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 (GS) force-balance solutions. At the heart of this technique is the new concept of weak observation, which allows multiple forward models to be associated with a single diagnostic observation. This new idea subsequently provides a means by which the space of GS solutions can be efficiently characterized via a prior distribution. The posterior evidence (a normalization 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 2006 Bayesian Anal. 1 833-59) to perform sampling and evidence calculations on high-dimensional, non-Gaussian posteriors. Initial BEAST equilibrium inference results are presented for two high-performance MAST discharges.