Dynamical evolution of large-scale, two-dimensional, fibril magnetic fields

We consider the dynamical behavior of a large-scale, two-dimensional, fibril magnetic field embedded in an ideal fluid of infinite electrical conductivity. The field is treated statistically, as a dilute gas composed of parallel, twisted, magnetic flux tubes in specified velocity and gravitational fields. The salient physical processes are the annihilation/coalescence of flux tubes through binary collisions and flux-tube precipitation, diffusion, and advection caused by their motions. The purpose is to study the size distribution, temporal, and latitudinal variations of emerging solar flux with a fibril magnetic field throughout the solar convection zone. The analysis suggests that the transport and in situ coalescence/annihilation of magnetic flux tubes through the solar convection zone may be responsible for the size spectrum, temporal, and latitudinal variations observed in the emerging magnetic flux during the solar cycle. Such a scenario in consistent with the previous works of Speigel and Weiss, and Schmitt and Rosner, which suggest that solar toroidal fields are produced near the base of the convection zone and are shredded into thin magnetic fibrils through a doubly diffusive magnetic buoyancy instability