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研究生:莊沂晟
研究生(外文):Yi-ChengChuang
論文名稱:在對稱性破壞的有限縱橫比托克馬克中α粒子在低碰撞頻率區的傳輸理論
論文名稱(外文):Transport theory of energetic alpha particles in low collisionality regimes in finite aspect ratio tokamaks with broken symmetry
指導教授:向克強
指導教授(外文):Ker-Chung Shaing
學位類別:碩士
校院名稱:國立成功大學
系所名稱:太空與電漿科學研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2019
畢業學年度:107
語文別:英文
論文頁數:56
中文關鍵詞:α粒子低碰撞頻率區傳輸理論
外文關鍵詞:alpha particleslow collisionality regimestransport theory
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對於托克馬克核融合反應爐的點火來說,局限高能α粒子能量的能力是非常重要並且已經在軸對稱托克馬克理論中被廣泛研究。然而,α粒子容易受到軸對稱破壞的影響,進而造成額外的粒子與能量損失。因此,我們需要一套討論在軸對稱破壞的α粒子傳輸理論。透過α粒子在減速過程中的速率所對應的折返頻率(deflection frequency),我們選擇討論相關性高的1⁄ν 區、超香蕉平台區和超香蕉區。論文中我們考慮有限縱橫比和有限的電漿參數β的效應讓理論結果更貼近實際情形。透過解反跳平均下的漂移動力學方程,我們可以用平衡態下的參數來表達額外傳輸損失的結果。我們在以上三區解出的各個解析結果可以透過近似方法來結合成統一的表達式。此一表達式可以用來估計在那些相關區的傳輸損失。我們也討論因為軸對稱性的破壞造成的傳輸損失對於強場托克馬克的影響。
Energetic alpha particles energy confinement is crucial for the ignition of nuclear fusion tokamak reactors and has been studied in axisymmetric tokamaks. However, the broken toroidal symmetry in real tokamaks enhances the particle and energy transport loss of alpha particles. Thus, it is important to have a transport theory for energetic alpha particles with broken symmetry to improve the result in axisymmetric tokamaks. Solutions for the 1/ν, superbanana plateau, and superbanana regimes are selected herein because the deflection frequency ν_D in these regimes correspond to the speed of alpha particles in the slowing down process. In particular, the finite aspect ratio and finite β effects are included to make the results realistic. By solving bounce averaged drift kinetic equation, the explicit expressions of the enhanced transport loss for alpha particles in relevant regimes are presented and are expressed in terms of equilibrium quantities. The analytic expressions in relevant regimes are combined into a unified formula with a rational approximation method. The unified formula can be used to model the enhanced transport losses of energetic alpha particles in relevant regimes. The implications of enhanced transport losses due to broken symmetry in high field tokamaks is discussed.
摘要 i
Abstract ii
致謝 iii
Table of Contents/目錄 iv
List of figures v
Nomenclature vi
Chapter 1 Introduction 1
1.1Tokamak and the Importance of Alpha Particles 1
1.2 Alpha Particle Confinement in Axisymmetric Tokamak 2
1.3 Motivation of the Thesis 3
1.4 Outline of the Thesis 7
Chapter 2 Magnetic Geometry 9
Chapter 3 Relevant Regimes for Energetic Alpha Particles 16
Chapter 4 Bounce Averaged Drift Kinetic Equation for Alpha Particles 20
4.1 Derivation of Bounce Average Drift Kinetic Equation 20
4.2 The Bounce Averaged Radial Drift Speed and Toroidal Drift Frequency 26
4.3 Resonance Pitch Angle Parameter 30
Chapter 5 Transport Flux 32
5.1 Definitions and Assumption 32
5.2 1ν Regime 33
5.3 Superbanana Plateau Regime 37
5.4 Superbanana Regime 40
5.5 A Unified Expression of Transport Fluxes in Low Collisionality Regimes 48
Chapter 6 The Implications for High Field Tokamaks 51
Chapter 7 Conclusion and Summary 53
Reference 54
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