Lecture 1 Introduction ........................................ 1
Lecture 2 Review of Scalars, Vectors, Tensors, and Dyads ...... 5
Lecture 3 Mass Conservation and the Equation of Continuity ... 19
Lecture 4 The Equation of Motion ............................. 25
Lecture 5 Energy Flow ........................................ 31
Lecture 6 The Electromagnetic Field .......................... 35
Lecture 7 Closures ........................................... 39
Lecture 8 Conservation Laws .................................. 43
Lecture 9 Ideal MHD and the Frozen Flux Theorem .............. 49
Lecture 10 Resistivity and Viscosity .......................... 55
Lecture 11 Similarity Scaling ................................. 65
Lecture 12 The Wöltjer Invariants of Ideal MHD,
Topological Invariance, Magnetic and Cross-
Helicity ........................................... 71
Lecture 13 Reduced MHD ........................................ 77
Lecture 14 Equilibrium: General Considerations—The Virial
Theorem ............................................ 85
Lecture 15 Simple MHD Equilibria .............................. 91
Lecture 16 Poloidal Beta, Paramagnetism, and Diamagnetism ..... 99
Lecture 17 "Force-Free" Fields ............................... 103
Lecture 18 Toroidal Equilibrium; The Grad-Shafranov
Equation .......................................... 107
Lecture 19 Behavior of Small Displacements in Ideal MHD ...... 121
Lecture 20 Linearized Equations and the Ideal MHD Force
Operator .......................................... 129
Lecture 21 Boundary Conditions for Linearized Ideal MHD ...... 133
Lecture 22 Proof that the Ideal MHD Force Operator is Self-
Adjoint ........................................... 137
Lecture 23 Waves in a Uniform Medium: Special Cases .......... 141
Lecture 24 Waves in a Uniform Medium: Arbitrary Angle of
Propagation ....................................... 147
Lecture 25 The Calculus of Variations and the Ideal MHD
Energy Principle .................................. 153
Lecture 26 Examples of the Application of the Energy
Principle ......................................... 159
Lecture 27 The Rayleigh-Ritz Technique for Estimating
Eigenvalues ....................................... 167
Lecture 28 The Gravitational Interchange Mode or g-Mode ...... 171
Lecture 29 Comments on the Energy Principle and the
Minimizing Eigenfunction .......................... 179
Lecture 30 Examples of the Application of the Energy
Principle to Cylindrical Equilibria ............... 183
Lecture 31 A Very Brief and General Tour of Suydam Analysis
for Localized Interchange Instabilities ........... 193
Lecture 32 Magnetic Reconnection ............................. 197
Lecture 33 Steady Reconnection: The Sweet-Parker Problem ..... 201
Lecture 34 Resistive Instabilities: The Tearing Mode ......... 205
Lecture 35 Resistive Instabilities: Closing Remarks .......... 213
Lecture 36 Turbulence ........................................ 219
Lecture 37 MHD Relaxation: Magnetic Self-Organization ........ 241
Lecture 38 Dynamos: Magnetic Field Generation and
Maintenance ....................................... 261
Appendix ...................................................... 283
Fluid Models of Magnetized Plasmas ............................ 285
Bibliography .................................................. 317
Index ......................................................... 319
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