A comparison of weak-turbulence and PIC simulations of weak electron-beam plasma interaction

TL;DR

This study compares weak-turbulence and particle-in-cell simulations of weak electron-beam plasma interactions, revealing how ion temperature affects wave resonance and establishing simulation particle number requirements.

Contribution

It provides a numerical validation of weak turbulence theory across different ion temperatures using PIC simulations, highlighting the impact of ion damping on wave interactions.

Findings

Good agreement in cold ion limit

Resonance broadening with increased ion temperature

Established particle number thresholds for accurate simulations

Abstract

Quasilinear theory has long been used to treat the problem of a weak electron beam interacting with plasma and generating Langmuir waves. Its extension to weak-turbulence theory treats resonant interactions of these Langmuir waves with other plasma wave modes, in particular ion-sound waves. These are strongly damped in plasma of equal ion and electron temperatures, as sometimes seen in, for example, the solar corona and wind. Weak turbulence theory is derived in the weak damping limit, with a term describing ion-sound wave damping then added. In this paper we use the EPOCH particle-in-cell code to numerically test weak turbulence theory for a range of electron-ion temperature ratios. We find that in the cold ion limit the results agree well, but increasing ion temperature the three-wave resonance becomes broadened in proportion to the ion-sound wave damping rate. This may be important in, for example, the theory of solar radio bursts, where the spectrum of Langmuir waves is critical. Additionally we establish lower limits on the number of simulation particles needed to accurately reproduce the electron and wave distributions in their saturated states, and to reproduce their intermediate states and time evolution.