Geavanceerde Monte-Carlomethoden voor kinetische neutrale deeltjes in de plasmarand van fusiereactoren

Fusion energy reactors on Earth have the potential of providing relatively clean and inexhaustible electricity to mankind. The challenge is enormous however, since the required conditions for such reactors involve temperatures ten times higher than at the core of the Sun. One way to achieve the ambitious goal of fusion power plants is intense international cooperation such as in the International Thermonuclear Experimental Reactor project, which aims at producing significant net energy from fusion for the first time. At the start of the assembly of the tokamak reactor, the Korean president Moon Jae-in poignantly described this exciting international cooperation with the words 'Dazzling stars in the night sky shine with fusion energy. Once we pool all the wisdom that the world has to offer, we will be able to have an artificial sun that lights our path towards the future.' - President Moon Jae-in, July 28 2020 The incredible conditions required for fusion on Earth present many technological challenges. A region of specific interest in tokamaks is the so-called plasma edge, which forms the transition from the 150,000,000 K hot plasma to the solid wall components at reasonable temperatures. The behaviour in the plasma edge determines key properties of the fusion reactor such as particle and energy exhaust, erosion, and other damage to the solid components. To properly design a fusion reactor, design choices have to be evaluated. Compared to building expensive prototypes, a much more cost-effective strategy is the evaluation of these design choices via computer simulations. Besides the plasma, neutral particles in the plasma edge also play a critical role in the fusion reactor performance. The behaviour of these neutrals is described via the Boltzmann-Bhatnagar-Gross-Krook model equation, which is also used to describe processes ranging from bacterial chemotaxis over rarefied gases dynamics to radiation transport. The computational cost of the neutral model currently forms a major bottleneck in the simulation of the plasma edge. This PhD aims at improving the computation of the neutral model. The first strategy to improve the computation of the neutral model employed in this PhD is to improve the understanding of currently used particle tracing Monte Carlo methods to solve the neutral model. Such particle tracing methods consist of a particle path simulation and an estimator to extract samples of the quantities of interest from these paths. We have gathered the most-used particle tracing simulation methods and estimators and elaborately derived and described these. For each of these different particle tracing methods, an extensive analytical and numerical study of its properties has been conducted in a simplified setting that still significantly extends the state of the art. From these studies, the non-trivial dependency of the optimal simulation-estimator combination on the problem parameters is found. Due to the highly heterogeneous problem parameters in a plasma edge problem, the results from this PhD enable the use of different estimation procedures for different regions of the plasma edge domain. This would yield significant improvements over the currently used approach of trial-and-error to find the best simulation and estimator for the entire simulation. As an additional area of research, the conservation properties of different simulations and estimators were analyzed and a rescaling strategy was developed and investigated. The second strategy pursued in this PhD is the development of new methods, namely asymptotic-preserving Monte Carlo methods. The aim for such methods in neutral simulation is prompted recently due to the proposed (semi-)detached operational regimes for fusion reactor performance. In such regimes, the solid components are protected from the plasma by a neutral cushion in which the neutrals experience very high collisionality. For simulation of the Boltzmann-Bhatnager-Gross-Krook model, this high collisionality results in a very high computational cost. Fortunately, these conditions also result in an advection-diffusion equation to become a valid approximation. To harness this limiting equation, a standard particle tracing method is hybridized with a random walk Monte Carlo method for the advection-diffusion equation, yielding so-called kinetic-diffusion schemes. The developed algorithms are unique in their use of the exact mean and variance of the random walk steps and the proper correlation between steps. Outside of the asymptotic regimes, the developed kinetic-diffusion schemes do still result in a bias. This small bias in the simulation is removed with a newly developed multilevel algorithm. With the improved simulation in place, estimators for the random walk motion in the kinetic-diffusion schemes are required. These estimators form the biggest challenge of the PhD, and are at the fringe of the state of the art. The bias of the proposed track-length-like estimators possess similar asymptotic-preserving properties as the kinetic-diffusion simulation methods and the new estimators display a significant decrease in statistical error compared to standard techniques. In some high-collisional regimes, a significant bias does persist however, which can be resolved via the multi-level approach.

Jaar van publicatie:2021

Toegankelijkheid:Open