Study on the dispersion relations of a relativistic annular electron beam guided by a finite axial magnetic field

Abstract

The relativistic annular electron beam guided by a finite axial magnetic field is studied in this paper, in which the electron beam is considered as a special media. Making use of the constitutive transformation and the Lorentz transformation in the four-dimensional space, the permittivity tensor of the stationary magnetized plasma, the permittivity tensor, the permeability tensor and the chiral tensor of the electron beam in the rest (laboratory) frame are acquired. And the boundary conditions, including the surface current density due to the ripple of the beam, have been obtained. As an example of the applications of this approach, the dispersion relations of a relativistic annular electron beam guided by a finite axial magnetic field in a waveguide has been studied. The results of numerical calculation show that the present approach is more accurate and can provide clearer mode information for the electron beam. In addition, the results also show the axial magnetic field can affect the dispersion curves of space charge wave via the surface current density of an electron beam. Thus this approach can be exploited in a number of electron beam-wave interaction systems, including some kinds of free electron devices, plasma filled Cherenkov radiated free electron lasers and masers.