ABSTRACT
The theory of self-excited dynamo action discussed throughout this volume was first suggested by Sir Joseph Larmor in 1919 to account for the magnetic field of sunspots. This concept was later formalised mathematically by Walter Elsasser (1946). The objective of this first chapter is to introduce the subject and provide the necessary background for the later developments. As such, we derive the relevant equations and discuss the usual approximations in Section 1.1, before introducing the concept of a homogeneous self-excited dynamo in Section 1.2. Having dispensed with these preliminaries, the existing theoretical results and necessary conditions for dynamo action are then presented in Section 1.3 and the essential distinction between steady and time-dependent velocities then follows in Section 1.4. In Section 1.5, we then introduce the concept of mean field electromagnetism, which will be a reoccuring topic throughout the book. Finally, in Section 1.6, we discuss the difficult large magnetic Reynolds number limit, which is relevant for astrophysical problems.
