Machine learning methods for probabilistic locked-mode predictors in tokamak plasmas

A rotating tokamak plasma can resonantly interact with an an error field, leading to locking and disruptions. Here we use machine learning (ML) methods to predict locking, to explore the avoidance of locking in real time. We use a simple coupled third order ODE model of the interaction of the magnetic perturbation with the error field, to gain experience with large sample sets for training the ML algorithms. This model describes qualitatively the locking and unlocking bifurcations. The independent ODE variables are the magnitude of the reconnected magnetic flux, its phase, and the plasma rotation, all at the mode rational surface; these quantities are the order parameters, completely characterizing the state, locked or unlocked (L,U). We have two control parameters: the magnitude of the error field and the rotation frequency associated with the momentum source. We use clustering methods to classify L and U states, and note the crucial importance of using normalized order parameters. We estimate the probability of locking in the region of control parameter space with hysteresis, i.e. with both L and U states. We note the analogy with phase transitions. We have modeled nonlinear saturation and resistive wall effects, resulting in a 5th order ODE system.