Theory of solid state cyclotron maser

A theory is developed for the cyclotron maser interaction between an electron beam and the electromagnetic waves in a cavity formed with a semiconductor having nonparabolic energy bands. The interaction originates from the dependence of the effective mass of the electron (hence cyclotron frequency) on its velocity due to nonparabolic energy-momentum relation. This mechanism is very similar to that for the cyclotron maser radiation in vacuum tubes where the relativistic variation of mass with velocity is utilized. The linear response of the electron beam to the cavity fields are obtained from Vlasov equation and the Maxwell's equations while collisions are treated with an approximate model. Analytical expressions for the beam-wave coupling coefficient, beam energy loss and the threshold power are derived for the fundamental and higher cyclotron harmonics. The dependence of these quantities on the various parameters such as cavity length, beam position, beam energy, magnetic field, etc. are discussed.