Linear and nonlinear dynamos

Abstract

AbstractMore than eighty years have passed since the idea of a solar dynamo was first put forward, and almost fifty years since Parker's pioneering paper. Yet dynamo theory remains a fertile subject and continues to raise new challenges, both physical and mathematical. So far, nearly all treatments have relied on mean field electrodynamics. The earliest models were linear but recent treatments have been nonlinear and increasingly sophisticated. During his career, Michael Stix has made major contributions to all branches of this subject. In this survey I shall review the historical development of dynamo theory, as applied to stars like the Sun, and then focus on some issues of current interest, ranging from axisymmetric calculations in spherical geometry to low‐order models. Finally, I shall look ahead to what is needed in order to develop fully consistent, three‐dimensional numerical models of the solar cycle. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)