Multi-layer perceptron based neural networks (NNs) are trained to predict the Troyon no-wall beta limits due to the onset of low-n (n = 1–3, n is the toroidal mode number) ideal external kink instabilities in tokamak plasmas. It is found that a well trained NN can predict the n = 1 no-wall beta limit within 10% relative error. The NN performance is somewhat worse for the n = 2 and 3 no-wall beta limits, but still a relative error within 20% is achievable. The trained NNs well reproduce the known dependences of the no-wall beta limits on the plasma pressure (pressure peaking factor) and current (plasma internal inductance) profiles. Other scalings are also easily established with NNs, for parametric dependences such as on the aspect ratio, the elongation and triangularity of the plasma boundary shape. The results show that the semi-analytically generated training database can be used to train NNs for predicting the no-wall limit in realistic experiments. These NN-based Troyon beta limit predictors can be incorporated into integrated modeling platforms, or directly implemented as a real time stability estimator for the purpose of disruption avoidance or mitigation during experiments.
Modifications to ideal stability by kinetic effects in NSTX