A Langevin approach to multi-scale modeling

TL;DR

This paper introduces a multi-scale modeling approach for plasmas that separates the distribution function into bulk and tail populations using Langevin equations, enabling more accurate and efficient simulations of non-Maxwellian distributions.

Contribution

It presents a novel Langevin-based method to split plasma distribution functions into genuine bulk and tail components with separate evolution equations.

Findings

Allows separate treatment of bulk and tail populations

Maintains non-negativity and physical properties of distributions

Facilitates multi-scale plasma simulations

Abstract

In plasmas, distribution functions often demonstrate long anisotropic tails or otherwise significant deviations from local Maxwellians. The tails, especially if they are pulled out from the bulk, pose a serious challenge for numerical simulations as resolving both the bulk and the tail on the same mesh is often challenging. A multi-scale approach, providing evolution equations for the bulk and the tail individually, could offer a resolution in the sense that both populations could be treated on separate meshes, or different reduction techniques applied to the bulk and the tail population. In this letter, we propose a multi-scale method which allows us to split a distribution function into a bulk and a tail so that both populations remain genuine, non-negative distribution functions and may carry density, momentum, and energy. The proposed method is based on the observation that the motion of an individual test particle in a plasma obeys a stochastic differential equation, also referred to as a Langevin equation. This allows us to define transition probabilities between the bulk and the tail and to provide evolution equations for both populations separately.