Quantum electrodynamic effects on the two-stream instability

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 $\xi$.

5 pages 2 figures, to appear in EuroPhysics Letters

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