Lagrangian Simulations of Current Sheet Formation During Relaxation of an Unstable Line-Tied Equilibrium

Our recent theory, based on reduced MHD equations, predicts the formation of current sheets (tangential discontinuities) in an ideal line-tied plasma when an unstable equilibrium relaxes to a state of minimum energy [C. S. Ng and A. Bhattacharjee, Phys. Plasmas {\bf 5}, 4028 (1998)]. This mechanism has important implications for the heating of the solar corona, first envisioned by E. N. Parker. Testing of this prediction using conventional Eulerian simulations is subjected to the intrinsic numerical difficulty that the magnetic field line mapping is not kept fixed explicitly, as required by the line-tied condition. In fact, field line mapping can change substantially by reconnection due to numerical resistivity. To overcome this obstacle, we have developed a Lagrangian relaxation algorithm to simulate the evolution of an unstable equilibrium by following the movement of magnetic field lines explicitly. Preliminary simulation results will be presented.