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E-raamat: Stability and Transport in Magnetic Confinement Systems

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Stability and Transport in Magnetic Confinement SystemsSuurem pilt
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Stability and Transport in Magnetic Confinement Systems provides an advanced introduction to the fields of stability and transport in tokamaks. It serves as a reference for researchers with its highly-detailed theoretical background, and contains new results in the areas of analytical nonlinear theory of transport using kinetic theory and fluid closure. The use of fluid descriptions for advanced stability and transport problems provide the reader with a better understanding of this topic. In addition, the areas of nonlinear kinetic theory and fluid closure gives the researcher the basic knowledge of a highly relevant area to the present development of transport physics.

This book is an advanced introduction to stability and transport in tokamaks, offering highly-detailed theoretical background, and new results in the areas of analytical nonlinear theory of transport using kinetic theory and fluid closure.
1 Introduction
1(10)
1.1 Principles for Confinement of Plasma by a Magnetic Field
1(3)
1.2 Energy Balance in a Fusion Reactor
4(3)
1.3 Magnetohydrodynamic Stability
7(1)
1.4 Transport
8(1)
1.5 Scaling Laws for Confinement of Plasma in Toroidal Systems
9(1)
1.6 The Standpoint of Fusion Research Today
9(2)
References
10(1)
2 Different Ways of Describing Plasma Dynamics
11(16)
2.1 General Particle Description, Liouville and Klimontovich Equations
11(2)
2.2 Kinetic Theory as Generally Used by Plasma Physicists
13(1)
2.3 Gyrokinetic Theory
14(1)
2.4 Fluid Theory as Obtained by Taking Moments of the Vlasov Equation
15(5)
2.4.1 The Maxwell Equations
16(1)
2.4.2 The Low Frequency Expansion
16(2)
2.4.3 The Energy Equation
18(2)
2.5 Gyrofluid Theory as Obtained by Taking Moments of the Gyrokinetic Equation
20(1)
2.6 One Fluid Equations
21(1)
2.7 Finite Larmor Radius Effects in a Fluid Description
22(5)
2.7.1 Effects of Temperature Gradients
25(1)
References
26(1)
3 Fluid Description for Low Frequency Perturbations in an Inhomogeneous Plasma
27(30)
3.1 Introduction
27(2)
3.2 Elementary Picture of Drift Waves
29(7)
3.2.1 Effects of Finite Ion Inertia
32(2)
3.2.2 Drift Instability
34(1)
3.2.3 Excitation by Electron-Ion Collisions
35(1)
3.3 MHD Type Modes
36(13)
3.3.1 Alfven Waves
37(1)
3.3.2 Interchange Modes
37(3)
3.3.3 The Convective Cell Mode
40(1)
3.3.4 Electromagnetic Interchange Modes
40(3)
3.3.5 Kink Modes
43(2)
3.3.6 Stabilization of Electrostatic Interchange Modes by Parallel Electron Motion
45(1)
3.3.7 FLR Stabilization of Interchange Modes
45(2)
3.3.8 Kinetic Alfve'n Waves
47(2)
3.4 Quasilinear Diffusion
49(3)
3.5 Confinement Time
52(1)
3.6 Discussion
53(4)
References
55(2)
4 Kinetic Description of Low Frequency Modes in Inhomogeneous Plasma
57(26)
4.1 Integration Along Unperturbed Orbits
57(6)
4.2 Universal Instability
63(2)
4.3 Interchange Instability
65(2)
4.4 Drift Alfve'n Waves and β Limitation
67(3)
4.5 Landau Damping
70(1)
4.6 The Magnetic Drift Mode
71(1)
4.7 The Drift Kinetic Equation
