Spectral power density extrema for microwave emission from a relativistic reflex triode

Spectral power density extrema are investigated for variable frequency and fixed beam radius, for variable beam radius and fixed frequency, and for both variable frequency and beam radius in the one-dimensional sheet model of the relativistic reflex triode. Approximate and exact formulations are given. A simple example is presented wherein the power spectrum exhibits gross features of the real situation. The extrema are seen to be closely related to the zeros of Bessel functions of the first kind or to zeros of equations involving both these Bessel functions and the Fourier-transformed current.