### 1.1 Scope of review

The cyclic regeneration of the Sun’s large-scale magnetic field is at the root of all phenomena collectively
known as “solar activity”. A near-consensus now exists to the effect that this magnetic cycle is to be
ascribed to the inductive action of fluid motions pervading the solar interior. However, at this writing
nothing resembling consensus exists regarding the detailed nature and relative importance of various
possible inductive flow contributions.
My assigned task, to review “dynamo models of the solar cycle”, is daunting. For my own survival - and
that of the reader - I will interpret my task as narrowly as I can get away with. This review will not discuss
in any detail solar magnetic field observations, the physics of magnetic flux tubes and ropes, the generation
of small-scale magnetic field in the Sun’s near-surface layers, hydromagnetic oscillator models of the solar
cycle, or magnetic field generation in stars other than the Sun. Most of these topics are all worthy of
full-length reviews, and do have a lot to bear on “dynamo models of the solar cycle”, but a line needs
to be drawn somewhere. I also chose to exclude from consideration the voluminous literature
dealing with prediction of sunspot cycle amplitudes, including the related literature focusing
exclusively on the mathematical modelling of the sunspot number time series, in manner largely or
even sometimes entirely decoupled from the underlying physical mechanisms of magnetic field
generation.

This review thus focuses on the cyclic regeneration of the large-scale solar magnetic field through the
inductive action of fluid flows, as described by various approximations and simplifications of the partial
differential equations of magnetohydrodynamics. Most current dynamo models of the solar cycle rely
heavily on numerical solutions of these equations, and this computational emphasis is reflected
throughout the following pages. Many of the mathematical and physical intricacies associated
with the generation of magnetic fields in electrically conducting astrophysical fluids are well
covered in a few recent reviews (see Hoyng, 2003; Ossendrijver, 2003), and so will not be
addressed in detail in what follows. The focus is on models of the solar cycle, i.e., constructs seeking
primarily to describe the observed spatio-temporal variations of the Sun’s large-scale magnetic
field.