磁旋管是一種建立在利用弱相對論效應的機制”電子迴旋脈射(ECM)”下所設計出的高功率同調電磁波源，利用外加磁場使得電子迴旋運動，經由系統性的調控，電子能與電磁波達成同步並交換能量，進而放大電磁波。

磁旋返波震盪器理論首見於蘇俄1960年代中期的文獻[4] ，前人曾研究利用非線性理論預期磁旋返波震盪器(gyro-BWO)之效率將會低於其他形式之磁旋管[1]，也認為TE模之效率會比TM模還來得高[3-4]，隨著可調頻元件需求的增加，能藉著調變磁場和電壓來調頻的磁旋反波振盪器漸漸抬頭，而近期有研究指出TM模適合被使用在這種反波元件上[6] ，而在本實驗室前期的研究指出，在線性的區間會使系統操作在後退波並且使其傳播常數更大的話，的確會使效率更好。

在第三章會談到如何使用物理的角度來解釋前人的結果，並且嘗試我們在線性理論模型所推測的提升效率之方法，而第四章是推導非線性且自洽的方程式，使的這樣的物理推測可以推廣到非線性的區間，並且進行模擬看看其操作在非線性區間會有怎麼樣的結果，最後我們可以想的到這樣的結果可以開創出一條新的道路，使其與TE mode有不同的操作條件，甚至可以使TM mode效率凌駕在TE mode之上。

The transverse magnetic (TM) modes have long been considered as the unsuitable waveguide modes for the operation of the electron cyclotron maser (ECM). This study investigates the linear behavior of the TM modes and reveals for the first time that certain TM modes might be suitable for gyrotrons --- ECM based devices. In addition, non-linear but non-self-consistent model shows that for a fixed field profile the efficiency could be as high as the transverse electric (TE) modes. Such interesting findings deserve more theoretical and experimental studies, and might facilitate some applications.

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