Effects of electron beam velocity spread, temperature, and self-fields on dispersion relation and growth rate for a Cherenkov radiation

Cherenkov radiation can be generated by the propagation of a realistic electron beam through a dielectric loaded waveguide in which the phase velocity of electromagnetic radiation modes slows down to the velocity of electron beam. We study the effects of electron beam velocity spread, temperature, and self-fields on dispersion relation and growth rate in a Cherenkov radiation when an axial magnetic field is present. A generalized dispersion relation is derived and shown that in addition to cyclotron, free-electron laser (FEL), and beam modes there are two other modes which are induced by thermal velocity of electron beam. For cyclotron mode, the effects of electron beam self-fields on the growth rate are investigated and shown that the growth rate in the presence of self-fields has a maximum value which is considerably greater than the saturation value of growth rate in the absence of self-fields. The optimum value of axial magnetic field at which the maximum growth can take place is determined for different electron beam densities. Then the effects of electron beam velocity spread and temperature on growth rate are studied and it is found that the electron beam temperature causes an increment in growth rate, while the velocity spread of electron beam has an opposite effect. (authors)