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This article presents investigations on the design of coaxial gyrotron cavities with mode-converting corrugations, operating at the second harmonic of the electron cyclotron frequency with output power of the order of megawatts. The suppression of the competing modes interacting at the fundamental cyclotron frequency is achieved by the combination of a corrugated coaxial insert and mode-converting corrugation on the outer wall. The outer corrugation couples the key competing modes to lower order modes with reduced quality factor. The design steps, which form a generally applicable design procedure, are described in detail. As an illustrative example, the proposed procedure is used for the design of a cavity for a fusion-relevant, second-harmonic MW-class gyrotron, operating at 170 GHz with the TE   $_{\bm{37, 18}}$    mode. From the simulations, it is found that for the proposed design, this mode is excited with an output power of around/   $\sim$   1.5 MW. Two additional paths for cavity optimization toward even higher output power are also presented.

Design of MW-Class Coaxial Gyrotron Cavities With Mode-Converting Corrugation Operating at the Second Cyclotron Harmonic