Introduction to Magnetohydrodynamics (2^nd Ed., Revised edition) Cambridge Texts in Applied Mathematics Series

Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.

Part I. From Maxwell's Equations to Magnetohydrodynamics: 1. A qualitative overview of MHD; 2. The governing equations of electrodynamics; 3. A first course in fluid dynamics; 4. The governing equations of MHD; Part II. The Fundamentals of Incompressible MHD: 5. Kinematics – advection, diffusion and intensification of magnetic fields; 6. Dynamics at low magnetic Reynolds number; 7. Dynamics at high magnetic Reynolds number; 8. An introduction to turbulence; 9. MHD turbulence at low and high magnetic Reynolds number; Part III. Applications in Engineering and Materials: 10. The world of metallurgical MHD; 11. The generation and suppression of motion in castings; 12. Axisymmetric flows driven by the injection of current; 13. MHD instabilities in aluminium reduction cells; Part IV. Applications in Physics: 14. The geodynamo; 15. Stellar magnetism; 16. Plasma containment in fusion reactors; Appendix A. Vector identities and theorems; Appendix B. Physical properties of liquid metals; References; Index.

P. A. Davidson is a professor in the Department of Engineering at the University of Cambridge. He has authored over 100 publications in the fields of magnetohydrodynamics and turbulence, including the books Turbulence: An Introduction for Scientists and Engineers (2015) and Turbulence in Rotating, Stratified and Electrically Conducting Fluids (2013). He is also an associate editor of the Journal of Fluid Mechanics.