A systemic approach to classification for knowledge discovery with applications to the identification of boundary equations in complex systems

In tokamak operation, the control of dangerous MHD instabilities, possibly in real-time scenarios, must rely on prompt robust diagnostics of the state and stability of the system. The set of magnetic signals measured on the outside of the plasma boundary, based on the Zakharov-Shafranov, Shkarowsky, Wootton (ZSSW) current moments, has been always used for reliable monitoring of key characteristics of the instantaneous equilibrium condition, such as the quantities Delta(Sh), the Shafranov centroid shift, beta(p) related to the thermal energy content, and l(i) related to the current profile peakedness. In addition, the fast pickup coils monitor the external magnetic field fluctuations due to internal MHD activity, however, without the possibility of radial localization of the source. Here, we explore the potential usefulness of more complete use of ZSSW moments in association with the information from fast B perturbation signals to detect tearing stability conditions. For clarity, we set up an analysis of the measurable response to tearing perturbations based on an exact equilibrium model, which is an extension of the Solov’ev case with the addition of an equilibrium, nonuniform plasma rotation Omega(psi). The relation of the selected (externally measurable) ZSSW moments to the calculated stability index is mapped for different rotation values. The footprint of the stability condition Delta’ < 0 on some current moments on the outer surface can then identify stability boundaries for different rotation conditions. This first discussion on an idealized exact model is proposed for testing the concept for application to realistic equilibria since it relies on a few externally monitorable quantities and very basic assumptions on the tearing modes physics.