這幾年出現的高功率、高頻率微波是一種新的微波技術，而且其應用範圍很廣，如:核融合中迴旋共振加熱電漿，基本物理的粒子加速研究以及高功率雷達等等。
而且我們知道高頻率電子迴旋加速器操作在基本模態時，需要較高的磁場，但是當操作在高次諧波時，其所需要的磁場反而與諧波數成反比，但是能量轉換效率會很快的降低，所以已有很多努力在改進操作在高次諧波時的效率。而其中有一種想法就是利用邊界為週期性的結構，以加強高階模態的諧波成份，並且達到更佳的操作效率，進而改善迴旋電子與高次諧波模態的交互作用。
本篇論文中，討論在N個槽的多葉片直圓柱導波管結構的大軌道電子層與波場的共振交互作用，而且希望能有較高的輸出頻率，所以我們只模擬操作在2π TE或TM模態下。數值分析我們是利用導出的公式解出被單一模態激發波之歸一化電場值的暫態非線性解，而求得能量轉換效率，因此由求得的能量轉換效率，我們可以比較出操作在TE或TM模態時，它的轉換效率何者為佳。

The high power high frequency microwave has emerged over the years as a new technology. The high power high frequency source has a wide range of application, such as cyclotron resonance heating plasma for fusion reactor, particle acceleration for basic research, and high power radar etc.
It is generally known that high frequency gyrotron requires high magnetic fields when they are operated at the fundamental mode. However, when they are operated at high harmonic, the magnetic field can then be reduced in inverse proportion to the number of the harmonic.However the energy conversion efficiency of high harmonic modes operation decreases rapidly. Therefore, a great deal of effort has been directed in improving the efficiency of high harmonic modes operation. One consideration of such effort is to utilize periodic structure at the boundary which will enhance the harmonic content of the higher order modes, thereby improving the interaction between the gyrating electrons and higher harmonic modes, leading to a better operational efficiency.
In this work, the discussion is on resonant interaction between a large orbit electron layer with the wave fields of an N-slotted multivane cylindrical waveguide structure. The numerical simulation is on TE or TM-2π modes because of its high output frequency.Equations describing the temporal evolution of the wave fields are being derived .The nonlinear coupled equations are solve numerically and the energy conversion efficiency can be evaluated. A comparison between the TE and TM modes show that TE-mode is always having a much better conversion efficiency than the TM- mode operation.

第一章:緒論 1
(1-1)簡介................................................ 1
(1-2)研究動機............................................ 3
第二章:理論分析 6
(2-1)簡介................................................ 6
(2-2)群聚現象............................................ 6
(2-3)負有效質量之物理意義................................ 7
(2-4)散射關係式與能量公式................................ 7
(2-5)電子與波場的共振交互作用............................ 9
(i)TM模態.......................................... 10
(ii)TE模態........................................... 13
(2-6)η的定義........................................... 16
第三章:電腦模擬方法 18
(3-1)簡介............................................... 18
(3-2)電子運動在空間模型的架構分析....................... 18
(3-3)基本假設........................................... 18
(3-4)電腦模擬方法與步驟................................. 20
(3-5)η值的計算.......................................... 23
第四章:結果討論 60
(4-1)簡介.............................................. 60
(4-2)討論.............................................. 60
第五章:結論 62
附錄A 64
附錄B 68
參考書目 72

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