Filamentation instability of self-focused hollow electron beam

A hollow electron beam has a finite beam thickness even for the beam electron distribution function in which all the electrons have the same canonical angular momentum. The thickness of the hollow electron beam with zero canonical angular momentum spread originates from the betatron oscillation amplitude of beam electrons. In this context, we investigate influence of the betatron oscillation on stability properties of the filamentation instability in a self-pinched hollow electron beam. It is shown that growth rate of the high azimuthal mode perturbations in body wave is substantially reduced by the amplitude of the betatron oscillation.