In plasma edge transport codes for nuclear fusion devices, fluid neutral models offer an interesting alternative to the currently used kinetic Monte Carlo simulations, especially for cases of high ion-neutral collisionality. In this paper, we elaborate a separate neutral energy equation in the state-of-the-art SOLPS-ITER code suite, which previously assumed perfect ion-neutral temperature equilibration. Furthermore, we study the coupled plasma-neutral solutions for a range of divertor operating regimes, proving the validity of these fluid neutral models for high-recycling and detached regimes.

Neutral gas physics and neutral interactions with the plasma are key aspects of edge plasma and divertor physics in a fusion reactor including the detachment phenomenon often seen as key to dealing with the power exhaust challenges. A full physics description of the neutral gas dynamics requires a 6D kinetic approach, potentially time dependent, where the details of the wall geometry play a substantial role, to the extent that, e.g., the subdivertor region has to be included. The Monte Carlo (MC) approach used for about 30 years in EIRENE [1], is well suited to solve these types of complex problems. Indeed, the MC approach allows simulating the 6D kinetic equation without having to store the velocity distribution on a 6D grid, at the cost of introducing statistical noise. MC also provides very good flexibility in terms of geometry and atomic and molecular (A&M) processes. However, it becomes computationally extremely demanding in high-collisional regions (HCR) as anticipated in ITER and DEMO. Parallelization on particles helps reducing the simulation wall clock time, but to provide speed-up in situations where single trajectories potentially involve a very large number of A&M events, it is important to derive a hierarchy of models in terms of accuracy and to clearly identify for what type of physics issues they provide reliable answers. It was demonstrated that advanced fluid neutral (AFN) models are very accurate in HCRs, and at least an order of magnitude faster than fully kinetic simulations. Based on these fluid models, three hybrid fluid-kinetic approaches are introduced: a spatially hybrid technique (SpH), a micro-Macro hybrid method (mMH), and an asymptotic-preserving MC (APMC) scheme, to combine the efficiency of a fluid model with the accuracy of a kinetic description. In addition, atomic and molecular ions involved in the edge plasma chemistry can also be treated kinetically within the MC solver, opening the way for further hybridisation by enabling kinetic impurity ion transport calculations. This paper aims to give an overview of methods mentioned and suggests the most prospective combinations to be developed.

Radial anomalous diffusion coefficients are among the largest sources of uncertainty in mean-field plasma-edge codes such as SOLPS-ITER. These coefficients are machine, scenario, and space-dependent, thus hampering the predictive and interpretive capability of these codes. In fact, modellers usually adjust these coefficients manually, based on expert judgement or on large, computationally expensive, parameter scans. Matching data from various diagnostics, each with their own experimental uncertainties, additionally complicates the problem of finding a good parameter set. In addition, standard non-linear regression techniques have shown to become prohibitive for expensive plasma-edge simulations with many unknown parameters, as gradient calculation was based on finite differences. In this paper, we apply algorithmic differentiation (AD) as an efficient and more accurate alternative for gradient calculation in large, continuously developed codes as SOLPS-ITER. In addition, the lack of uncertainty information and danger of data overfitting, key limitations of regression techniques, are overcome by combining data and uncertainties from different diagnostics in a Bayesian framework. We implement for the first time such a Bayesian inference framework into SOLPS-ITER, using gradient-based optimization with gradients obtained through tangent AD to find the maximum a posteriori (MAP) values of the parameters. The recently developed κ turbulence model is employed to limit the number of unknown parameters compared to full spatial profiles of diffusion coefficients. The Bayesian MAP-estimation is compared to standard regression techniques on a small-scale tokamak. We adopt fictitious experimental data obtained from a reference SOLPS-ITER solution with artificial measurement noise.

The neutral atoms in the plasma edge of nuclear fusion devices are typically modeled using either a fluid or kinetic approach. The kinetic approach is most accurate, but it has two main disadvantages. First, the usual solution of the high-dimensional kinetic equation using Monte Carlo techniques introduces statistical noise, which hampers the convergence of the coupled plasma-neutral model. Second, the computational time strongly increases for highly collisional regimes. For these reasons, deterministic fluid neutral models remain an attractive alternative, in particular for the highly collisional conditions where their accuracy is expected to be high. In recent years, efforts have been undertaken to improve the agreement between the fluid and kinetic approach by introducing consistent transport coefficients and consistent boundary conditions in the fluid models. In this work, these so-called advanced fluid neutral models are further enhanced by introducing different strategies to cope with the high heterogeneity of the ion-neutral collisionality encountered in realistic plasma-edge geometries, namely isotropic neutral flux limiters and an automated selection criterion for the optimal neutral boundary conditions. The validity of the resulting fluid neutral models is thoroughly assessed for various representative simulation cases with different geometries, divertor collisionalities, and wall materials, including, for the first time, simulations in a realistic ITER plasma edge geometry. Strong quantitative agreement between the fluid and kinetic models is achieved for cases with highest divertor collisionality.

A spatially hybrid fluid-kinetic approach for the efficient simulation of plasma-edge neutrals is extended with a kinetic-fluid condensation process and an automated approach to select a fluid or kinetic treatment at each point along the divertor targets. With the proposed hybrid fluid-kinetic methods, the dominant charge-exchange reaction can be largely removed from the kinetic neutral simulation. The hybrid methods achieve quantitative agreement with the standard kinetic approach, with relative errors on the peak target plasma density and peak target ion flux density of 5-30%, while the CPU time for the kinetic neutral solver is reduced by a factor 3 to 6.