Stability of magnetically insulated electron flow

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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.