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

In tokamaks, plasma shape control is often achieved through a so-called isoflux 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, e.g., 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, i.e., 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.