Current reflux from an electron beam transmitted in a plasma ion channel

In this paper, the mechanism by which current reflux forms from a plasma-focused electron beam is studied theoretically and numerically by considering nonlinear interactions between the beam and plasma. We demonstrate that a moving virtual cathode can be generated at the end of a plasma ion channel due to the influence of the boundary plasma electrons on the beam, and that this accounts for reflux formation. In addition, the reflux formation condition is derived and analyzed via the beam envelope and space-charge-limited current theories. The results indicate that the virtual cathode tends to form at defocusing positions of the beam. Particle-in-cell simulations are used to verify the theoretical results and to show that the beam divergence and energy spread increase during current reflux formation.