Approaching the solar dynamo

The origin of the solar magnetic field remains a stubborn challenge of astrophysics. At the solar surface the magnetic field assumes a complex, hierarchical structure in space and time. Systematic features such as the solar cycle and the butterfly diagram point to the existence of a deep-rooted large-scale predominantly toroidal magnetic field. In this review of solar dynamo theory new developments in our understanding of processes relevant for the solar dynamo are discussed. In recent years there has been significant progress with regard to tachocline physics, magnetic helicity conservation, the α effect, magnetic pumping, and the storage and amplification of the magnetic field. Remaining uncertainties about the nature of the deep-seated magnetic field and the α effect have thus far prevented the formulation of a coherent model for the solar dynamo. It is proposed that further progress is best achieved through a combination of approaches including high-resolution numerical simulations and global mean-field modeling. Along these lines some recent numerical simulations of magnetic pumping and flux expulsion in a magnetic layer are presented. The computations were performed with a new anelastic Cartesian finite-difference MHD code, which is the appropriate tool for studying processes near the base of stellar convection zones with a high spatial resolution. Possible implications for the solar dynamo are discussed.