Effect of a dc electric field on the trapping dynamics of a cold electron beam

Abstract

The self-consistent modification of the trapping dynamics of a low density cold electron beam due to the external application of a dc electric field is considered. For dc fields smaller than the peak amplitude of the saturated beam-plasma instability, the beam energy remains clamped while the wave amplitude grows secularly. Large traveling potential wells appear and create strongly focused charge clumps. By considering the role of wave dissipation, an exact dynamic Bernstein–Greene–Kruskal equilibrium is found analytically. It consists of a singular charge clump which propagates through the medium at constant velocity even though a dc field is present. The numerical study of the basic equations shows that the system evolves asymptotically to this singular state. A variety of experimentally relevant properties associated with the trapping dynamics is investigated, including the stability of the dynamic nonlinear equilibrium to sideband growth.