Quantum electrodynamic effects on the two-stream instability

We consider the quantum electrodynamic corrections to the two-stream instability. We find these corrections vanish at first order unless a guiding magnetic field 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 , with , where α is the fine-structure constant and Bcr 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 and, actually, up to linear corrections in ξ.