To provide the required mode selectivity for a megawatt 280 Ghz gyrotron, a coaxial resonator operating in a high order TE mode is considered. Mode discrimination is achieved both by exploring the differences in the transverse structures of the competing modes and investigating a suitable geometry for the coaxial insert. In the resonator studied here, the frequency separation between the design mode TE20,12,1 is about 0,6% and the ratio of the corresponding Q factors is as high as 6,5. Unlike the coaxial resonator, in the hollow cavity without the inner conductor the fundamental spectrum of eigenfrequencies is more dense, and all TE modes within the frequency interval 271-288 GHz have approximately the same Q factor.
