Azimuthal instability of radiation in gyrotrons with overmoded resonators

Stability of efficient operation at one of the high-order modes is of great importance for the development of megawatt-level gyrotrons intended for plasma experiments in controlled fusion reactors. Typically such gyrotrons operate at modes with large azimuthal indices, which form a rather dense spectrum of eigenfrequencies. Therefore, instead of considering interaction of electrons with a large number of such modes it is more convenient to analyze the spatial-temporal evolution of an envelope formed by a superposition of these modes with the electrons. In all previous studies of stability of such envelopes it was assumed that some kind of azimuthal nonuniformity is present in the initial condition for the wave envelope. However, the physical reason for this nonuniformity, which is apparently the nonuniformity of the electron emission, was not analyzed. In the present paper, the relation between the emission nonuniformity and resulting nonuniformity of the wave envelope is established. Then, results of numerical simulations are given, which demonstrate various changes in the gyrotron dynamics caused by the azimuthal instability of the wave envelope. These results allow one to determine the maximum azimuthal index of the operating mode and show that this maximum index can depend on the degree of azimuthal nonuniformity of the electron emission.