planck equation that models electron dynamics in plasmas with high electric fields and relativistic temperatures, enabling more accurate predictions of runaway phenomena.

Contribution

The paper presents a fully non-linear, relativistic kinetic solver capable of modeling electron behavior under strong electric fields, extending beyond previous linear or non-relativistic approaches.

Findings

Transition to electron slide-away occurs at lower field strengths than previously predicted.

NORSE accurately models non-Maxwellian electron distributions in high-field plasmas.

The solver can handle large electric fields and relativistic temperatures effectively.

Abstract

Energetic electrons are of interest in many types of plasmas, however previous modeling of their properties has been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modeling of the momentum-space dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted.