| The High Average Power Laser (HAPL) project is aimed at a chamber design with a solid first wall in pursuit of sustained Laser Inertial Confinement Fusion. The wall must be able to withstand cyclic high temperatures and the corresponding thermal stresses. Tungsten was proposed as a suitable armor for the wall, because as a refractory metal, it has a high melting temperature and can act as a stress dampener. The nature of the surface loading consists of x-rays, ions, and neutrons, which through mainly thermal loading, create a biaxial surface stress. This condition causes the surface to roughen as ridges and valleys form to relieve the elastic energy. As the valleys deepen they eventually become cracks and traditional fracture mechanics can be used to determine the life of the first wall.;Beginning from the Asaro-Tiller-Grinfeld instability, sharp interface calculations can be performed to determine the surface profile as a result of the interplay between surface stress energy and mass transport mechanisms. One successful approach to determine interface evolution is phase field theory and its embodiment in the numerical level-set method. Applications of the method included problems of solid/liquid and solid/vapor interfaces. In the present method, however, we develop a numerical procedure for surface profile tracking directly without the need to develop partial differential equations for the phase field, which typically smooth out sharp interfaces.;Surface roughening instabilities, which are driven by a competition between elastic and surface energy contributions, are shown to be significantly controlled by plastic energy dissipation. We consider here a general parametric description of the surface of a stressed solid and through a mechanical kinetic transport mechanism, follow the temporal evolution of the surface morphology. It is found that once a groove reaches a certain depth and curvature, an instability is created that cannot be followed through elasticity alone. It is shown in this thesis that these morphological instabilities do not experience unbounded growth, as predicted by consideration of elastic energy alone, and that their growth will be severely limited by dislocation emission from high curvature grooves. Comparisons between perturbation theory and the present numerical approach are given along with comparisons to results from laser, ion, and x-ray experiments. Finally, the model is applied to the conditions of Inertial Confinement Fusion chamber walls to determine the number of cycles for crack nucleation. |
