Stability analysis of sheared non-neutral relativistic cylindrical electron beams in applied magnetic fields

A self-consistent stability analysis of relativistic non-neutral cylindrical electron flows propagating along applied magnetic fields is considered within the framework of the macroscopic cold-fluid-Maxwell equations. The full influence of the equilibrium self-electric and self-magnetic fields is retained. Then the E × B drift (E being the radial electric field created by the uncompensated charge) generates a radial shear, vz(r) and vθ(r). The effect of the shear in the axial velocity component, as reflected in the relative axial motion of adjacent concentric layers of beam particles, is investigated. The self-consistent treatment of the problem thus shows that the equilibrium state considered in this paper is unstable.