Space-charge and thermal effects in relativistic crossed-field devices

Abstract

In this paper, a fully kinetic theory for the relativistic electron flow in a crossed-field device is developed and analyzed. The theory takes into account self-electric, self-magnetic, and thermal effects and allows determining the final stationary state achieved by the electrons in phase-space. A number of different possible stationary modes are identified and described in detail. Particular attention is given to the study of how space charge and thermal effects affect the magnetic insulation when the external magnetic field exceeds the Hull cutoff field. In the nonrelativistic limit, it is found that there is only a single mode transition that leads to the loss of the magnetic insulation. This transition is completely independent of the electron density and occurs for relatively large injection temperatures. On the other hand, in a moderate relativistic regime a much richer scenario is found with the onset of a series of stationary state mode transitions as both electron density and injection temperature are varied. In particular, it is found that the transitions and the consequent loss of magnetic insulation may occur even at very low injection temperatures. Self-consistent numerical simulation results are also presented and used to verify the theoretical findings.