Stability of gyrotron operation in very high-order modes

Future controlled fusion reactors require the development of MW-class gyrotrons at higher frequencies. To withstand the ohmic heating in the resonator walls, such gyrotrons should operate in higher order modes than the present-day tubes. This is why the analysis of stability of operation in such modes is of vital importance for future gyrotrons. In this paper, the stability of gyrotron operation is analyzed by using two methods: the representation of the resonator field as an azimuthally rotating nonstationary wave envelope, which can slowly vary in time and along azimuthal and axial coordinates, and as a superposition of eigenmodes whose non-stationary fields have self-consistent axial profiles of the fields. The theory is illustrated by two examples of European 170 GHz gyrotrons developed for ITER.