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Accuracy-based Simulation Strategies for Plasma Edge Simulations for Nuclear Fusion Devices
Book - Dissertation
Nuclear fusion has the potential to provide the world's energy needs with safe, sustainable and virtually limitless energy. A key challenge in the realization of magnetically confined nuclear fusion is the power exhaust in the so-called divertor region near the reactor walls, which has to withstand enormous power loads. To predict and analyze divertor performance, accurate plasma edge simulations are indispensable. State-of-the-art plasma edge codes, such as B2-EIRENE, solve non-linear plasma and neutral transport equations iteratively. While plasma transport is modeled with fluid equations and implemented with a finite volume (FV) code, neutral transport requires a kinetic equation, implemented with a Monte Carlo (MC) code. In an MC code, particle trajectories are traced out to determine the average behavior of the particles. However, a statistical error remains on the result, which has a large impact on the convergence of the coupled FV-MC system. This complicates accuracy analysis and makes plasma edge simulations time-consuming. The goal of this PhD is to improve the speed and accuracy of B2-EIRENE simulations by optimizing the simulation strategy. Based on a detailed accuracy analysis, where all numerical error contributions are quantified, the coupling technique and the numerical parameters can be chosen more adequately. That way, a solution can be obtained in less computational time without losing accuracy. Or, similarly, a more accurate solution can be computed in the same computational time. First, we examine convergence and accuracy in a systematic way for several coupling techniques using a simplified 1D plasma edge model. Several error contributions are defined and methods to estimate these errors are proposed. We found the Random Noise coupling technique, where particle trajectories are uncorrelated between iterations, to be superior to Correlated Sampling, where trajectories are correlated, and Robbins Monro, where averaged values are used during the simulation. When the results of consecutive statistically stationary iterations are averaged in post-processing, an order of magnitude speed-up can be obtained without losing accuracy compared to the traditional simulation approach without averaging. Subsequently, we perform a first comprehensive accuracy analysis of B2-EIRENE simulation for a partially detached ITER divertor plasma. The speed-up obtained with averaging enabled simulations with on higher resolution discretization grids, which were previously unfeasible. A grid resolution study reveals that the discretization error in typical simulations is very large with some peak values increasing more than 40%. With a more suitable parameter choice, the total numerical error was limited to 15% within a feasible computational time. Finally, we extend the developed methodology for time-dependent FV-MC simulations and iterative MC codes using simplified 1D models. The extensions demonstrate the generality of the developed framework, which opens the way to accuracy analysis for many more applications within plasma edge simulations as well as in other fields where coupled stochastic-deterministic codes are emerging.