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研究生:陳武城
研究生(外文):Wu-Cheng Chen
論文名稱:迴旋電子束在會切位形結構磁場的動力機制
論文名稱(外文):Dynamics of Gyrating Electron Beam in a Cusp-magnetic Field Configuration
指導教授:程光蛟
學位類別:碩士
校院名稱:國立臺灣海洋大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:61
中文關鍵詞:迴旋電子束會切位形磁場導波管
外文關鍵詞:gyrating electron beamCusp-magnetic Fieldcavity
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眾所皆知,由於高功率和高頻的微波被廣泛應用於毫米波雷達、通訊以及電漿加熱等,為此則發展出不同的微波元件。在眾多的微波元件中,較有效率的電子迴旋管已成為近代微波源較好的選擇之一。
由於在諧波模態操作的傳統磁旋管,能量轉換效率 很快的跌落,為此電子迴旋管採用磁場會切位形結構(cusp-magnetic field)及大軌道迴旋機制,此磁場的作用在使高能電子束迴旋,並與導波管靠近內壁之高次諧波產生能量共振交互作用,其最大優點是磁場大小與第N次諧波成反比,裝置尺寸相對的縮小,且迴旋電子能量與迴旋半徑成正比,於大軌道機制下提高了相對論效應使負質量不穩定現象增強,其將更有利於高頻微波的能量轉換與輻射。
本文從基礎之物理原理開始,藉由數值模擬來討論單一電子的動力機制,以瞭解電子空間上軌跡的變化。模擬方法為採用四階阮奇庫打法來處理圓柱座標系統下之電子動力方程式(描述速度及位置的六個一階微分方程組)。建立電腦數值模擬的模型後,改變各項環境初始條件並歸納分析之,將有助於實際系統的建立架設及設計最佳化之思考方向。
It is known that high power and high frequency microwaves have been widely applied to millimeter-wave radar, wireless communication and plasma heating and this in few a generates intensive research in developing the required microwave sources. In many microwave devices, electron cyclotron tube has became the choice for microwave source over the years.

However, because the energy conversion efficiency of the conventional gyrotron decreases rapidly at harmonic operation, so Gyrotrons utilizes the cusp-magnetic field and large-orbit axis-encircling motion. This kind of magnetic field turns the motion of high-energy axis-accelerating electron beams into an axis-encircling one and makes it closer to the wall of the wave guide for better energy resonance interaction with the high-order harmonic waves.

The advantages are a) the magnitude of magnetic field is inversely proportional to the N harmonic wave, b) size reduction of gyrotron, c) the energy of electron beams is directly proportional to the radius of the electron and d) enlarged moving path increases the relativistic effect to make the unstable effect of negative mass for better transition and radiation of high-frequency microwave.

On the basis of basic physical principles, the dynamic mechanism of a single electron was studied in this thesis to understand the changes of electron trajectories by numerical simulation. The Runge-Kutta method was used to resolve these dynamic equations (six first-order differential equations for describing velocity and position). Analyze by varying numerical simulation parameters (e.g., initial radius, transition width, magnetic field), some conclusions will be obviously to know.
中文摘要................................................I
英文摘要................................................II
符號說明................................................III
文字目錄................................................IV
圖表目錄............................................... VI

第一章 緒論..........................................1
1.1. 概述.................................... 1
1.2. 歷史沿革................................ 7
1.3. 研究動機與目的...................... .... 14

第二章 理論分析.....................................16
2.1. 電子迴旋運動之動力方程式.................. 16
2.1.1. 基本物理原理........................ 16
2.1.2. 電子迴旋管內之電場與磁場.............18
2.1.3. 圓柱座標系統表示式...................22
2.1.4. 圓柱座標系統下之電子動力方程式 ................................................24

第三章 模擬方法.....................................27
3.1. 方程式歸一化.............................. 27
3.2. 數值方法...................................30
3.2.1. 阮奇-庫打法(Runge-Kutta method)的簡介.30
3.2.2. Runge-Kutta法二階式與四階式..........31
3.2.3. 四階R-K法求解聯立方程組..............34
3.3. 電腦模擬流程...............................38

第四章 模擬結果.....................................40
4.1. 改變均勻靜磁場( )..........................40
4.2. 改變外部電壓...............................45
4.3. 改變轉移區寬度( )..........................49
4.4. 改變磁場擾量(α)...........................53

第五章 結論........................................57
參考文獻...............................................59
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