Slipping instability of an inhomogeneous relativistic electron beam

Abstract

The charged particle beams, such as electrons, ions, and plasma compression flow, have received considerable attention due to their applications in science and technology; therefore, studying the stability of these beams is of particular importance. Here, we examine theoretically the stability properties of a cold relativistic electron beam with a transverse velocity shear and non-uniform density profile. We consider a plane-parallel beam propagating along an external magnetic field and evaluate its macroscopic equilibrium state. We derive the dispersion relation of the slipping instability based on the linear electrodynamics of an inhomogeneous plasma and kinetic theory. In this model, the oscillation spectrum and the growth rate are derived by using the eikonal equation and the quasi-classical quantization rule. A linear velocity shear and a non-linear density gradient are assumed. Furthermore, we analyze numerically the dispersion relation of the slipping instability. The impacts of the inhomogeneity parameter and the relativistic factor on the properties of the slipping instability are discussed.