Ion hose instability of an intense beam with a Bennett profile

A steady-state model has been formulated to describe the propagation of an intense relativistic electron beam into vacuum after passage through a localized plasma. A self-consistent relativistic Vlasov-based equilibrium, which leads to the Bennett radial density profile, has been found for the downstream electron-ion beam. The ion hose instability of this self-pinched beam is examined with emphasis placed on the equilibrium case in which the ions are cold, stationary, and provide total charge neutralization. Typical system parameters are V0 = 1 MV, I0 = 20 kA, Rb = 1 cm, Rw/Rb = 10, Te = 200 keV, β = Vb/C = .65. A simple description of the ion hose instability is given by the rigid beam model