Abstract
A mathematical model of a high-current electron beam with a compensated charge is developed. The effect of the 3D axially symmetric magnetic field induced by the beam current is taken into account. The model is based on the method of current tubes, which makes it possible to calculate electron trajectories in the presence of an external axially symmetric magnetic field. It is demonstrated that, in the presence of an external axially symmetric magnetic field, the beam rotates around its axis and the azimuthal current is induced. The shapes of electron trajectories are strongly affected by the magnetic field of the azimuthal current. The electron trajectories are calculated for various beam currents and external magnetic fields. It is shown that a significant nonlinearity leads to crossing of the trajectories of the initially laminar beam, sheath formation after passing the crossover, and collisionless thermalization of the beam. The boundary of the region inside which the beam can stably overcome the first crossover is determined.
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