An interpretable isoflux-based observer for plasma shape control errors in tokamaks

In tokamaks, plasma shape control is often achieved through a so-called approach that regulates the poloidal flux differences between a reference point and a set of control points and magnetic field values at suitable locations to obtain the desired shape. Despite its simplicity, this approach presents two primary drawbacks: first, a method is needed to translate desired shape modifications, , radial or vertical shifts, into variations of the poloidal flux and magnetic field references; second, interpreting controller performance metrics may not be straightforward, since control errors are expressed in terms of physical quantities, , flux differences, magnetic fields, that cannot be directly related to positional errors. In this work, we propose a comprehensive methodology to establish relationships that link variations of poloidal flux and magnetic field values concerning a nominal plasma equilibrium in a predefined set of shape control points to local deformations of the Last Closed Flux Surface (LCFS). The effectiveness of this approach is demonstrated on the Tokamak à Configuration Variable (TCV) model through extensive simulations that consider various plasma configurations and shape modifications.