NONEQUILIBRIUM AND CURRENT SHEET FORMATION IN LINE-TIED MAGNETIC-FIELDS

Parker's model of coronal heating [E. N. Parker, Astrophys. J. 174, 49 9 (1972)] is considered within the framework of ideal reduced magnetoh ydrodynamics. It is shown that there can be at most one smooth magneto static equilibrium for a given smooth footpoint mapping between two en d plates to which field lines are line-tied. If such a smooth equilibr ium is deformed continuously by further footpoint motion so that it be comes unstable, there is no other smooth equilibrium for the plasma to relax to, and the system tends to a nonequilibrium state containing s ingular currents (''current sheets''). It is shown that this process c an occur as the system relaxes asymptotically to a state of minimum en ergy (possibly in infinite time). Numerical simulations that begin fro m smooth initial conditions containing current layers are presented. A s the current layers become increasingly intense due to footpoint moti on and eventually cross a threshold for instability, the magnetic rela xation observed in the simulation shows a tendency to form nonequilibr ium states with current sheets. A necessary geometrical criterion that determines the sites of current sheet formation in models without nul ls or closed field lines is given. According to this criterion, the ra te of velocity amplification, analogous to the Lyapunov exponent in no nlinear dynamics, becomes unbounded at singularities. (C) 1998 America n Institute of Physics. [S1070-664X(98)01411-6].