Stability theory of a plasma diode with counter-streaming relativistic electron and positron flows

The basics of the stability theory have been developed for a plasma diode, in which flows of relativistic electrons and positrons come from opposite electrodes and move without collisions in a self-consistent electric field. The regime is studied when all particles reach opposite electrodes. As an example, the stability of steady states of such a diode is considered. An integrodifferential equation for the amplitude of the electric field perturbation is derived. For the case of a uniform stationary field, an analytical solution of this equation is found. Plasma dispersion and the effect of the relativistic factor γ0 on it are studied. It is shown that there is a threshold for the electron current density, above which the solutions become unstable, and an aperiodic instability develops in the plasma. The value of the inter-electrode distance corresponding to the threshold is equal to [γ0(γ0+1)]1/2πλD, where λD is the relativistic Debye–Hückel length. This coincides with the known result for the non-relativistic case at γ0→1.