Bayesian inference of axisymmetric plasma equilibria

We present a Bayesian approach for inferring axisymmetric plasma equilibria from measurements of the magnetic field and plasma pressure. This method delivers a set of posterior solutions for plasma current and pressure distribution that align with the given measurements and satisfy magnetohydrodynamic (MHD) force balance. In this method, the toroidal plasma current and magnetic field coils are modelled as a collection of axisymmetric current-carrying beams. The remaining parameters, such as plasma pressure and poloidal current flux, are represented as a function of poloidal magnetic flux, determined by a two-dimensional distribution of axisymmetric current. The profiles of plasma pressure and poloidal current flux are modelled as Gaussian processes, and their smoothness is determined according to Bayesian model selection based on the principle of Occam's razor. The force balance constraint derived from MHD is taken into account at every plasma current beam. Experimental observations collected by diagnostics are compared with predictions from the predictive (forward) models. The complex, high-dimensional posterior probability distribution is explored by using a novel algorithm leveraging the Gibbs sampling scheme. The method is developed within the Minerva framework and applied to the JET tokamak experiment.