THE DYNAMICS OF MAGNETIC-FLUX RINGS

Understanding the evolution of magnetic fields in the presence of turbulent convection is essential for understanding the solar cycle dynamo. In this paper, we present results from numerical simulations of closed magnetic fibrils moving in a steady ''ABC'' flow, which we believe approximates some of the important characteristics of a turbulent, convecting flow field. Three different evolutionary scenarios are found: expansion to a steady, deformed ring; collapse to a compact fat flux ring; and occasionally, evolution toward an advecting, oscillatory state. There is a ''critical length scale'' for a closed magnetic fibril which divides the collapsing and expanding solutions. A simple scaling analysis predicts the existence of the expanding and collapsing solutions, as well as the amplitude of the asymptotic field strength for the expanding solutions. The form of the asymptotic field strength, B(as), is well approximated by B(as) congruent-to 3.7rho2/3l2/3V(m)4/3PHI-1/3 where rho is the mass density, l is the size scale of the most vigorous motions, V(m) is the velocity amplitude associated with the size scale, and PHI is the magnetic flux per fibril. The scaling analysis further suggests that small-scale turbulent velocities are unimportant for amplification of strong magnetic fields.