Lecture Notes in Physics

With an Appendix on Extended MHD

By: Dalton D. Schnack

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Paperback | 14 March 2012

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340 Pages

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22.86 x 15.24 x 1.91

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Review of Scalars, Vectors, Tensors, and Dyads.- Mass Conservation and the Equation of Continuity.- The Equation of Motion.- Energy Flow.- The Electromagnetic Field.- Closures.- Conservation Laws.- Ideal MHD and the Frozen Flux Theorem.- Resistivity and Viscosity.- Similarity Scaling.- The W#x00F6;ltjer Invariants of Ideal MHD, Topological Invariance, Magnetic and Cross-Helicity.- Reduced MHD.- Equilibrium: General Considerations#x2014; The Virial Theorem.- Simple MHD Equilibria.- Poloidal Beta, Paramagnetism, and Diamagnetism.- #x201C;Force-Free#x201D; Fields.- Toroidal Equilibrium; The Grad#x2013;Shafranov Equation.- Behavior of Small Displacements in Ideal MHD.- Linearized Equations and the Ideal MHD Force Operator.- Boundary Conditions for Linearized Ideal MHD.- Proof that the Ideal MHD Force Operator is Self-Adjoint.- Waves in a Uniform Medium: Special Cases.- Waves in a Uniform Medium: Arbitrary Angle of Propagation.- The Calculus of Variations and the Ideal MHD Energy Principle.- Examples of the Application of the Energy Principle.- The Rayleigh#x2013;Ritz Technique for Estimating Eigenvalues.- The Gravitational Interchange Mode or -Mode.- Comments on the Energy Principle and the Minimizing Eigenfunction.- Examples of the Application of the Energy Principle to Cylindrical Equilibria.- A Very Brief and General Tour of Suydam Analysis for Localized Interchange Instabilities.- Magnetic Reconnection.- Steady Reconnection: The Sweet#x2013;Parker Problem.- Resistive Instabilities: The Tearing Mode.- Resistive Instabilities: Closing Remarks.- Turbulence.- MHD Relaxation: Magnetic Self-Organization.- Dynamos: Magnetic Field Generation and Maintenance.

Industry Reviews

From the reviews:

"The present book ... is a set of lectures taught by the author at the University of Wisconsin, Madison. ... the monograph is extremely pleasant to read, examples are well chosen and illuminating, and the ultimate aim of interesting students in the field of MHD will most likely be successful." (Manuel Nunez Jimenez, Mathematical Reviews, Issue 2011 j)

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