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

Abstract

A rotating tokamak plasma can interact resonantly with the external helical magnetic perturbations, also known as error fields. This can lead to locking and then to disruptions. We leverage machine learning (ML) methods to predict the locking events. We use a coupled third-order nonlinear ordinary differential equation model to represent the interaction of the magnetic perturbation and the plasma rotation with the error field. This model is sufficient to describe qualitatively the locking and unlocking bifurcations. We explore using ML algorithms with the simulation data and experimental data, focusing on the methods that can be used with sparse datasets. These methods lead to the possibility of the avoidance of locking in real-time operations. We describe the operational space in terms of two control parameters: the magnitude of the error field and the rotation frequency associated with the momentum source that maintains the plasma rotation. The outcomes are quantified by order parameters that completely characterize the state, whether locked or unlocked. We use unsupervised ML methods to classify locked/unlocked states and note the usefulness of a certain normalization of the order parameters. Three supervised ML classifiers are used in suite to estimate the probability of locking in the region of control parameter space with hysteresis, i.e., the set of control parameters for which both locked and unlocked states can exist. The results show that a neural network gives the best estimate of the locking probability. An analogy of the present locking model with the van der Waals equation of state is also provided.

Probabilistic locked mode predictor in the presence of a resistive wall and finite island saturation in tokamaks

“…We extend the model used in Ref. 28 in two ways to improve its fidelity. The first is the inclusion of a resistive wall (RW), separated by vacuum from another outer perfectly conducting surface where the error field is specified.…”

“…Because of the inherent hysteresis, i.e., hysteretic behavior, associated with mode-locking, our approach focuses on estimating the locking probability of a toroidal plasma, conditional on control parameters that represent changing plasma conditions either intrinsically or due to feedback control. Akc ¸ay et al 28 is the first example of this approach, which introduced a third-order reduced model to study locking of a resonant perturbation driven by an external error field, and leveraged machine learning (ML) methods to estimate the probability of locking as a function of two control parameters, namely, the error field and the torque driving the plasma rotation. In the present paper, we extend this locking model to have a resistive wall in addition to an error field, and an effect that accounts for the saturation of the mode.…”

“…In step (2), following the same procedure as in Ref. 28, we estimate the locking probability-defined as the probability of a plasma state becoming L over a timescale longer than the feedback time-as a function of the three aforementioned pairs of control parameters, using a fully connected neural network 24 as a classifier. This type of NN is also referred to as a multi-layer perceptron (MLP-NN).…”

A Control Oriented Strategy of Disruption Prediction to Avoid the Configuration Collapse of Tokamak Reactors

“…The choice of the features to be provided as inputs to the predictors are typically identified manually by the experts and require various forms of pre-processing. All the main real-time signal processing techniques available both in the time domain [34][35][36][37][38][39][40][41][42][43][44] and in the frequency domain [45] have been implemented. Approaches based on mixture of time and frequency domains, such as wavelet transforms, have not been neglected either [46].…”

Disruption prediction with artificial intelligence techniques in tokamak plasmas

“…domain [5][6][7][8][9][10][11][12][13][14][15] . These techniques have been complemented with tools in the frequency domain 16 , based on Fourier transforms.…”