Dynamo theory and the origin of small scale magnetic fields

Dynamo action describes the sustained conversion of kinetic energy into magnetic energy throughout the bulk of an electrically conducting fluid. Dynamo processes are commonly invoked to explain the origin of the solar cycle and of the large scale component of the solar magnetic field. The origin of small scale magnetic fields can also be understood in terms of dynamo processes. Recent advances in the theory of dynamo operating in fluids with high electrical conductivity - fast dynamos, indicate that most sufficiently complicated chaotic flows should act as dynamos. The resulting magnetic fields have a complex structure characterised by amplitude and polarity fluctuations on small scales. Some of the geometrical properties of these fluctuations can be described in terms of scaling behaviour and exponents. We review some of these ideas and illustrate them by simple examples. Possible extensions to the (nonlinear) dynamical regime are also discussed.