How large can the electron to proton mass ratio be in Particle-In-Cell simulations of unstable systems?

TL;DR

This paper investigates the maximum electron to proton mass ratio in Particle-In-Cell simulations of plasma instabilities, analyzing how increasing this ratio affects the simulation's physical accuracy during the linear instability phase.

Contribution

It introduces a criterion to determine the maximum feasible mass ratio in PIC simulations without altering the fundamental physics, focusing on the linear instability regime.

Findings

No exact similarity law exists for changing the mass ratio.

A criterion for the maximum mass ratio based on unstable mode hierarchy.

Application to relativistic electron beam crossing plasma case.

Abstract

Particle-in-cell (PIC) simulations are widely used as a tool to investigate instabilities that develop between a collisionless plasma and beams of charged particles. However, even on contemporary supercomputers, it is not always possible to resolve the ion dynamics in more than one spatial dimension with such simulations. The ion mass is thus reduced below 1836 electron masses, which can affect the plasma dynamics during the initial exponential growth phase of the instability and during the subsequent nonlinear saturation. The goal of this article is to assess how far the electron to ion mass ratio can be increased, without changing qualitatively the physics. It is first demonstrated that there can be no exact similarity law, which balances a change of the mass ratio with that of another plasma parameter, leaving the physics unchanged. Restricting then the analysis to the linear phase, a criterion allowing to define a maximum ratio is explicated in terms of the hierarchy of the linear unstable modes. The criterion is applied to the case of a relativistic electron beam crossing an unmagnetized electron-ion plasma.