Abstract
Recent progress in the disruption event characterization and forecasting framework has shown that machine learning guided by physics theory can be easily implemented as a supporting tool for fast computations of ideal stability properties of spherical tokamak plasmas. In order to extend that idea, a customized random forest (RF) classifier that takes into account imbalances in the training data is hereby employed to predict resistive wall mode (RWM) stability for a set of high beta discharges from the NSTX spherical tokamak. More specifically, with this approach each tree in the forest is trained on samples that are balanced via a user-defined over/under-sampler. The proposed approach outperforms classical cost-sensitive methods for the problem at hand, in particular when used in conjunction with a random under-sampler, while also resulting in a threefold reduction in the training time. In order to further understand the model’s decisions, a diverse set of counterfactual explanations based on determinantal point processes (DPP) is generated and evaluated. Via the use of DPP, the underlying RF model infers that the presence of hypothetical magnetohydrodynamic activity would have prevented the RWM from concurrently going unstable, which is a counterfactual that is indeed expected by prior physics knowledge. Given that this result emerges from the data-driven RF classifier and the use of counterfactuals without hand-crafted embedding of prior physics intuition, it motivates the usage of counterfactuals to simulate real-time control by generating the β N levels that would have kept the RWM stable for a set of unstable discharges.
Highlights
The resistive wall mode (RWM) is a global mode of instability of high pressure tokamak fusion plasmas that can lead to disruption of the plasma current and termination of the discharge [1, 2]
Given that this result emerges from the data-driven random forest (RF) classifier and the use of counterfactuals without hand-crafted embedding of prior physics intuition, it motivates the usage of counterfactuals to simulate real-time control by generating the βN levels that would have kept the RWM stable for a set of unstable discharges
A tearing mode is another mode of instability of tokamak plasmas that is more localized to rational magnetic surfaces rather than having a more global eigenfunction such as the RWM [5, 6]
Summary
The resistive wall mode (RWM) is a global mode of instability of high pressure tokamak fusion plasmas that can lead to disruption of the plasma current and termination of the discharge. In past post-discharge analysis efforts [3, 4], an exponential rise in an n = 1 toroidal mode number poloidal magnetic field measurement (known as the RWM sensor) on the time scale of magnetic flux penetration through conducting surfaces surrounding the plasma, τ w, was used as the primary indicator of RWM instability While this signal defines the existence of the RWM it requires that the mode be unstable. Complex physics software tools that analysed these kinetic resonances, such as MISK [9] and MARS-K [10] were developed and benchmarked [11, 12] While these tools were useful to understand the physics of RWM stability, they were too complex to execute in real-time to predict instabilities in a manner such that they could be avoided. One can use the counterfactual generation process to explore situations that are actionable in a real control system, such as lowering the βN level slightly above the computed no-wall limit
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