Lectures in Magnetohydrodynamics: With an Appendix on Extended MHD

Front Matter....Pages i-xiii
Introduction....Pages 1-4
Review of Scalars, Vectors, Tensors, and Dyads....Pages 5-18
Mass Conservation and the Equation of Continuity....Pages 19-24
The Equation of Motion....Pages 25-29
Energy Flow....Pages 31-33
The Electromagnetic Field....Pages 35-38
Closures....Pages 39-42
Conservation Laws....Pages 43-47
Ideal MHD and the Frozen Flux Theorem....Pages 49-53
Resistivity and Viscosity....Pages 55-64
Similarity Scaling....Pages 65-69
The Wöltjer Invariants of Ideal MHD, Topological Invariance, Magnetic and Cross-Helicity....Pages 71-76
Reduced MHD....Pages 77-83
Equilibrium: General Considerations— The Virial Theorem....Pages 85-89
Simple MHD Equilibria....Pages 91-98
Poloidal Beta, Paramagnetism, and Diamagnetism....Pages 99-101
“Force-Free” Fields....Pages 103-105
Toroidal Equilibrium; The Grad–Shafranov Equation....Pages 107-120
Behavior of Small Displacements in Ideal MHD....Pages 121-128
Linearized Equations and the Ideal MHD Force Operator....Pages 129-131
Boundary Conditions for Linearized Ideal MHD....Pages 133-136
Proof that the Ideal MHD Force Operator is Self-Adjoint....Pages 137-140
Waves in a Uniform Medium: Special Cases....Pages 141-145
Waves in a Uniform Medium: Arbitrary Angle of Propagation....Pages 147-152
The Calculus of Variations and the Ideal MHD Energy Principle....Pages 153-158
Examples of the Application of the Energy Principle....Pages 159-165
The Rayleigh–Ritz Technique for Estimating Eigenvalues....Pages 167-170
The Gravitational Interchange Mode or g -Mode....Pages 171-177
Comments on the Energy Principle and the Minimizing Eigenfunction....Pages 179-182
Examples of the Application of the Energy Principle to Cylindrical Equilibria....Pages 183-192
A Very Brief and General Tour of Suydam Analysis for Localized Interchange Instabilities....Pages 193-195
Magnetic Reconnection....Pages 197-200
Steady Reconnection: The Sweet–Parker Problem....Pages 201-204
Resistive Instabilities: The Tearing Mode....Pages 205-211
Resistive Instabilities: Closing Remarks....Pages 213-218
Turbulence....Pages 219-240
MHD Relaxation: Magnetic Self-Organization....Pages 241-259
Dynamos: Magnetic Field Generation and Maintenance....Pages 261-281
Back Matter....Pages 1-38