Stability of magnetically insulated electron flow

Abstract

The stability of magnetically insulated electron flow is studied for wavelengths longer than gyrolengths and frequencies lower than gyrofrequencies. This is done by using a general theory that allows for a distribution of electrons of different canonical momentum and total energy. The stability theory leads to a set of integro-differential equations for the eigenfunctions of the potentials. The integral portion of the equations relates positions across the flow that are connected by the finite size of the electron orbits. A general stability criterion is found. The stability of the flow is determined by the distribution of the electrons in canonical-momentum–total-energy space. The criterion can be stated roughly as depending upon whether the distribution function increases or decreases with drift velocity. If it increases, the flow is unstable.