Wouter Dekeyser

Tokamak plasma edge modelling including the main chamber wall

Quantifying main chamber wall recycling, erosion and resulting material migration, at least on the basis of known or empirical far scrape-off layer (SOL) processes, is still highly uncertain, despite its relevance for ITER and fusion reactor design studies. This affects, for example, the design problem of first mirror performance of many optical diagnostics in the harsh ITER environment. Poor computational access is not least due to a fundamental technical limitation in apparently all current tokamak edge plasma fluid codes, which implicates a wide computationally unresolved gap between the outermost plasma layer treated in codes and the real vessel wall. We show how the current ITER version of the B2-EIRENE code (SOLPS-4.3) can be extended to cover also this far SOL, on the same footing as the rest of the plasma transport model. We discuss consequences of this new model for estimating plasma power and particle sink terms caused by a fairly realistic wall in ITER based on the conventional Bohm criterion along all plasma–wall interfaces.Corrections were made to this article on 14 July 2011. The authors have been assigned to the correct affiliations.

Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors

The plasma and neutral transport in the plasma edge of a nuclear fusion reactor is usually simulated using coupled finite volume (FV)/Monte Carlo (MC) codes. However, under conditions of future reactors like ITER and DEMO, convergence issues become apparent. This paper examines the convergence behaviour and the numerical error contributions with a simplified FV/MC model for three coupling techniques: Correlated Sampling, Random Noise and Robbins Monro. Also, practical procedures to estimate the errors in complex codes are proposed. Moreover, first results with more complex models show that an order of magnitude speedup can be achieved without any loss in accuracy by making use of averaging in the Random Noise coupling technique.

Divertor target shape optimization in realistic edge plasma geometry

Tokamak divertor design for next-step fusion reactors heavily relies on numerical simulations of the plasma edge. Currently, the design process is mainly done in a forward approach, where the designer is strongly guided by his experience and physical intuition in proposing divertor shapes, which are then thoroughly assessed by numerical computations. On the other hand, automated design methods based on optimization have proven very successful in the related field of aerodynamic design. By recasting design objectives and constraints into the framework of a mathematical optimization problem, efficient forward-adjoint based algorithms can be used to automatically compute the divertor shape which performs the best with respect to the selected edge plasma model and design criteria. In the past years, we have extended these methods to automated divertor target shape design, using somewhat simplified edge plasma models and geometries. In this paper, we build on and extend previous work to apply these shape optimization methods for the first time in more realistic, single null edge plasma and divertor geometry, as commonly used in current divertor design studies. In a case study with JET-like parameters, we show that the so-called one-shot method is very effective is solving divertor target design problems. Furthermore, by detailed shape sensitivity analysis we demonstrate that the development of the method already at the present state provides physically plausible trends, allowing to achieve a divertor design with an almost perfectly uniform power load for our particular choice of edge plasma model and design criteria.

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

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...

An automated approach to magnetic divertor configuration design

At present, several plasma boundary codes exist that attempt to describe the complex interactions in the divertor SOL (Scrape-Off Layer). The predictive capability of these edge codes is still very limited. Yet, in parallel to major efforts to mature edge codes, we face the design challenges for next step fusion devices. One of them is the design of the helium and heat exhaust system. In past automated design studies, results indicated large potential reductions in peak heat load by an increased magnetic flux divergence towards the target structures. In the present study, a free boundary magnetic equilibrium solver is included into the simulation chain to verify these tendencies. Additionally, we expanded the applicability of the automated design method by introducing advanced “adjoint” sensitivity computations. This method, inherited from airfoil shape optimization in aerodynamics, allows for a large number of design variables at no additional computational cost. Results are shown for a design application of the new WEST divertor.

Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method

As magnetic confinement fusion progresses towards the development of first reactor-scale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimization-based design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation of the design problems is given, and conditions characterizing the optimal designs are formulated. Using a continuous adjoint framework, design sensitivities can be computed at a cost of only two edge plasma simulations, independent of the number of design variables. Furthermore, by using a one-shot method the entire optimization problem can be solved at an equivalent cost of only a few forward simulations. The methodology is applied to target shape design for uniform power load, in simplified edge plasma geometry.

Optimal shape design for divertors

Owing to the complex physics of the plasma edge, numerical simulation tools are indispensable for the evaluation of novel divertor concepts. Simulation-based divertor design is computationally extremely expensive, however, not in the least due to the large number of design variables. In this work, we show how shape optimisation methods can prove very valuable in partially automating the design process. We apply the continuous adjoint method to design divertor targets for maximum power load spreading. Shape sensitivities are derived using the material derivative approach. The resulting sensitivities depend on boundary data only, and can be computed very efficiently. Through numerical tests, we also prove that their accuracy is good. Next, the performance of two gradient-based optimisation algorithms and a so-called one-shot method is compared. Using the latter method, optimal solutions are obtained in a computational effort less than five times the time needed for a single analysis simulation.

Achievements and challenges in automated parameter, shape and topology optimization for divertor design

Plasma edge transport codes play a key role in the design of future divertor concepts. Their long simulation times in combination with a large number of control parameters turn the design into a challenging task. In aerodynamics and structural mechanics, adjoint-based optimization techniques have proven successful to tackle similar design challenges. This paper provides an overview of achievements and remaining challenges with these techniques for complex divertor design. It is shown how these developments pave the way for fast sensitivity analysis and improved design from different perspectives.