Steady States of a Diode with Relativistic Electron and Positron Beams

The steady states of a diode in which electrons and positrons come from opposite electrodes with relativistic velocities have been studied. Such a situation may occur, e.g., in the plasma of pulsar diodes. Both the mode when charged particles reach the opposite electrode and the mode when a portion of particles is reflected by the potential barriers within the inter-electrode gap are considered. It is established that with a fixed potential difference between the electrodes, the solutions are determined by only three dimensionless parameters: the inter-electrode distance $$\delta $$ , the relativistic factor of the entering electrons $${{\gamma }_{0}}$$ , and the electric field strength at the left electrode $${{\varepsilon }_{0}}$$ . The whole variety of solutions is represented by a set of curves in $$\{ {{\varepsilon }_{0}},\delta \} $$ plane. It turned out that these curves qualitatively coincide with the branches of the solutions in the non-relativistic case. The relativistic factor effect on structure of the solution branches has been analysed.