Space Charge Waves in a Cylindrical Waveguide with Arbitrary Wall Impedance

摘要

Properties of the space charge waves in a solid relativistic electron beam propagating in a cylindrical waveguide is 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 the axial momentum spread on the 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 appropriate choice of dielectric constant epsilon and thickness of the dielectric material, it is shown that a strong mode coupling occurs, exhibiting the growth rate of instability comparable to the beam plasma frequency. The physical mechanism of instability is the Cherenkov radiation. (Author)