This concise and self-contained primer is based on class-tested notes for an advanced graduate course in MHD. The broad areas chosen for presentation are the derivation and properties of the fundamental equations, equilibrium, waves and instabilities, self-organization, turbulence, and dynamos. The latter topics require the inclusion of the effects of resistivity and nonlinearity.
Together, these span the range of MHD issues that have proven to be important for understanding magnetically confined plasmas as well as in some space and astrophysical applications. The combined length and style of the thirty-eight lectures are appropriate for complete presentation in a single semester.
An extensive appendix on extended MHD is included as further reading.
Author(s): Dalton D. Schnack (auth.)
Series: Lecture Notes in Physics 780
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2009
Language: English
Pages: 323
Tags: Atoms and Molecules in Strong Fields, Plasma Physics;Extraterrestrial Physics, Space Sciences;Geophysics/Geodesy;Fluids;Nuclear Fusion
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
