Coupling Instability of a Warm Relativistic Electron Beam with Ion-Channel Guiding

In this paper, the coupling instability of warm relativistic electron beam (WREB) propagating through the ion channel guiding is investigated in detail. Obtaining the equilibrium state of the system by considering the self-electric and azimuthal magnetic field, the fluid-Maxwell equations as well as linear perturbation theory are employed to derive the dispersion relation of the excited modes in the system. Numerical analysis of the obtained dispersion relation shows that the electromagnetic (EM) instability can be induced nearly the center of the beam through coupling between the fast electron plasma wave (FEPW), originated from the longitudinal oscillation of WREB, and fast forward electromagnetic wave (FFEW). In this sense, growing the perturbation amplitude occurs due to transport the kinetic energy of WREB to the EM wave at the specific frequency range, where the phase velocity of FEPW and FFEW is coincided. The results of the present investigation will greatly contribute to the understanding of the stability of the warm relativistic electron beam in laboratory experiments, such as in free electron laser experiments, where the ion-channel guiding is used to confine the electrons against the self-repulsive forces generated by the beam itself.