## 1 Disruptions in Tokamaks: An Operational Perspective  
Many systems, both natural and man-made, can be stable for long times and may look quite resilient but, in reality, they are not immune to catastrophic collapse. Some of the failures leading to collapse are relatively straightforward to interpret and do not seem worthy of particular attention; indeed, they can be consistently avoided once the proper precautions are put in place. Other collapses are due to very subtle and extremely difficult to predict causes. Earthquakes, and in general failures due to atmospheric phenomena, belong to the second category. In recent years, various efforts have been devoted to developing mathematical tools more appropriate to investigating and predicting these catastrophic and typically rare phenomena. Machine learning tools, of the type described in this paper, constitute an additional family in the arsenal of mathematical approaches, which can be used to study catastrophic events [1]. In the field of Magnetic Confinement Nuclear Fusion, disruptions are the most striking example of catastrophic failures difficult to predict. Therefore, they are one of the most severe problems to be faced by the Tokamak magnetic configuration in the attempt to design and operate commercial reactors. Disruptions are also a not negligible difficulty for the present largest devices, such as JET, and indeed they pose a not irrelevant constraint to high current operation. Moreover, JET disruptivity with the new ITER-like Wall (ILW) remains too high for the next generation of machines, since at low q\({}_{95}\) the percentage of disruptions can easily exceed 25%. To put this value in perspective, on DEMO even, one unmitigated disruption could severely damage the reactor [2]. Since they constitute a potential serious hazard to the integrity of Tokamak devices, disruptions are the subject of extensive studies at present. From the perspective of ultimate remedial actions that can be undertaken, various methods of mitigation are being investigated, particularly massive gas injection and shatter pellets. A complementary approach to manage the problem of disruptions is based on avoidance, i.e., on the sufficiently early detection of problems in the discharges and the consequent implementation of corrective actions to avoid the abrupt termination of the plasma. From an operational perspective, robust and reliable prediction methods are a prerequisite to any mitigation or avoidance strategy. Unfortunately, the theoretical understanding of the causes of disruptions is not sufficient to guarantee reliable forecasts, particularly on the time scales required for avoidance. Lacking solid and detailed theoretical models of disruptions, the development of an operation-based description of Tokamak plasmas aimed at determining the boundaries of the safe space, in terms of physically controllable quantities, has been attempted. One of such empirical descriptions of plasma stability is the so-called Hugill diagram, which combines the low q and density limits [3]. The low q limit is expressed in terms of 1/q\({}_{95}\), where q\({}_{95}\) is the safety factor at 95% of the plasma radius. The density limit is typically based on the Murakami factor n\({}_{\text{e}}\)R/B\({}_{\text{T}}\), where n\({}_{\text{e}}\) is the mean electron density, R the plasma major radius and B\({}_{\text{T}}\) the toroidal field. For a large JET database with the ILW (see Section 4), the Hugill diagram is reported in Figure 1. Unfortunately, such a plot has very poor predictive and interpretative capability, since the disruptive and safe regions overlap almost completely in this space. Similar considerations apply to another popular diagram, used to investigate the so-called beta limit [3]. The parameter \(\beta\) is typically used to quantify the level of the plasma pressure compared to the magnetic pressure. It is therefore natural to expect that pressure-driven instabilities could limit the level of \(\beta\) achievable in a certain configuration.