Introduction

The Sun's magnetic field cannot be due to a simple MHD oscillator, since there is no sign of an accompanying large oscillation in velocity. Understanding how the field can be generated instead by dynamo action in a cyclic way is a key question in solar MHD, which has not yet been fully answered, but on which huge progress has been made over the past 30 years. Here we first summarise the observational clues and describe the terminology and history (Sec. 8.1). Then we describe Cowling's theorem (Sec. 8.2) and the early basis for turbulent dynamo theory (Sec. 8.3), namely, Parker's classic 1955 paper and the more systematic mathematical formalism of Mean-Field MHD. This is followed with accounts of flux-transport dynamos (Sec. 8.4) and tachocline dynamos (Sec. 8.5). The latter includes overshoot and interface dynamos, while the former includes the early heuristic Babcock-Leighton ideas and their more recent development. Finally, two complementary approaches are outlined (Sec. 8.6), namely, complex global computations at one extreme and simple low-order models at the other, and brief comments are given on stellar dynamos.

The present chapter offers no more than a glimpse at a huge topic, but further details may be found in the excellent books by Moffatt (1978), Parker (1979a), Krause and Rädler (1980), Proctor and Gilbert (1994), Hughes et al. (2007), Dormy and Soward (2007) and in reviews by Choudhuri (1999), Mestel (1999), Schüssler (2005), Weiss (2005), Weiss and Thompson (2009) and Charbonneau (2010, 2013).