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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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