Electron-hose instability in the ion-focused regime

A relativistic electron beam propagating through an ummagnetized, underdense plasma exhibits a transverse instability due to the coupling of the beam centroid to plasma electrons at the ``ion-channel'' edge. The transverse wake field corresponding to this ``electron-hose'' effect is calculated in the ``frozen-field'' approximation for a low-current, cylindrical beam in a radially infinite plasma. The asymptotic growth of beam-centroid oscillations is computed, and the growth length is found to be very rapid, indeed much less than the betatron period of the beam. Results for a radially finite plasma and for a slab beam are noted. Damping and saturation mechanisms are discussed.