Dispersion relation and growth rate in a Cherenkov free electron laser: Finite axial magnetic field

A theoretical analysis is presented for dispersion relation and growth rate in a Cherenkov free electron laser with finite axial magnetic field. It is shown that the growth rate and the resonance frequency of Cherenkov free electron laser increase with increasing axial magnetic field for low axial magnetic fields, while for high axial magnetic fields, they go to a saturation value. The growth rate and resonance frequency saturation values are exactly the same as those for infinite axial magnetic field approximation. The effects of electron beam self-fields on growth rate are investigated, and it is shown that the growth rate decreases in the presence of self-fields. It is found that there is an optimum value for electron beam density and Lorentz relativistic factor at which the maximum growth rate can take place. Also, the effects of velocity spread of electron beam are studied and it is found that the growth rate decreases due to the electron velocity spread.