Wave growth rate in a cylindrical metal waveguide with ion-channel guiding of a relativistic electron beam

This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide. To derive the dispersion equations of the beam–wave interaction, it solves relativistic Lorentz equation and Maxwell's equations for appropriate boundary conditions. It has been found in this waveguide structure that the TM_0m modes are the rational operating modes of coupling between the electromagnetic modes and the betatron modes. The interaction of the dispersion curves of the electromagnetic TM_0m modes and the upper betatron modes is studied. The growth rates of the wave are obtained, and the effects of the beam radius, the beam energy, the plasma frequency, and the beam plasma frequency on the wave growth rate are numerically calculated and discussed.