One dimensional PIC simulation of relativistic Buneman instability

TL;DR

This paper uses one-dimensional PIC simulations to study the relativistic Buneman instability, revealing how relativistic effects reduce growth rates and alter energy scaling, with results aligning with fluid theory predictions.

Contribution

The study provides the first detailed numerical analysis of relativistic Buneman instability evolution, highlighting the impact of relativistic effects on growth rates and energy scaling.

Findings

Maximum growth rate decreases with relativistic effects.

Energy density ratio scales as 1/γ_{e0}^2 at saturation.

Simulation results agree with fluid theoretical predictions.

Abstract

Spatio-temporal evolution of the relativistic Buneman instability has been investigated in one dimension using an in-house developed particle-in-cell simulation code. Starting from the excitation of the instability, its evolution has been followed numerically till its quenching and beyond. As compared to the well understood non-relativistic case, it is found that the maximum growth rate ($\gamma_{max}$) reduces due to relativistic effects and varies with $\gamma_{e0}$ and m/M as $\gamma_{max} \sim \frac{\sqrt{3}}{2\sqrt{\gamma_{e0}}}\biglb(\frac{m}{2M}\bigrb)^{1/3}$, where $\gamma_{e0}$ is Lorentz factor associated with the initial electron drift velocity ($v_{0}$) and (m/M) is the electron to ion mass ratio. Further it is observed that in contrast to the non-relativistic results[Hirose,Plasma Phys. 20, 481(1978)] at the saturation point, ratio of electrostatic field energy density ($\sum\limits_{k} |E_{k}|^{2}/8\pi$) to initial drift kinetic energy density ($W_{0}$) scales with $\gamma_{e0}$ as $\sim 1/\gamma^{2}_{e0}$. These simulation results are found to be in good agreement with that derived using fluid theory.