Numerical simulation of a catastrophe model for coronal mass ejections

In 1978, W. Van Tend and M. Kuperus proposed a simple catastrophe model for magnetically driving coronal mass ejections, prominence eruptions, and two‐ribbon flares. Their model, which is based on simple circuit concepts, suggests that a stable configuration containing a current filament will lose equilibrium when the filament current exceeds a critical value. Here we use a two‐dimensional numerical simulation to test how the Van Tend‐Kuperus model works in an ideal MHD fluid. The simulation exhibits the expected loss of mechanical equilibrium near the predicted critical value, but the current filament moves only a short distance upward before coming to rest at a new equilibrium. However, this new equilibrium contains a current sheet which is resistively unstable to magnetic reconnection, and if magnetic reconnection occurs rapidly, the filament can continue to move upward at Alfvénic speeds.