A Unified Method for Inference of Tokamak Equilibria and Validation of Force-Balance Models Based on Bayesian Analysis

A new method, based on Bayesian analysis, is presented which unifies the inference of plasma equilibria parameters in a Tokamak with the ability to quantify differences between inferred equilibria and Grad-Shafranov force-balance solutions. At the heart of this technique is the new concept of weak observation, which allows multiple for-ward models to be associated with a single diagnostic observation. This new idea subsequently provides a means by which the the space of GS solutions can be effi-ciently characterised via a prior distribution. The posterior evidence (a normalisation constant of the inferred posterior distribution) is also inferred in the analysis and is used as a proxy for determining how relatively close inferred equilibria are to force-balance for different discharges/times. These points have been implemented in a code called BEAST (Bayesian Equilibrium Analysis and Simulation Tool), which uses a special implementation of Skilling’s nested sampling algorithm [Skilling, Bayesian Analysis 1(4), 833–859 (2006)] to perform sampling and evidence calculations on high-dimensional, non-Gaussian posteriors. Initial BEAST equilibrium inference re-sults are presented for two high-performance MAST discharges