Resistive wall effect on the stability of planar relativistic Brillouin flow

Previous treatments of relativistic Brillouin flow stability are extended to the case of nonzero anode resistivity, for the case of wave propagation across the equilibrium magnetic field. It is found that transverse magnetic (TM) waves are unstable at frequencies below the equilibrium cyclotron frequency, unlike the case for a perfectly conducting anode. Transverse electric (TE) waves, always oscillatory in the case of a perfectly conducting anode, are damped; an explicit expression for the damping rate, valid for large conductivities, is given.