磁旋管是一種建立在電子迴旋脈射(electron cyclotron maser)機制下從入射電子中提取能量的高功率同調電磁波源，利用外加磁場使電子做迴旋運動並藉由腔體設計使電子與電磁波同步進而提取能量。

由於TM模態的軸向電場會導致群聚機制變得複雜，因此早期的研究普遍認為TM模態的效率會低於TE模態，但近期的研究發現TM模態操作在後退波的條件下，軸向電場會使電子的軸向角群聚(Axial bunching)與方位角群聚(Azimuthal bunching)由競爭關係轉為合作關係，因此TM模態出乎意料的在後退波的條件下反而擁有良好的群聚效應，為了對TM模態反波振盪器做進一步的研究，模式競爭就是一個不得不面對的問題，為了解決模式競爭的問題，後面會用幾種不同的方式來分析TM模態的起振電流。

第二章會介紹目前實驗室所使用的非線性理論模擬，藉由降低電流觀察效率的變化，以紀錄振盪發生所需的最低電流，接著會介紹兩種線性理論的推導，第三章是利用Laplace transform計算均勻結構中能存在的四種不同的波，並得到電磁波在波導管內的場形，藉此尋找作用長度與起振電流之間的關係，第四章則會推導電磁波沿波導管方向變化的微分方程，用以計算非均勻結構的起振電流。

The transverse magnetic (TM) modes have been considered as the unsuitable waveguide modes for gyrotron. Recent scientific evidence seems to indicate that TM modes might be suitable for gyrotron backward-wave oscillator because Axial bunching and Azimuthal bunching will cooperate for gyrotron backward-wave oscillator. For solve the mode competition problem, this study use two method to calculate starting current. Finally, we use the equation that we derive in this paper to simulate the starting current and compare the different between two method.

目錄
摘要 1
Abstract 2
第一章 緒論 4
1-1微波的歷史發展 4
1-2磁旋管種類 5
1-3電子迴旋脈射(ECM)原理 7
第二章 TM模態Bunching機制 8
第三章 非線性自洽理論 11
3-1 TM模態場方程式 11
3-2電子動力學 14
3-3模式競爭 17
第四章 線性理論 18
4-1 Laplace transform 18
4-2 Numerical Method 32
第五章 模擬與分析 36
第六章 結論 44
參考文獻 45

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