Abstract
A photonic crystal cavity of the transverse electric (TE) mode is designed to support the third harmonic interaction with a 30 keV–0.7 A axis-encircling electron beam at the operating frequency of the Ka-band, where a magnetic field of 0.38 T is used. The lattice parameters of a square lattice of alumina rods are determined to fit the TE301-like mode in the photonic-band-gap spectral region, and the output signal of a fundamental waveguide mode is conveniently coupled to a conventional waveguide. A particle-in-cell code simulation predicts the single mode operation with the output power of concerning 2.9 kW, corresponding with an efficiency rating of 14%. This scheme can be extended to a n-th harmonic gyrotron using the rectangular cavity of a TEm01-like mode.