Quantum electrodynamic effects on counter-streaming instabilities in the whole k space

In a recent work [Bret, EPL 135, 35001 (2021)], quantum electrodynamic (QED) effects were evaluated for the two-stream instability. It pertains to the growth of perturbations with a wave vector oriented along the flow in a collisionless counter-streaming system. Here, the analysis is extended to every possible orientation of the wave vector. The previous result for the two-stream instability is recovered, and it is proved that, even within the framework of a three-dimensional (3D) analysis, this instability remains fundamentally 1D even when accounting for QED effects. The filamentation instability, found for wave vectors normal to the flow, is weakly affected by QED corrections. As in the classical case, its growth rate saturates at large k(perpendicular to). The saturation value is found independent of QED corrections. Also, the smallest unstable k(perpendicular to) is independent of QED corrections. Surprisingly, unstable modes found for oblique wave vectors do not follow the same pattern. For some, QED corrections do reduce the growth rate. But, for others, the same corrections increase the growth rate instead. The possibility for QED effects to play a role in unmagnetized systems is evaluated. Pair production resulting from gamma emission by particles oscillating in the exponentially growing fields is not accounted for.

Automated summary

This article investigates the problem of two-stream instability and the impact of QED corrections on it, extending the results of previous work. The results indicate that even when considering QED effects, the two-stream instability remains fundamentally 1D, and the filamentation instability with wave vectors normal to the flow is weakly affected by QED corrections. It is worth noting that the unstable modes with oblique wave vectors respond differently to QED corrections.