Bayesian modelling of Thomson scattering and multichannel interferometer diagnostics using Gaussian processes

Abstract

Electron temperature and density profiles consistent with JET high resolution Thomson scattering (HRTS) and far infrared (FIR) interferometer data are inferred by a Bayesian joint model using Gaussian processes. Forward models predicting diagnostic data including instrument effects such as optics and electronics are developed independently for both diagnostic systems in the Minerva framework, and combined as one joint model. The full joint posterior distribution of the electron temperature and density profiles, the hyperparameters of the Gaussian processes and calibration factor is explored by Markov chain Monte Carlo (MCMC) sampling. The posterior distribution of the electron density(temperature) profile is obtained by marginalising all the possible combinations of the electron temperature(density) profile, the hyperparameters and calibration factor. Therefore, the method removes profile dependency on the hyperparameters completely in addition to eliminating oftenused avoidable constraints such as monotonicity and parametrisation on the profiles. The posterior distribution of the calibration factor is also calculated explaining both the HRTS and the FIR interferometer data simultaneously. Thus, absolute electron density can be obtained from the HRTS without additional experiments measuring the calibration factor.

Proof of concept of a fast surrogate model of the VMEC code via neural networks in Wendelstein 7-X scenarios

“…The values of the GP HPs are uniformly sampled from a hyper-rectangle, whose boundaries are given in table 2. These values are adapted from previous works where the plasma profiles in W7-X are modeled via GPs [34,49,54,58].…”

Overview of the JET preparation for deuterium–tritium operation with the ITER like-wall

“…where the length scale σ x (x) is given as an arbitrary function. We need a function with different smoothness (gradient) in the core and edge regions and a smooth transition between the two for the length scale, and for this reason, we choose a hyperbolic tangent function [9,10], which is:…”

“…In order to find all possible plasma current distributions as well as the poloidal current flux and pressure profiles consistent with magnetic field and pressure measurements simultaneously, the current tomography and equilibrium models employ a number of predictive models of the following plasma diagnostics: magnetic sensors (pickup coils, saddle coils and flux loops) [8], polarimeters [15], interferometers [10,13,14], lithium beam emission spectroscopy [16,17] and high-resolution Thomson scattering (HRTS) systems [10]. All the lines of sight and observation positions of all these plasma diagnostics are shown in Figure 3.…”

“…Since the electron density calibration factor C TS and the position shift of all spatial channels along the laser path S TS of the HRTS system are cross-calibrated with other plasma diagnostics, they are regards as additional unknown parameters. The predictive model of the JET HRTS system [10] is given by:…”

“…Here, the axisymmetric plasma model with the Gaussian process prior and the one with the equilibrium prior are called the current tomography model and the equilibrium model, respectively. In addition to these prior distributions, both models employ predictive models of magnetic sensors (pickup coils, saddle coils and flux loops) [8], polarimeters [14,15], interferometers [14], lithium beam emission spectroscopy [16,17] and high-resolution Thomson scattering (HRTS) systems [10] in order to find all possible plasma current distributions as well as pressure and poloidal current flux profiles consistent with all their measurements simultaneously at one of the large-scale fusion experiments, the Joint European Torus (JET) [18]. Since these models involve a large number of unknown parameters and observations as well as multiple predictive models of scientific instruments, it is, therefore, inevitable to use a framework that is capable of handling and keeping track of all these parameters, assumptions, predictive models and observations in such a complex model.…”