Space charge waves in a cylindrical waveguide with arbitrary wall impedance

Abstract

Properties of the space charge waves in a solid relativistic electron beam propagating in a cylindrical waveguide are investigated, including the important influence of arbitrary wall impedance. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations. In order to examine the influence of axial momentum spread on stability behavior, it is assumed that all electrons have a Lorentzian distribution in the axial canonical momentum. One of the most important features of the analysis is that, for short axial wavelength perturbations, the eigenfunction can be described by a Bessel function. Moreover, the condition for zero phase velocity of the space charge wave is also obtained, in connection with collective ion acceleration. Space charge wave properties for a dielectric loaded waveguide are also investigated. For the appropriate choice of the dielectric constant ε and thickness of the dielectric material, it is shown that strong mode-coupling occurs, exhibiting the growth rate of instability comparable to the beam plasma frequency. The physical mechanism of instability is Cerenkov radiation.