磁旋振盪器是利用電子迴旋脈射機制(electron cyclotron maser)產生同調電磁波，具有高功率、可連續調頻與寬頻寬的特性，在整個毫米及次毫米波源之研究或應用佔有相當重要的地位與發展潛力。在過去的研究中，大多認為TE模態的效率會高於TM模態磁旋管，因TM模態的縱向電場造成群聚機制的複雜，但在實驗室前期的研究中，分析了TM模態的縱向電場造成不同的群聚機制，結果顯示系統在後退波時會比前進波有更好的表現。
　第二章會介紹計算TM模態所需要使用的非線性理論計算公式，分析電子與電磁場交互作用的微分方程式；第三章則是利用非線性理論進行模擬，觀察不同結構的非線性理論行為。
　本論文以TM11模態進行非線性理論模擬，並比較在不同的結構下進行比較，試著找出好的能量轉換效率或是更廣的可調頻率。目前的結果，能量轉換效率約為38%，而可調頻率範圍可達約6 GHz。

The transverse magnetic (TM) mode has been considered as the unsuitable waveguide mode for the operation of the gyrotron for a long time. Because of TM mode’s bunching mechanism is more complicate than TE mode. But in early research shows that TM mode is good for backward-wave operation. Unlike the TE modes, the TM modes has z-component of the electric field and it cause backward-wave interaction the azimuthal bunching and axial bunching will have the same bunching point. From this bunching mechanism, this study use TM11 mode and different structure to simulate energy translation efficiency between electrons and electromagnetic wave. For tapered structure, energy translation efficiency is 38% and tunable frequency bandwidth about 6 GHz at velocity ratio of 2.

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