Electron flow stability in magnetically insulated vacuum transmission lines

We evaluate the stability of electron current flow in high-power magnetically insulated transmission lines (MITLs). A detailed model of electron flow in cross-field gaps yields a dispersion relation for electromagnetic (EM) transverse magnetic waves [R. C. Davidson et al., Phys. Fluids 27, 2332 (1984)] which is solved numerically to obtain growth rates for unstable modes in various sheath profiles. These results are compared with two-dimensional (2D) EM particle-in-cell (PIC) simulations of electron flow in high-power MITLs. We find that the macroscopic properties (charge and current densities and self-fields) of the equilibrium profiles observed in the simulations are well represented by the laminar-flow model of Davidson et al. Idealized simulations of sheared flow in electron sheaths yield growth rates for both long (diocotron) and short (magnetron) wavelength instabilities that are in good agreement with the dispersion analysis. We conclude that electron sheaths that evolve self-consistently from space-charged-limited emission of electrons from the cathode in well-resolved 2D EM PIC simulations form stable profiles.