Mode locking in reversed-field pinch experiments

The MHD mode trajectory in the Madison Symmetric Torus reversed-field pinch has been found to obey the sine-Gordon equation. Corresponding to experiment, a perturbation analysis predicts the locations of mode locking to be at the vacuum chamber poloidal and/or toroidal gaps. The mode's energy dissipates when it locks, as shown by a decaying spiral phase-plane trajectory. Unlocked modes travel around the torus without an abrupt energy loss. By varying key machine parameters obtained by statistical analysis, the probability of locking in accordance with the experimental results can be predicted.