Axisymmetric electron flows investigated on the basis of exact solutions to the equation of a nonrelativistic nonstationary beam

Abstract

Variants describing axisymmetric flows are revealed among known invariant solutions to the equations of a nonstationary beam. Two new stationary solutions expressed in terms of elementary functions are obtained. A number of oscillation regimes are analyzed qualitatively. The exterior problem for a previously unknown flow is solved, and the field outside a beam is calculated for two nonstationary flows with stationary current tubes.