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Automated Magnetic Control Design for Optimal Power Exhaust in Divertor Tokamak Reactors

A key challenge to obtain a clean and sustainable power supply by controlled nuclear fusion is dealing with the high heat load that impinges on the plasma-facing components of tokamak fusion devices. In ITER (Latin for 'the way'), the plasma-facing components will consist of so-called 'monoblocks', which are tungsten (W) blocks mounted on a copper-chromium-zirconium (CuCrZr) cooling tube with a copper (Cu) interlayer. However, it is expected that this solution will be inadequate for future DEMO - derived from 'demonstration' - reactors where even higher steady state heat loads will occur, and it remains to be shown whether they can handle the high temporal heat load excursions caused by plasma instabilities such as Edge Localized Modes (ELMs). Therefore, both heat load reduction techniques and improved design of the plasma-facing components are crucial to extend their physical lifetime. 

W-Cu functionally graded materials (FGMs) are a promising material concept that allows tailoring the material properties in any location of the monoblock to reduce stress. However, the material distribution is often determined by trial-and-error, which is time-consuming and does not always exploit the full potential of these FGMs. Unlike design by trial-and-error, adjoint-based numerical optimization tools can automatically determine the best possible design in a computationally efficient way given a quantifiable performance metric or cost function, and are therefore of particular interest.

For ELMs, dedicated mitigation techniques are envisaged that increase the ELM occurrence frequency to reduce the ELM energy content and, consequently, the temporal heat load peak. Although promising results have been achieved in existing fusion devices, it remains to be shown whether these techniques will be sufficient for ITER and future DEMO reactors to prevent excessive erosion and damage of the plasma-facing components.

The first goal of the thesis is to numerically assess the potential of W-Cu FGMs to improve the monoblock lifetime by determining the optimal material distribution under steady heat load conditions. Hereto, the design of the FGM monoblock is formulated as an optimization problem and solved using an adjoint-based optimization algorithm. Secondly, the thesis aims to quantify the influence of ELM mitigation strategies on the ITER monoblock lifetime by analyzing the temperature and deformation evolution of the monoblock when repeatedly exposed to mitigated ELMs.

In the first part of the thesis, the cost function, design variables, and constraints for the FGM optimization problem are formulated, based on the temperature and stress distribution in the material. Additional temperature constraints are imposed locally to prevent tungsten recrystallization and embrittlement, and copper melting. An augmented Lagrangian optimization framework is elaborated to deal with the many temperature-dependent constraints that arise after discretizing the optimization problem. Additionally, a discrete adjoint approach is used to compute the design gradient in a fast and accurate way. The optimized FGM designs show a significant reduction of the local stress concentrations compared to reference designs without violating the temperature constraints. This shows the potential of the optimization tool for finding improved designs under complex state-dependent constraints. Finally, the cost function formulation and stress-free temperature where shown to have a profound influence on the resulting design and its performance. 

The second part of the thesis aims at the simulation of the thermal and mechanical behavior of the ITER monoblock when subject to repeated ELM exposure. The ELM heat load contribution is modeled using correlations from literature, which already show that although increasing the ELM frequency will lead to a decrease in temporal peak heat flux, the time-averaged heat flux will increase. A first estimate of the monoblock lifetime is made based on a novel 'recrystallization budget', which states that if the thickness of the recrystallized top layer exceeds 2 mm after 2000 hours of operation, the monoblock will have failed. The recrystallized tungsten fraction is computed using an anisothermal Johnson-Mehl-Avrami-Kolmogorov model. A new upper limit on the mitigated ELM frequency of 25-50 Hz is found, depending on the assumed inter-ELM heat flux, if this recrystallization budget holds for ELMy conditions. Finally, the first steps are set to refine these estimates by investigating the detailed plastic behavior of the monoblock's plasma-facing surface. Hereto, a plastic deformation model is set up and solved using a generalized Newton algorithm. A preliminary analysis shows that cyclic plastic deformation occurs only in the top 0.1 mm tungsten layer, but that cracks could appear after only several hours of operation, based on empirical fatigue data. 

Date:20 Sep 2016 →  9 Sep 2021
Keywords:Edge Localized Modes, ITER, functionally graded materials, fusion, monoblock, optimization, numerical simulation, thermal and mechanical design
Disciplines:Nuclear energy, Numerical modelling and design, Heat transfer, Calculus of variations and optimal control, optimisation, Continuum mechanics
Project type:PhD project