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Lectures in Magnetohydrodynamics

With an Appendix on Extended MHD

  • Book
  • © 2009

Overview

Authors:
  1. Dalton D. Schnack

    1. Dept. Physics, University of Wisconsin, Madison, U.S.A.

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  • The combined length and style of the thirty-eight lectures in this concise primer are appropriate for complete presentation in a single semester and make it the only self-contained advanced graduate text in the field
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics (LNP, volume 780)

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Table of contents (38 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Introduction

    • Dalton D. Schnack
    Pages 1-4

  3. Review of Scalars, Vectors, Tensors, and Dyads

    • Dalton D. Schnack
    Pages 5-18

  4. Mass Conservation and the Equation of Continuity

    • Dalton D. Schnack
    Pages 19-24

  5. The Equation of Motion

    • Dalton D. Schnack
    Pages 25-29

  6. Energy Flow

    • Dalton D. Schnack
    Pages 31-33

  7. The Electromagnetic Field

    • Dalton D. Schnack
    Pages 35-38

  8. Closures

    • Dalton D. Schnack
    Pages 39-42

  9. Conservation Laws

    • Dalton D. Schnack
    Pages 43-47

  10. Ideal MHD and the Frozen Flux Theorem

    • Dalton D. Schnack
    Pages 49-53

  11. Resistivity and Viscosity

    • Dalton D. Schnack
    Pages 55-64

  12. Similarity Scaling

    • Dalton D. Schnack
    Pages 65-69

  13. The Wöltjer Invariants of Ideal MHD, Topological Invariance, Magnetic and Cross-Helicity

    • Dalton D. Schnack
    Pages 71-76

  14. Reduced MHD

    • Dalton D. Schnack
    Pages 77-83

  15. Equilibrium: General Considerations— The Virial Theorem

    • Dalton D. Schnack
    Pages 85-89

  16. Simple MHD Equilibria

    • Dalton D. Schnack
    Pages 91-98

  17. Poloidal Beta, Paramagnetism, and Diamagnetism

    • Dalton D. Schnack
    Pages 99-101

  18. “Force-Free” Fields

    • Dalton D. Schnack
    Pages 103-105

  19. Toroidal Equilibrium; The Grad–Shafranov Equation

    • Dalton D. Schnack
    Pages 107-120

  20. Behavior of Small Displacements in Ideal MHD

    • Dalton D. Schnack
    Pages 121-128
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Keywords

About this book

Magnetohydrodynamics, or MHD, is a theoretical way of describing the statics and dynamics of electrically conducting uids. The most important of these uids occurring in both nature and the laboratory are ionized gases, called plasmas. These have the simultaneous properties of conducting electricity and being electrically charge neutral on almost all length scales. The study of these gases is called plasma physics. MHD is the poor cousin of plasma physics. It is the simplest theory of plasma dynamics. In most introductory courses, it is usually afforded a short chapter or lecture at most: Alfven ´ waves, the kink mode, and that is it. (Now, on to Landau damping!) In advanced plasma courses, such as those dealing with waves or kinetic theory, it is given an even more cursory treatment, a brief mention on the way to things more profound and interesting. (It is just MHD! Besides, real plasma phy- cists do kinetic theory!) Nonetheless, MHD is an indispensable tool in all applications of plasma physics.

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 Núñez Jiménez, Mathematical Reviews, Issue 2011 j)

Authors and Affiliations

  • Dept. Physics, University of Wisconsin, Madison, U.S.A.

    Dalton D. Schnack

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