磁旋管是一種基於考慮了弱相對論效應後所設計出的高功率同調波源元件。此元件藉由一外加磁場使電子作迴旋運動(Cyclotron motion)，並透過特定的設計和調控作用條件使電磁波與入射電子進行交互作用進而將電磁波放大。

前人曾做過研究認為使用TM模的磁旋管效率會遠小於使用TE模的磁旋管。但近期的研究發現，當使TM模的磁旋管作用在返波時的效率並沒有過去所認為的這麼差勁。主要原因是當作用在返波時，TM模擁有的軸方向的電場會使原本應該是互相競爭的兩種Bunching 機制(Azimuthal Bunching和Axial Bunching)變成互相合作關係，而使電子更容易和電磁波進行交互作用後減速並放出能量給電磁波。且經由數值模擬計算後也發現使用TM模的磁旋管確實也有不錯的效率。

在第二章會推導出TM模的色散關係，在進行數值分析前，藉由分析求得的方程式可發現和先前的研究一樣的事實即TM模的效率應當和波的行進方向有關，當作用在後退波條件時的效率會比作用在前進波時的效率還要好。

第三章則會將第二章求得的方程式做數值分析後與TE模做比較，並深入探討各項參數造成的影響。結果可發現TM模雖然不如過去所認為的這麼不堪，但和TE模相比還是稍微遜色。並且TM01模的效果又比TM11模來的更差一些，但這點也符合過去的研究結果。

People thought that gyrotrons was not good in TM-mode, but our lab recent studies found that TM-mode gyrotrons seemed to have possibility.

To proof this fact, I’m going to derive dispersion relation equation, since the dispersion relation equation is the one of important equations of describing electromagnetic wave system. In theoretic, if the dispersion relation have been derived, the property of the electromagnetic wave system can be known simultaneously.

In chapter 2, the dispersion relation equation would be derived, and there would have some simple discussion on the equation which the result is identical with previous studies.

In chapter 3, there would have the numerical analyze result, and would have deeper discussion about the system and physic and the result would identical with previous studies similarly.

Abstract 2
摘要 3
第一章 微波管歷史的簡介 8
1-1 微波的歷史發展 8
1-2 ECM以及Gyrotron(磁旋管)的簡介 9
1-3 Gyrotron(磁旋管)的種類 10
1.3.1 磁旋單腔振盪器(gyromonotron oscillator) 10
1.3.2 磁旋速調管(gyroklystron) 11
1.3.3 磁旋行波放大器(gyrotron travelling-wave amplifier) 11
1.3.4 磁旋返波振盪器(gyrotron backward-wave oscillator) 11
1.3.5 磁旋返波放大器(gyrotron backward-wave amplifier) 12
第二章 色散關係(Dispersion Relation) 13
2-1 研究目的 13
2-2 推導所需的方程式 14
2.2.1 場方程式 14
2.2.2 馬克斯威爾方程式(Maxwell’s equations) 15
2.2.3 relativistic Vlasov equation 16
2.2.4 小訊號假設(small signal assumption) 16
2-3 推導過程 17
2.3.1 Bessel function summation theorem 17
2.3.2 座標轉換 18
2.3.3 f1的推導結果 18
2.3.4 色散關係方程式(Dispersion relation equation)的推導 21
第三章 結果與討論 25
3-1 色散關係方程式隱含之物理意義探討 25
3.1.1 Beam-wave resonant condition 25
3.1.2 Coupling strength 25
3.1.3 波的行進方向造成的影響 25
3-2 與TE模的色散關係比較 26
3-3 磁旋行波放大器 29
3.3.1 TM11模 30
3.3.2 TM01模 32
3-4 磁旋返波放大器 36
3.4.1 TM11模 37
3.4.2 TM01模 39
3.4.3 TE01模 41
3-5 各項參數的影響 43
3-6 增益(gain) 48
第四章 結論 49
參考文獻 50

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