Numerical Simulations of Tungsten under Helium Irradiation

Magnetic confinement fusion is a promising technology for electricity production due to available fuel and low waste products. However, the construction of a nuclear fusion reactor remains a scientific challenge. One of the main issues is the resistance of the plasma facing materials exposed to very harsh operating conditions. Tungsten is the leading candidate for the divertor, a crucial plasma facing component. This dissertation focuses on modeling the behavior of tungsten under irradiation conditions relevant to the divertor operations using a multi-scale modeling approach. In particular, high fluxes of helium ions at low energy impact the divertor and are responsible for changes in the tungsten microstructure such as the formation of helium blisters and ''fuzz"-like structures which can ultimately lead to erosion, degradation of materials performance and materials failure. A spatially dependent cluster dynamics model is introduced in order to model the evolution of the tungsten microstructure under irradiation. This continuum model is based on kinetic rate theory and handles each material defect type independently. Under the assumptions of a low dilute limit and no spatial correlation between defects, this leads to a large system of non-linear reaction-diffusion equations. Hence, the results addressed in this thesis consist in the determination of the kinetic parameters for the cluster dynamics model, the construction of a solver which efficiently deals with the large non-linear system of partial differential equations, the determination of the applicability of the model to fusion relevant conditions, and the model results for a variety of irradiation conditions. The input kinetic parameters to the cluster dynamics model are the defects' diffusion coefficients, binding energies and capture radii. These can be determined using a molecular dynamics and density functional theory simulations as well as empirical data. The challenge lies in obtaining a consistent set of kinetic parameters. Therefore, a method to determine the value of the diffusion coefficients for small helium, interstitial and vacancy defects at various temperatures using only molecular dynamics simulations is presented. Binding energies are also determined using molecular dynamics, and when combined with the diffusion coefficients they form a consistent set of kinetic parameters. An efficient implementation of a parallel solver is presented to deal with the large number of stiff non linear reaction diffusion equations. The implementation of a SDIRK scheme using a modified version of the SPIKE algorithm gives excellent parallelization results and suggests that this implementation would also be efficient for an extension of the model to two or three dimensions. Convergence results for a variety of SDIRK schemes show a convergence order reduction of the numerical scheme due to the stiffness of the reaction and diffusion terms. A comparison between simulation results using the cluster dynamics model and experimental results is essential to assess the validity of the model. Comparison with thermal helium desorption spectrometry experiments at low flux and fluence shows an excellent agreement between simulation and experiments and indicate that the model captures the key physical properties affecting the evolution of the tungsten microstructure. Further comparison with molecular dynamics simulations at extremely high fluxes provides an insight in the expected limitations of the model due to surface effects and dilute limit approximations breakdown when applied to fusion relevant conditions. Results of the model under fusion relevant conditions show the formation of large helium bubbles under the surface at a temperature dependent depth. The results are very sensitive to both irradiation flux and temperature. At large temperatures, a small concentration of large bubbles forms first deep under the tungsten surface, and forms a ``plug" which moves towards the surface until eventually the dilute limit approximation breaks down, indicating that the sub-surfaces bubbles become interlinked. At small temperatures, a larger concentration of smaller bubbles forms close to the surface until eventually surface effects such as bubble bursting are expected to occur. These results are found to be in good agreement with a similar analytical reaction diffusion model for fusion relevant conditions. More work is needed to simulate past the dilute limit breakdown and examine the possibility of taking into account surface effects