𝑇𝑀11 模式陀螺管的波束效率是通過向下錐形徑向剖面實現的幾何調諧來優化向更高波束效率方向，主要是通過實現交互結構的幾何調諧。幾何調諧涉及調諧半徑𝑟𝑤和交互長度𝐿tot，這與調諧波束參數如偏置因子α和波束電流𝐼𝑏的調諧相結合。研究的主要焦點是兩種結構：I. 在第二階軸向模式(2nd OAM)中具有高效率𝜂𝑏>50%的單錐形交互結構；以及 II. 具有高波束效率𝜂𝑏>50%的雙錐形交互結構，其中僅激發基本軸向模式(FAM)。這是通過交互結構的幾何調諧，然後調諧波束參數實現的。錐度是基於以往關於TE模式陀螺管優化的知識的方法。結果表明，幾何調諧不僅有助於提高波束效率，而且還通過增加其起振電流SOC來幫助減輕HOAMs的競爭。這導致抑制了它們的振蕩，從而消除了由它們的激發可能引起的潛在競爭。此外，還分析了結構的長度和半徑剖面等幾何參數之間的關係，以及通過色散關係和耦合強度圖繪製的不同腔模和諧波模式引起的競爭。該研究旨在提供關於𝑇𝑀11模式陀螺管優化的見解，並提出朝著高波束效率方向的簡單指南。目的還在於將該研究提供的結果與當前TE模式陀螺管的實現進行比較，以及在設計TM-模式陀螺管時將其用作未來參考。最終目的是提供一些關於通過幾何調諧抑制HOAMs以及在設計TM-模式陀螺管時可能需要考慮的約束的見解。

The beam efficiency of the TM11-mode gyrotron is optimized towards a higher beam efficiency, mainly through implementation of geometrical tuning by a down-tapered radial profile for the interaction structure. The geometrical tuning involves the tuning of the radius 𝑟𝑤 and the interaction length 𝐿tot, this is in conjunction to the tuning of the beam parameters such as the pitch factor 𝛼, and the beam current 𝐼𝑏. There are two structures which will be the main focus of the study: I. Single tapered interaction structure with high efficiency 𝜂𝑏>50% in the 2nd Order Axial Mode (2nd OAM), and II. Double tapered interaction structure with a high beam efficiency 𝜂𝑏>50% in which only the Fundamental Axial Mode (FAM) is excited. This is achieved through the geometrical tuning of the interaction structure followed by the tuning of the beam parameters. The taper is taken as an approach based on previous knowledge on the optimization of TE-mode gyrotrons. Results show that the geometrical tuning does not only aid in the beam efficiency enhancement, but also provides an aid in the mitigation of the competition provided by the HOAMs via increasing their Start Oscillation Current SOC. This results in the suppression of their oscillation thus eliminating potential competition that may arise from their excitations. Furthermore, relations between the geometrical parameters such as the length and the radius profile of the structure are analyzed as well as the competition arising from different cavity modes and harmonic modes through the dispersion relation and the coupling strength plots. This work aims to provide insight into the optimization of the TM11-mode gyrotron as well as propose a simple guideline for the optimization towards a high beam efficiency. The aim is also so that the results provided from this research can be compared with the current implementation of the TE-mode gyrotrons as well as using it for future reference when designing a TM-mode gyrotron. The final aim is to provide some insight into the suppression of HOAMs through geometrical tuning and what constraints might be needed to take into consideration when designing a TM-mode gyrotron.

Table of Contents
Abstract .......................................................................................................................... i
摘要................................................................................................................................ ii
Acknowledgement ...................................................................................................... iii
1. Chapter 1 Introduction ........................................................................................ 1
The Gyrotron ............................................................................................. 1
The Electron Cyclotron Maser ................................................................. 2
Types of Gyrotron Devices ...................................................................... 5
2. Chapter 2: Theory of Nonlinear Self-Consistent TM-mode Gyrotrons .......... 7
Field Equations .......................................................................................... 7
Electron Dynamics ................................................................................... 11
Boundary Conditions .............................................................................. 13
3. Chapter 3: Single Taper Optimization ............................................................. 14
Geometrical Tuning ................................................................................. 14
Radial Tuning ............................................................................ 15
Length Tuning ............................................................................. 18
Parametric Analysis 𝒓𝒓𝟏𝟏 𝒗𝒗𝒗𝒗.𝑳𝑳𝟏𝟏 .................................................. 19
Beam Parameter Tuning ......................................................................... 21
Pitch Factor 𝜶𝜶 Tuning ............................................................ 22
Beam Voltage 𝑽𝑽𝒃𝒃 Tuning .......................................................... 23
Beam Current 𝑰𝑰𝒃𝒃 Tuning .......................................................... 25
Optimized Single-Taper Result............................................................. 28
3.4 Lossy Section Implementation and Mode Suppression ........................ 29
Mode Suppression via Geometrical Tuning ........................................ 32
4. Chapter 4: Double-Taper Optimization ........................................................... 34
Geometrical Tuning of the Second Taper ............................................ 36
Geometrical Tuning of the 2nd Taper .......................................... 37
Parametric Analysis 𝒓𝒓𝟏𝟏 𝒗𝒗𝒗𝒗.𝑳𝑳𝟎𝟎 .................................................... 38
Total Length Tuning 𝑳𝑳𝒕𝒕𝒕𝒕𝒕𝒕 𝒗𝒗𝒗𝒗𝒗𝒗 𝑳𝑳𝟏𝟏 .............................................. 40
Beam Parameter Tuning ....................................................................... 42
Pitch Factor 𝜶𝜶 Tuning .............................................................. 43
Beam Voltage 𝑽𝑽𝒃𝒃 Tuning ............................................................ 45
Beam Current 𝑰𝑰𝒃𝒃 Tuning ............................................................ 46
Optimized Double Taper Structure ...................................................... 47
Velocity Spread Inclusion ........................................................................ 48
v
Structure Comparison ............................................................................. 49
5. Chapter 5: Time Domain Corroboration ......................................................... 50
Time Dependent Simulation Results ...................................................... 50
Multimode Competition .......................................................................... 52
6. Chapter 6: Conclusion ....................................................................................... 56
7. References: .......................................................................................................... 58

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