THE DYNAMICS OF MAGNETIC-FLUX RINGS

Understanding the evolution of magnetic fields in the presence of turb ulent convection is essential for understanding the solar cycle dynamo . In this paper, we present results from numerical simulations of clos ed magnetic fibrils moving in a steady ''ABC'' flow, which we believe approximates some of the important characteristics of a turbulent, con vecting flow field. Three different evolutionary scenarios are found: expansion to a steady, deformed ring; collapse to a compact fat flux r ing; and occasionally, evolution toward an advecting, oscillatory stat e. There is a ''critical length scale'' for a closed magnetic fibril w hich divides the collapsing and expanding solutions. A simple scaling analysis predicts the existence of the expanding and collapsing soluti ons, 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 vigo rous motions, V(m) is the velocity amplitude associated with the size scale, and PHI is the magnetic flux per fibril. The scaling analysis f urther suggests that small-scale turbulent velocities are unimportant for amplification of strong magnetic fields.