72(1)
4.8 Dielectric Properties of Low Frequency Vortex Modes
73(3)
4.9 Finite Larmor Radius Effects Obtained by Orbit Averaging
76(4)
4.10 Discussion
80(1)
4.11 Exercises
80(3)
References
81(2)
5 Kinetic Descriptions of Low Frequency Modes Obtained by Gyroaveraging
83(18)
5.1 The Drift Kinetic Equation
83(7)
5.1.1 Moment Equations
87(1)
5.1.2 The Magnetic Drift Mode
88(1)
5.1.3 The Tearing Mode
89(1)
5.2 The Linear Gyrokinetic Equation
90(6)
5.2.1 Applications
94(2)
5.3 The Nonlinear Gyrokinetic Equation
96(3)
5.4 Gyro-Fluid Equations
99(2)
References
100(1)
6 Low Frequency Modes in Inhomogeneous Magnetic Fields
101(80)
6.1 Anomalous Transport in Systems with Inhomogeneous Magnetic Fields
101(2)
6.2 Toroidal Mode Structure
103(4)
6.3 Curvature Relations
107(3)
6.4 The Influence of Magnetic Shear on Drift Waves
110(3)
6.5 Interchange Perturbations Analysed by the Energy Principle Method
113(3)
6.6 Eigenvalue Equations for MHD Type Modes
116(12)
6.6.1 Stabilization of Interchange Modes by Magnetic Shear
116(3)
6.6.2 Ballooning Modes
119(9)
6.7 Trapped Particle Instabilities
128(3)
6.8 Reactive Drift Modes
131(8)
6.8.1 Ion Temperature Gradient Modes
132(3)
6.8.2 Electron Temperature Gradient Mode
135(1)
6.8.3 Trapped Electron Modes
136(3)
6.9 Competition Between Inhomogeneities in Density and Temperature
139(1)
6.10 Advanced Fluid Models
140(10)
6.10.1 The Development of Research
141(3)
6.10.2 Closure
144(2)
6.10.3 Gyro-Landau Fluid Models
146(1)
6.10.4 Nonlinear Kinetic Fluid Equations
147(1)
6.10.5 Comparisons with Nonlinear Gyrokinetics
148(2)
6.11 Reactive Fluid Model for Strong Curvature
150(14)
6.11.1 The Toroidal ηi Mode
151(3)
6.11.2 Electron Trapping
154(2)
6.11.3 Transport
156(2)
6.11.4 Normalization of Transport Coefficients
158(1)
6.11.5 Finite Larmor Radius Stabilization
159(1)
6.11.6 The Eigenvalue Problem for Toroidal Drift Waves
160(3)
6.11.7 Early Tests of the Reactive Fluid Model
163(1)
6.12 Electromagnetic Modes in Advanced Fluid Description
164(4)
6.12.1 Equations for Free Electrons Including Kink Term
165(2)
6.12.2 Kinetic Ballooning Modes
167(1)
6.13 Resistive Edge Modes
168(7)
6.13.1 Resistive Ballooning Modes
170(3)
6.13.2 Transport in the Enhanced Confinement State
173(2)
6.14 Discussion
175(6)
References
176(5)
7 Transport, Overview and Recent Developments
181(10)
7.1 Stability and Transport
181(1)
7.2 Momentum Transport
181(6)
7.2.1 Simulation of an Internal Barrier
183(1)
7.2.2 Simulation of an Edge Barrier
184(3)
7.3 Discussion
187(4)
References
187(4)
8 Instabilities Associated with Fast Particles in Toroidal Confinement Systems
191(8)
8.1 General Considerations
191(1)
8.2 The Development of Research
192(1)
8.3 Dilution Due to Fast Particles
193(1)
8.4 Fishbone Type Modes
194(1)
8.5 Toroidal Alfven Eigenmodes
195(2)
8.6 Discussion
197(2)
References
198(1)
9 Nonlinear Theory
199(20)
9.1 The Ion Vortex Equation
199(8)
9.2 The Nonlinear Dielectric
207(1)
9.3 Diffusion
208(4)
9.4 Fokker-Planck Transition Probability
212(3)
9.5 Discussion
215(4)
References
215(4)
General References 219(2)
Answers to Exercises 221(4)
Index 225
Jan Weiland, Chalmers University of Technology, elfjw@chalmers.se
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