Electron diffusion and leakage currents in magnetically insulated diodes

The diffusion of stochastic electrons and the associated leakage current is investigated for magnetically insulated diodes and gaps. The model system is planar and periodic in the drift direction of the electrons. The stochasticity results from periodic perturbations of nonrelativistic, constant-density equilibria. When the perturbation is sufficiently large to generate a globally stochastic region containing the electron source, a leakage current is established. The steady-state Fokker–Planck equation is solved using quasilinear diffusion coefficients. The resulting distribution is normalized to the globally stochastic fraction of the equilibrium electrons to obtain the leakage current. For realistic perturbations, the analysis yields leakage current values that are in good agreement with earlier experimental results. A ‘‘supercritical’’ insulating field, which is a function of the perturbation parameters, is calculated.