Our book

Published in 2014 by Cambridge University Press, this is the first book to present modern ray tracing theory and its application in plasma physics. The emphasis is on methods and concepts that are generally applicable, including methods for visualizing ray families in higher dimensions. My co-authors are Allan Kaufman (UC Berkeley, retired), Alain Brizard (St. Michael's College), and Steve Richardson (Naval Research Lab).

A self-contained exposition is given of the mathematical foundations of ray tracing theory for vector wave equations, based upon the Weyl theory of operator symbols. Variational principles are used throughout. These provide an elegant means to derive the wave action conservation law from a Noether symmetry, and a means to derive a Lorentz-covariant ray theory. Phase space variational principles are also used to provide a unified treatment of caustics, tunnelling, mode conversion, and gyroresonant wave-particle interactions.

Many examples are presented to show the power of these ideas to simplify and solve problems in plasma wave theory. Each chapter ends with a set of problems that allow the reader to explore the topics in more depth.