Dynamo Models of the Solar Cycle

This paper reviews recent advances and current debates in modeling the solar cycle as a hydromagnetic dynamo process. Emphasis is placed on (relatively) simple dynamo models that are nonetheless detailed enough to be comparable to solar cycle observations. After a brief overview of the dynamo problem and of key observational constraints, we begin by reviewing the various magnetic field regeneration mechanisms that have been proposed in the solar context. We move on to a presentation and critical discussion of extant solar cycle models based on these mechanisms. We then turn to the origin and consequences of fluctuations in these models, including amplitude and parity modulation, chaotic behavior, intermittency, and predictability. The paper concludes with a discussion of our current state of ignorance regarding various key questions relating to the explanatory framework offered by dynamo models of the solar cycle.