Resistive hose instability of a beam with the Bennett profile

The resistive hose instability of a self-pinched relativistic beam is examined with emphasis placed on the important case of the Bennett current profile J_B(r) ∝ (1+r²/a²)^-2. Previously known results applicable to a general profile are recovered and extended in several directions. An essential new feature in this study is the use of distributed particle mass to model orbital phase-mixing effects produced by the anharmonic pinch field. Resonant growth is considerably reduced, and the instability when viewed in the beam reference frame is shown to be convective rather than absolute. The peak amplitude of a disturbance wave packet moves from the point of its inception in the beam pulse toward the pulse tail. The disturbance subsequently damps if the pulse length is finite; thus, propagation over distances that are long compared with the particle betatron wavelength is possible. The predicted growth rate and group velocity of the mode are shown to be in fair agreement with the results of numerical simulation.