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系統識別號 U0026-1808201415002400
論文名稱(中文) 磁拘束電漿具共振磁場擾動的粒子傳輸動力與流體模型
論文名稱(英文) kinetic and fluid modelling of particle transport for magnetic confinement plasma with resonance magnetic perturbation
校院名稱 成功大學
系所名稱(中) 太空與電漿科學研究所
系所名稱(英) Institute of Space and Plasma Sciences
學年度 102
學期 2
出版年 103
研究生(中文) 張倞杰
研究生(英文) Chang, Ching-Chieh
學號 la6001103
學位類別 碩士
語文別 英文
論文頁數 35頁
口試委員 口試委員-陳秋榮
口試委員-河森榮一郎
口試委員-西田靖
指導教授-西村泰太郎
中文關鍵字 傳輸  擾動磁場  磁島  雙絕熱方程式 
英文關鍵字 Transport  Stochastic magnetic field  Island  Double adiabatic. 
學科別分類
中文摘要 這篇論文主要為探討再 TOKAMAK 邊緣具混沌磁場下的粒子與熱的傳輸
現象,內容包含 動力學理論數值模擬電子與質子的密度和溫度。值得注意
的是在混沌磁場中依然有磁島存在,且對傳輸現象有重要影響。另一方面,被
拘束粒子因為絕熱不變量存在而不受混沌磁場影響,所以對傳輸現象影響很小。
經由將三維軌道投影至一維,我們以熱擴散方程式來研究此傳輸現象。這裡也
使用了 Chew-Goldberger-Low (CGL) 流體模型以及 "雙絕熱方程式" 用以推
導被拘束粒子的密度與溫度。
英文摘要 This thesis investigates the particle and heat transport in the presence of stochas-
tic magnetic field in a tokamak edge. The particles' density and temperature evolution,
both ions and electrons, by kinetic computation is presented. It is suggested that the
remnants of the magnetic islands in seemingly fully stochastic magnetic field plays
an important role in regulating transport. On the other hand, the trapped particles,
having their own adiabatic invariants are insensitive to magnetic stochasticity and do
not contribute much to the transport. By projecting the orbit in full three dimensional
space to one dimensional radial space, we investigate the transport phenomenon by
diffusion type equations. Fluid model by hew-Goldberger-Low (CGL) model and the
double adiabatic condition have been employed in providing theoretical analysis.
論文目次 1 Introduction 3
2 Magnetic configuration of tokamaks 6
2.1 Pseudo toroidal coordinates and magnetic field line equation . 6
2.2 Guiding center equation of motion . . . . . . . . . . . . . . . . 8
2.3 Computational results . . . . . . . . . . . . . . . . . . . . . . 11
3 Approximation by diffusion equation 19
3.1 Solutions of diffusion equation . . . . . . . . . . . . . . . . . . 20
3.2 Solutions of Burgers’ equation . . . . . . . . . . . . . . . . . . 24
4 Application of Chew-Goldberger-Low fluid model 28
5 Summary and discussions 34

List of Figures
2.1 Pseudo-toroidal coordinates . . . . . . . . . . . . . . . . . . . 7
2.2 Poincar´e plots of magnetic field lines. Electron density and
temperature evolution. . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Poincar´e plots of magnetic field lines. Electron density and
temperature evolution. A single poloidal mode (m = 9) is
employed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Ion density and temperature evolution, same parameters as in
Fig.2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Ion density and temperature evolution, Br/B0 = 4.0 × 10−3. . 16
2.6 Ion density and temperature evolution, ε = 0.33. . . . . . . . . 17
2.7 Electron and ion diffusion coefficient. . . . . . . . . . . . . . . 18
3.1 Profile of diffusion equation. . . . . . . . . . . . . . . . . . . . 22
3.2 Diffusion equation with island effect. . . . . . . . . . . . . . . 23
3.3 The density and temperature evolution when the source particles
are added. . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 Burger’s equation time advanced. . . . . . . . . . . . . . . . . 26
3.5 An attempt to demonstrate convective effects in kinetic computation.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1 Two dimensional profile of ion density n(r, θ) and parallel temperature
Tk(r, θ). . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Time evolution of the fluid adiabatic invariant Tk(r, θ)B2/n2
for trapped particles. . . . . . . . . . . . . . . . . . . . . . . . 33
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