Steady states of relativistic electron-positron plasma diode

Steady states of a diode with relativistic electron and positron flows being supplied by opposite electrodes are considered. The particles move in the plasma without collisions. For a fixed potential difference between the electrodes, the solutions are characterized by three dimensionless parameters: the electric field strength at the left electrode $\varepsilon_0$, the interelectrode distance $\delta$, and the relativistic factor of emitted electrons $\gamma_0$. Branches of solutions are plotted in the $\{\varepsilon_0, \delta\}$-plane. They qualitatively coincide with those in the nonrelativistic case. As the relativistic factor increases, the branches shrink along the $\varepsilon_0$ axis and stretch along the $\delta$ axis.