Stability of relativistic laminar flow equilibria for electrons drifting in crossed fields

Abstract

The stability of the electron flow in magnetically insulated transmission lines and diodes, and in microwave devices is an important issue. Presented in this paper are the results of an electromagnetic, linear stability analysis of transverse magnetic waves propagating along the direction of electron drift in a planar system described by a relativistic laminar flow equilibrium. In general, this equilibrium features cold electrons executing E×B drifts in self-consistently calculated electromagnetic fields. For this paper, a class of laminar flow equilibria in which the relativistic plasma and cyclotron frequencies are multiples of one another was chosen, and the electrons were taken to be confined to a layer placed in a vacuum gap between two conductors. This configuration is driven unstable by two separate mechanisms which tap the free energy associated with the sheared velocity field of the layer. At long wavelengths, the interaction of positive and negative energy surface waves results in the diocotron instability. At shorter wavelengths, the interaction of surface waves and sheets of electrons resonant at the local Doppler-shifted cyclotron frequencies leads to a pair of unstable branches of the dispersion relation which are referred to collectively as the magnetron instability. The scaling of the growth rates with equilibrium parameters and the relative importance of the two instabilities are discussed.