Abstract

In this introductory lecture, some historical landmarks in geomagnetism will be reviewed, in lead-up to a discussion of the α-effect, which, since the 1970s, has played a central role in mean-field dynamo theory. In the case of the Earth (and some other planets) the magnetic Reynolds number Rm of the random motions in the liquid core that contribute to the α-effect is not large, and a low-Rm approxi-mation can be exploited with some confidence in determining the crucial param-eter α. The situation is very different in solar-type stars where Rm is very large, and where a satisfactory theory is still lacking. The situation is particularly chal-lenging when the issue of dynamic ’α-quenching’ is addressed. Nevertheless, mean-field theory in the ‘magnetostrophic’ approximation is likely to remain in-dispensable for the foreseeable future, given that direct numerical simulation will never be able to come near to the actual physical parameters of the Earth and the Sun.