Third harmonic working based on the Smith–Purcell radiation in a closed structure

Smith–Purcell radiation is well analyzed in an open structure; however, it is seldom studied in a closed structure. In a high order mode resonant system, the harmonics of the spoof surface plasmon in the subwavelength hole array will be transformed into Smith–Purcell radiation and the radiation energy will be embedded in a high order mode of this resonant system. The spoof surface plasmon and the high order mode have the same field distribution in the beam channel by a special design, and then, the electron beam will interact with them simultaneously. Based on the phenomenon and mechanism, an effective method that works on the higher order harmonic is proposed. It is possible to mitigate the frequency limits as well as the start current limits in vacuum electronic devices, and the mode competition issue is also improved because of the frequency-locked characteristic.