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A First Course in Magnetohydrodynamics
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Author: Clarke, David Alan (Saint Mary's University, Nova Scotia) Publisher: Cambridge University Press ISBN: 9781009381475 Cover: HARDCOVER Date: 2025年02月 DESCRIPTION This text introduces readers to magnetohydrodynamics (MHD), the physics of ionised fluids. Traditionally MHD is taught as part of a graduate curriculum in plasma physics. By contrast, this text - one of a very few - teaches MHD exclusively from a fluid dynamics perspective, making it uniquely accessible to senior undergraduate students. Part I of the text uses the MHD Riemann problem as a focus to introduce the fundamentals of MHD: Alfven's theorem; waves; shocks; rarefaction fans; etc. Part II builds upon this with presentations of broader areas of MHD: fluid instabilities; viscid hydrodynamics; steady-state MHD; and non-ideal MHD. Throughout the text, more than 125 problems and several projects (with solutions available to instructors) reinforce the main ideas. Optionally, large-font lesson plans for a 'flipped-style' class are also available to instructors. This book is suitable for advanced undergraduate and beginning graduate students, requiring no previous knowledge of fluid dynamics or plasma physics. Draws on the author's extensive experience in teaching courses on MHD at undergraduate and graduate level and as a researcher in MHD who has developed some of the most robust MHD algorithms based on ideas within the text Its focus in the first part on the fundamentals of MHD and from a wave mechanics (fluid dynamics) perspective makes this text uniquely accessible to senior undergraduate students Includes chapters dedicated to advanced topics such as fluid instabilities, viscid hydrodynamics, steady-state MHD, and non-ideal MHD A summary of important prerequisite material for the book is provided in eight appendices TABLE OF CONTENTS Part I. 1-D MHD in Ten Weeks: 1. The Fundamentals of Hydrodynamics 2. Selected Applications of Hydrodynamics 3. The Hydrodynamical Riemann Problem 4. The Fundamentals of Magnetohydrodynamics 5. MHD Waves and Discontinuities 6. The MHD Riemann Problem Part II. Additional Topics in (M)HD: 7. Fluid Instabilities 8. Viscid Hydrodynamics 9. Steady-State MHD 10. Non-Ideal MHD Appendices: A. Essentials of Vector Calculus B. Essentials of Electrodynamics C. The 'Conics' of PDEs D. The Secant Method E. Roots of a Cubic F. Sixth-Order Runge-Kutta G. Coriolis' Theorem H. The Diffusion Equation
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