Quantum electrodynamic effects on the two-stream instability

TL;DR

This paper investigates how quantum electrodynamic effects influence the two-stream instability, showing that these effects modify the instability's growth rate and wave vector, especially in the presence of a guiding magnetic field, within certain parameter ranges.

Contribution

It provides the first analysis of QED corrections to the two-stream instability, including magnetic field effects, extending classical results to quantum regimes.

Findings

QED corrections vanish at first order without magnetic field

Quantum effects reduce the growth rate and wave vector of the instability

Results are valid for small quantum parameter , up to linear order

Abstract

We consider the quantum electrodynamic corrections to the two-stream instability. We find these corrections vanish at first order unless a guiding magnetic field $\mathbf{B}_0$ is considered. With respect to the classical version of the instability, quantum electrodynamic effects reduce the most unstable wave vector and its growth rate by a factor $\sqrt{1+\xi}$, with $\xi = \frac{\alpha}{9\pi} (B_0/B_{cr})^2$, where $\alpha$ is the fine-structure constant and $B_{cr}$ the Schwinger critical magnetic field. Although derived for a cold system, these results are valid for the kinetic case. The results are valid in the range $\xi \ll 1$ and, actually, up to linear corrections in $\xi$.