Self-consistent nonstationary processes in phase-mixed electron beams focused by mobile ions

This paper is devoted to the analysis of nonstationary self-consistent processes in electron beam propagation in the presence of mobile ions. This problem is of particular interest for the recently developed plasma-assisted slow-wave oscillators (pasotrons). In pasotrons beam focusing is provided by ions (in contrast to other high-power microwave sources where the beam is focused by a strong external magnetic field). Typically, pasotrons operate in rather long pulses with a pulse duration on the order of 100 micros and larger. In such a time scale, the ion motion can play a significant role, and therefore, the self-consistent nonstationary processes in the beam transport and ion motion become important. In particular, the interaction with beam electrons may result in ion axial acceleration. In the present paper, a theory that describes these nonstationary self-consistent processes is developed, taking account of the phase mixing of electrons having a spread in their initial transverse velocities. The paper also contains some simulation results obtained for typical pasotron parameters.