Stability of charged beam propagation through a relativistic hollow electron beam

Stability properties of a charged beam propagation through a relativistic hollow electron beam are investigated, in connection with present experimental applications in the collective particle accelerator. The stability analysis is carried out for long axial wavelength and low-frequency perturbations. A closed algebraic dispersion relation for coupled transverse oscillations is obtained for the solid and hollow beams with sharp-boundary density profiles. One of the most important features in the analysis is that the typical growth rate of the transverse oscillation is order of the hollow beam diocotron frequency, thereby severely limiting the solid beam propagation through a relativistic hollow electron beam. However, for a solid beam with a small radius, the fundamental mode perturbation (i.e., the dipole oscillation) is the most unstable mode.