The art of mapping the magnetosphere

A comprehensive review is presented of the mathematical methods used to represent magnetic fields in the Earth's magnetosphere, of the way existing data‐based models use these methods and of the associated problems and concepts. The magnetic field has five main components: the internal field, the magnetopause, the ring current, the tail and Birkeland currents. Methods of representing separately each of these are discussed, as is the deformation of magnetic fields; Appendix B traces the connection between deformations and the Cauchy integral. A summary section lists the uses of data‐based models and their likely future evolution, and Appendix A supplements the text with a set of problems.