Quasilinear theory of mode interaction in gyrotrons with azimuthally inhomogeneous electron emission

A theory is developed which describes the effect of the azimuthal inhomogen eity of the electron current on the gyrotron operation. The theory is simpl ified by using a quasilinear approach, which allows one to study analytical ly the stability of oscillations in free-running and phase-locked gyrotron oscillators with inhomogeneous current emission. Also the numerical analysi s of nonstationary processes in a three-mode gyrotron oscillator is carried out. The results show that, at low currents, the inhomogeneity may cause e xcitation of additional modes at the frequency of the operating one. At hig her currents, one can observe the onset of phase-locked triplets with equid istant frequency spectrum. As the inhomogeneity increases, this enhances th e beating effects in such triplets, e.g., the mode amplitudes exhibit some oscillations whose period is inversely proportional to their frequency sepa ration and whose modulation increases with the inhomogeneity in the beam cu rrent. (C) 2001 American Institute of Physics.