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Freidberg J.P. Ideal Magnetohydrodynamics
| 12.11.2011, 23:06 |
1. Introduction 1.1. Ideal MHD and Magnetic Fusion 1.2. Units References 2. The MHD Model 2.1. Introduction 2.2. Description of the Ideal MHD Model 2.3. Derivation of the Ideal MHD Model 2.3.1. Starling Equations 2.3.2. Two-Fluid Equations 2.3.3. Low-Frequency Long-Wave length Asymptotic Expansions 2.3.4. The Single-Fluid Equations 2.3.5. The Ideal MHD Limit 2.4. Region of Validity 2.4.1. Overall Criteria 2.4.2. Conservation of Mass 2.4.3. Momentum Equation 2.4.4. Energy Equation 2.4.5. Ohm's I-aw 2.4.6. Summary of Validity Conditions 2.5. Collisionlcss MHD 2.6. Summary Reference Problems 3. General Properties of Ideal MHD 3.1. Introduction 3.2. Boundary Conditions 3.2.1. Perfectly Conducting Wall 3.2.2. Insulating Vacuum Region 3.2.3. Plasma Surrounded by External Coils 3.3. Local Conservation Relations 3.4. Global Conservation Laws 3.4.1. Perfectly Conducting Wall 3.4.2. Insulating Vacuum Region 3.4.3. Plasma Surrounded by External CoUs 3.5. Conservation of Fhix: "Frozen" Field Line Picture 3.6. Summary References Problems 4. Equilibrium: General Considerations 4.1 Introduction 4.2. Basic Equations 4.3. The Virial Theorem 4.4. Toroidicity 4.5. Magnetic Flux Surfaces 4.6. Surface Quantities: Basic Plasma Parameters and Figures of Merit 4.7. Equilibrium Degrees of Freedom 4.8. The Basic Problem of Toroidal Equilibrium 4.9. Summary References General References Problems 5. Equilibrium; One-Dimensional Configurations 5.1. Introduction 5.2. The В Pinch 5.3. The Z Pinch 5.4. The General Screw Pinch 5.5. Summary. References Problems 6. Equilibrium: Two-Dimensional Configurations 6.1. Introduction 6.2 The Grad-Shafranov Equation 6.2.1. Derivation 6.2.2. Plasma Parameters and Figures of Merit 6.3. The Reversed Field Pinch 6.4. The Ohmically Heated Tokamak 6.5. The High-p Tokamak 6.6. Noncircular Tokamaks 6.7. The Flux-Conserving Tokamak 6.8. The Spherical Tokamak 6.9. Tokamaks with Divertors 6.10. Summary References General References Problems 7. Equilibrium; Three Dimensional Configurations 7.1. Introduction 7.2. The Parallel Current Constraint 7.3. Helical Sideband Equilibria 7.4. The Elmo Bumpy Torus (EBT) 7.5. Steliarator Equilibria 7.6. Stellarators, lleliotrons, and Torsatrons 7.7. Summary References General References Problems 8. Stability: General Considerations 8.1. Introduction 8-2. Definition of Stability 8.3. Waves in an Infinite Homogeneous Plasma 8.4. General Linearized Stability Equations 8-4.1. Initial Value Formulation 8.4.2. Normal-Mode Formulation. 8.5. Properties of the Force Operator F 8.5.1. Selt-Adjoinmess of F 8.5.2. Real Omega^2 8.5.3. Orthogonality of the Normal Modes 8.5.4. Spectrum of F 8.6. Ulements of Variational Calculus 8.7. Variational Formulation 8.8. The Energy Principle 8.8.1. Statement and Proof of the Energy Principle 8.8.2. The Extended Energy Principle 8.8.3. The Intuitive Form of 6WF 8.8.4. Summary 8.9. In compressibility 8.10. Vacuum Versus Force-Free Plasma 8.11. Classification of MIID Instabilities 8.11.1. Internal/Fixed Boundary Modes 8.11.2. External/Free- Boundary Modes 8.11.3. Pressure-Driven Modes 8.11.4. Current-Driven Modes 8.12. Summary References General References Problems 9. Stability: One-Dimensional Configurations 9.1. Introduction 9.2. The в Pinch 9.3. The Z Pinch 9.3.1. m <> Modes 9.3.2. m = 0 Mode 9.4. The General Screw Pinch 9.4.1. Evaluation of W 9.4.2. The Full Normal-Mode Formulation 9.4.3. Suydam's Criterion 9.4.4. Newcomb's Analysis 9.4.5. The Oscillation Theorem 9.4.6. The Effect of a Resistive Wall 9.5. The Reversed Field Pinch 9.5.1. Introduction 9.5.2. Internal Pressure-Driven Modes 9.5.3. Internal Current-Driven Modes 9.5.4. External Modes 9.5.5. Discussion of Ideal Stability Results 9.5.6. The Force-Free Paramagnetic Model.. 9.5.7. Taylor's Theory 9.5.8. Overview of the RFP 9.6. The ''Straight" Tokamak 9.6.1. Introduction 9.6.2. Internal Pressure-Driven Modes 9.6.3. Internal Current-Driven Modes 9.6.4. External Modes (The m=1 Krnskal-Shafranov Limit) 9.6.5. External Modes (m > 2 External Kinks) 9.6.6. Summary 9.7. Summary References General References Problems. 10. Stability: Multidimensional Configurations 10.1. Introduction 10.2. General Reduction of dW for Ballooning Modes 10.3. The Relationship between the "Magnetic Well" and "Average Curvature" 10.3.1. Introduction 10.3.2. Flux Function in a Closed-Line System 10.3.3. Closed-Line Flux Coordinates 10.3.4. The Interchange Condition 10.3.5. The Relation between Average Curvature and Magnetic Well 10.3.6. Summary 10.4. The Elmo Bumpy Toms (EBT) 10.4.1. Introduction 10.4.2. The Effect of Rigid External Currents 10.4.3. EBT Flux Coordinates 10.4.4. The Ballooning Mode Equation 10.4.5. Interchange Stability 10.4.6. Ballooning Mode Stability 10.4.7. Summary of EBT 10.5. Tokamaks 10.5.1. Introduction 10.5.2. Tokamak Flux Coordinates 10.5.3. The Tokamak Ballooning-Mode Equation: Shear versus Periodicity 10.5.4. Interchange Stability: The Mercier Criterion 10.5.5. Ballooning Modes 10.5.6. Low-n Internal Modes 10.5.7. External Modes 10.5.8. Numerical Results: The Sykes Limit, the Troyon Limit 10.5.9. n = 0 Axisymmetric Modes 10.5.10. Overview of the Tokamak 10.6. Stellarators 10.6.1. Introduction 10.6.2. General Description of Stellarator Instabilities 10.6.3. Creating a Magnetic Well in a Stellarator 10.6.4. Design of a Stellarator Experiment 10.7. Summary References Problems Appendices Appendix A Appendix В Appendix С Appendix D Index
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