中文摘要：

定义了光子带隙谐振腔（photonic-band-gap cavity,PBGC）的等效半径,论证了使用该半径将PBGC等效为具有模式选择性的金属圆柱谐振腔的有效性,揭示了其在PBGC设计过程中的指导性作用.基于等效半径的运用,建立起光子带隙谐振腔回旋管振荡器（PBG回旋管）的自洽非线性理论,并对工作于TE32模的PBG回旋管作了理论分析和数值计算.目前的研究表明：高频电磁场沿角向呈行波或驻波的不同极化形式对PBG回旋管的注-波互作用过程具有较大的影响;较之电子回旋基波,该器件中二次谐波与TE-32模式波的互作用效率更高,提示由于PBGC优秀的选模能力,可望实现回旋管中高阶横向电磁模与高次电子回旋谐波的有效耦合,为相关研究提供了新的线索.

英文摘要：

The effective radius of photonic-band-gap cavity （PBGC） is defined,the validity of using it to treat PBGC as a mode selective cylindrical metal cavity is demonstrated,the guiding role of it in the design of PBGC is revealed,and a self-consistent nonlinear theory is established for gyrotron oscillator with PBGC （ PBG gyrotron） based on it. The results of theoretical analysis and numerical calculation show that the azimuthal polarized form （traveling wave or standing wave） of RF field has an obvious effect on the beam-wave interacting process and the device operating at second harmonic can achieve higher electron efficiency than that working at fundamental wave under TE-32 mode,which means PBG gyrotron is capable of operating at both high order electromagnetic mode and high order electronic cyclotron harmonic effectively owing to the excellent mode selective ability of PBGC. This gives a new clue to the research of gyrotron oscillator.