A First Course in Magnetohydrodynamics

Introduces magnetohydrodynamics (MHD) from a fluid dynamics perspective, accessible to undergraduates and non-plasma physics specialists.

David Alan Clarke (Author)

9781009381475, Cambridge University Press

Hardback, published 12 June 2025

526 pages
25.8 x 18.5 x 3.5 cm, 1.19 kg

'A First Course in Magnetohydrodynamics is an invaluable reference for students and researchers desiring a deeper understanding of MHD wave phenomena and the underpinnings of modern MHD codes. Clarke's love of the subject shines through in the pedagogical treatment, which features historical anecdotes, detailed derivations, meticulous supporting figures, and intuition-building discussions. The two-part format is ideal for teaching either 10- or 13-week courses, and the extensive problem sets and projects complete the offering. All in all, the text is a magnificent achievement.' Michael L. Norman, University of California

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: Alfvén'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.

Preface
Introduction
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
Variable Glossary
References
Index.

Subject Areas: Plasma physics [PHFP]