Asymptotic and nonlinear evolution of the electron-hose instability of a REB propagating in the ion-focused regime

If a relativistic electron beam is propagated in an ion-focused regime (IFR) channel which is surrounded by a broad region of lower density plasma, a hose instability can occur, due to interaction between the beam and plasma electrons far outside the beam. We have calculated linearized dispersion relations and asymptotic growth, and performed particle simulations which reveal the nonlinear behavior. Three cases are considered: (1) Beam in a broad uniform underdense plasma (no localized channel). The instability is absolute, rapidly growing, and in typical cases of interest is not stabilized nonlinearly until the beam is disrupted. (2) Beam in a flat-topped channel of density nc, surrounded by uniform plasma at lower density np. The instability is absolute, but the growth rate is reduced. Stabilization due to phase mixing occurs when the beam leaves the channel. (3) Beam in a rounded channel of density nc(r), surrounded by uniform plasma. The instability is convettive, and the growth rate is small by order np/nc(0).