Abstract
A linear, fully relativistic and electromagnetic analysis of waves perturbing the Brillouin flow state on planar, magnetically insulated gaps is presented. Three independent classes of waves are treated individually; transverse-magnetic waves propagating normal to the insulating magnetic field, transverse-electric waves propagating in the same direction, and a set of waves propagating along the magnetic field. Dispersion relations governing discrete modes of oscillation for each class are found and solved for some cases of interest. Only the transverse-magnetic waves are found to be unstable due to the existence of a Doppler-shifted plasma reasonance layer at frequencies above the plasma frequency. The scaling of the growth rate for this instability with respect to parameters characterizing the equilibrium state is examined. In addition to these discrete modes, spectral continua associated with localized resonance phenomena in the electron sheath bounding the cathode are described and explained.
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