• H. Fares, Y. Kuwamura, M. Yamada
  Kanazawa University, Kanazawa

In the Cherenkov free electron laser, the interacted electron with the electromagnetic (EM) wave can be represented as a point particle or as a spatially spreading electron wave in the classical or quantum mechanical framework, respectively. In our previous theoretical analysis for the optical region, the electron is described by a plane wave with finite spreading length. This electron wave model was successfully implied for the optical region whereas the spreading length of the electron wave is greater than the wavelength of the optical wave. In this work, when the EM wavelength is sufficiently greater than the spreading length of the electron wave, such as in the microwave region, the electron is assumed to be a spatially localized point particle. This classical analysis is performed using same parameters used in the quantum electron wave model, such as a coupling coefficient between the electron beam and the EM field and the electron relaxation time. Also, we present analytical expressions to describe the stimulated and spontaneous emissions. We show that the classical treatment is consistent with the quantum analysis applied in the optical regime.