Inference of experimental radial impurity transport on Alcator C-Mod: Bayesian parameter estimation and model selection

Abstract

We present a fully Bayesian approach for the inference of radial profiles of impurity transport coefficients and compare its results to neoclassical, gyrofluid and gyrokinetic modeling. Using nested sampling, the Bayesian impurity transport inference () framework can handle complex parameter spaces with multiple possible solutions, offering great advantages in interpretative power and reliability with respect to previously demonstrated methods. employs a forward model based on the package, built on the success of the well-known code (Dux 2003 Fusion Sci Technol. 44 708–15), to simulate impurity transport in magnetically-confined plasmas. In this paper, we focus on calcium (Ca, Z = 20) laser blow-off injections into Alcator C-Mod plasmas. Multiple Ca atomic lines are diagnosed via high-resolution x-ray imaging crystal spectroscopy and vacuum ultra-violet measurements. We analyze a sawtoothing I-mode discharge for which neoclassical and turbulent (quasilinear and non-linear) predictions are also obtained. We find good agreement in diffusion across the entire radial extent, while turbulent convection and density profile peaking are estimated to be larger in experiment than suggested by theory. Efforts and challenges associated with the inference of experimental pedestal impurity transport are discussed.

Holismokes

“…However, these methods are only for finding the lenses; a mass model is necessary for further studies. Mass models of gravitational lenses are often described by parameterized profiles, where the parameters are optimized, for instance via Markov chain Monte Carlo (MCMC) sampling (e.g., Jullo et al 2007;Suyu & Halkola 2010;Sciortino et al 2020;Fowlie et al 2020). These techniques are very time and resource consuming as modeling one lens can take weeks or months, and they are thus difficult to scale up for the upcoming amount of data.…”

Experimental Inference of Neutral and Impurity Transport in Alcator C-Mod Using High-Resolution X-Ray and Ultra-Violet Spectra

“…We significantly expand on previous work presented in Ref. [5], where a fully-Bayesian framework was applied for the first time to an Alcator C-Mod high-performance discharge. Here, we present new statistical techniques that have recently been added to this Bayesian workflow.…”

“…The experimental setup of the work described here is the same as presented in Ref. [5]. All the data of interest is from quasi-steady phases of plasma discharges with no Edge-Localized Modes (ELMs).…”

“…Our forward model is based on Aurora [84], a toolbox for particle transport, neutrals and radiation that grew out of the work presented in this paper, as well as research in Refs. [5] and [11]. Aurora's impurity transport simulations use a 1.5D geometry to model the timedependent evolution of charge states of a chosen ion.…”

“…To sidestep difficulties incurred in quantifying experimental cross-field particle fluxes (Γ), we make use of the common parametrization using diffusion (D) and convection (v), given by Γ ≡ −D ∇n + v n, where n is the density of a chosen plasma species. This allows one to compare theory and experiment without over-reliance on exact characterizations of particle sources and other experimental details [5]. The inference of D and v radial profiles is a challenging inverse problem, where one must iterate over a forward model that predicts spatio-temporal profiles of impurity charge state densities until matching some experimental observations.…”