Transport Processes in the Plasma

Neutral particles play a crucial role in the plasma edge due to their strong interaction with the plasma. To capture all physics details most often a kinetic equation is solved using a Monte Carlo (MC) approach. Unfortunately, the MC noise hampers the convergence assessment of the solution of the coupled plasma-neutral equations. Moreover, the MC calculation time increases for high-collisional detached cases. In these high-collisional cases, however, the kinetic model may be well-approximated by a fluid neutral model, which can be solved deterministically. In this paper, we assess different fluid neutral models by comparing the resulting plasma sources to the sources from an MC simulation of the kinetic equation. The fluid models take into account the microscopic cross-sections and rate coefficients from the AMJUEL-HYDHEL databases, as well as the microscopic TRIM reflection model. We accomplish the latter without the introduction of any user-defined fitting parameters. We show that a pure pressure-diffusion equation provides accurate results for the particle source, but is inaccurate for the parallel momentum and ion energy source. Adding a parallel momentum equation gives maximum errors of about 9% for the momentum and 32% for the energy source. These errors are further reduced to respectively 6% and 14% by adding a separate neutral energy equation.

https://iopscience.iop.org/article/10.1088/1741-4326/aa8009/pdf

Development and assessment of 2D fluid neutral models that include atomic databases and a microscopic reflection model

In plasma edge simulations using the SOLPS-ITER code, the simulated Scrape-Off Layer plasma domain has historically been restricted to magnetic flux surfaces contacting divertor targets at both ends. We present here a newly developed numerical solver for the B2.5 plasma solver in SOLPS-ITER, allowing the numerical grid to be extended to the true vessel boundaries. The new, unstructured Finite Volume scheme can deal with arbitrary grids and magnetic topologies in the 2D poloidal plane. It includes a correct numerical treatment of possibly misaligned faces and cells w.r.t. the magnetic field to cope with, for example, strong divertor target shaping. The solver combines the benefits of an accurate numerical separation of fast parallel and slow radial transport, with a realistic description of the wall geometry, and the possibility of local grid refinement to capture sharp features in the Scrape-Off Layer flows. Generalized sheath boundary conditions are presented that can be imposed at all vessel boundaries, removing an important modeling uncertainty related to the specification of ad hoc decay length boundary conditions at the outer flux surfaces. The resulting model is applied to an AUG single-null case, a standard benchmark case for SOLPS-ITER. We analyze in particular the impact of the extended plasma model on upstream and divertor plasma conditions, and the improved predictions of heat and particle loads to the main chamber wall. The extended solver also allows for a much improved qualitative agreement between fluid and kinetic neutral simulations, because the fluid neutral solution, which is obtained on the plasma grid, now also extends to the true main chamber and divertor vessel boundaries.

Plasma edge simulations including realistic wall geometry with SOLPS-ITER

The SOLPS-ITER code suite is used worldwide for plasma edge modeling, the interpretation of experiments, as well as for the design of the ITER divertor. The numerical scheme of the plasma solver of the code, B2.5, is based on the assumption of perfectly orthogonal grids in the poloidal plane, aligned with the magnetic field, while in practice grids are often strongly distorted to match divertor target shapes. Neglecting these grid distortion leads to qualitatively and quantitatively incorrect results for fluid neutral simulations, and may affect results in cold (detached) divertors even when using kinetic neutral simulations. In this contribution, we present the first results of a newly implemented 9-point stencil in B2.5 to properly handle misaligned grids. The new scheme is then applied to fluid neutral simulations of a well-diagnosed and previously modeled Alcator C-Mod discharge. Results are compared with the original 5-point scheme neglecting grid distortion effects, as well as with simulations including a full kinetic neutral model. We conclude that the 9-point stencil is essential to correctly model the transport of fluid neutrals on distorted grids, and to capture the effects of divertor closure on the fluid neutral behavior.

Implementation of a 9-point stencil in SOLPS-ITER and implications for Alcator C-Mod divertor plasma simulations

A wall-aligned grid generator for non-linear simulations of MHD instabilities in tokamak plasmas

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assuming equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition fo...

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

/pdf/implementation-of-a-consistent-fluid-neutral-model-in-solps-4jwbvutlj9.pdf

Implementation of a consistent fluid‐neutral model in SOLPS‐ITER and benchmark with EIRENE

Plasma edge transport simulations typically rely on Monte-Carlo simulations for the kinetic neutral transport. However, for detached operating conditions the dominance of charge-exchange reactions between plasma and neutrals leads to excessive computational costs of these Monte-Carlo simulations. Since the fluid assumption becomes valid in these highly-collisional conditions, the use of a fluid neutral model is interesting to reduce computational costs. In this paper, we show within the SOLPS-ITER code suite that while our recently developed fluid neutral model is able to accurately represent the neutral transport in the divertor, it is unable to capture the kinetic effects near the outer wall. Due to this model flaw, discrepancies in plasma state arise between the fluid plasma-neutral model and a simulation with kinetic neutrals after converging the model equations. As a solution, we present a spatially hybrid neutral model that captures these kinetic effects near the wall, while benefiting from the fluid approach in the divertor region. Moreover, by using the kinetic code in the region outside the plasma grid, the method is able to accurately account for neutral transport through the voids surrounding the plasma and into pumps. We show on a case with a simplified ‘slab’ geometry that the results of the proposed hybrid model compare excellently to those of the kinetic solution.

A spatially hybrid fluid-kinetic neutral model for SOLPS-ITER plasma edge simulations

We elaborate a hybrid fluid-kinetic model for neutral particles in the plasma edge. A macro/fluid model with kinetic corrections in the closure terms of the fluid moment equations is solved in the entire domain. The kinetic corrections follow from a Monte Carlo simulation of the micro/kinetic part. We compare two hybrid models with different underlying fluid approximations: (i) a pure pressure-diffusion equation; and (ii) a continuity and parallel momentum equation with pressure-diffusion transport only retained in the directions perpendicular to the magnetic field lines. We asses their performance for a high recycling slab case with fixed background plasma. Compared to a Monte Carlo simulation of the full kinetic equation, the statistical error on the particle source is reduced with 40% and 47% for respectively the hybrid model without and with the parallel momentum equation for the same computational time. For the parallel momentum source there is only a reduction for the model with parallel momentum equation (about 69%). Unfortunately, the statistical error on the ion energy source slightly increases for both hybrid models.

Niels Horsten

Papers

Development and assessment of 2D fluid neutral models that include atomic databases and a microscopic reflection model

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

Implementation of a consistent fluid‐neutral model in SOLPS‐ITER and benchmark with EIRENE

A spatially hybrid fluid-kinetic neutral model for SOLPS-ITER plasma edge simulations

Hybrid fluid-kinetic model for neutral particles in the plasma edge