Electron‐hose instability of a relativistic electron beam in an ion‐focusing channel

A relativistic electron beam, propagating in an underdense ion‐focusing channel that is embedded within a broad region of underdense plasma, is shown to be subject to a hose instability due to coupling with plasma electrons at the edge of the pure‐ion region. The instability is studied by means of linearized analytic calculations of dispersion relations and asymptotic growth, numerical integrations of the linearized dynamical equations, and three‐dimensional particle simulations of the full nonlinear evolution. Three cases are considered: (1) If the plasma density n i0(r), prior to the introduction of the beam, is uniform, the instability is absolute, grows very rapidly, and does not saturate nonlinearly until the thrashing of the beam carries it into the quasineutral plasma region. Thus the instability prevents orderly beam propagation. (2) If n i0(r) consists of a central channel with constant density, surrounded by lower density plasma, the instability is again absolute, but with a reduced growth rate. Over a limited range, propagation without significant disturbance is possible. If the propagation range is long, the instability is stabilized by phase mixing when the beam leaves the channel. The beam then is recentered, with consequent emittance growth. (3) If n i0(r) consists of a central channel with a rounded density profile, surrounded by lower density plasma, the instability is convective in the beam frame. If parameters are chosen correctly, the instability does not significantly inhibit long range propagation.