Deciphering gas implantation rate effects on bubble nucleation in tungsten

We use the object kinetic Monte Carlo code KSOME to study the sub-surface helium clustering behaviour in tungsten at various conditions relevant to plasma exposure of divertor surfaces. In particular, we have investigated helium implantation fluxes from 10$^{\mathrm{20}}$ to 10$^{\mathrm{27}}$ m$^{\mathrm{-2}}$s$^{\mathrm{-1}}$ at temperatures from 400K to 1600K for 100-eV helium ions implanted below tungsten surfaces as a function of pre-existing vacancy concentration. For these conditions, the helium retention rate, the surface areal density of adatoms, and the number density of clusters are analysed. A phase diagram is constructed to summarize the results, which maps the ratio of self-trapped helium to vacancy-trapped helium with respect to the helium flux, the target temperature, and the concentration of pre-existing vacancy. According to the phase diagram, the boundary between the self-trapping dominant regime and the vacancy-trapping dominant regime can be distinguished. In general, pre-existing vacancies are dominant in trapping helium atoms for low fluxes and high temperatures, while self-trapping is dominant for high fluxes. These results provide important insight into the mechanisms of helium clustering for plasma facing components in fusion reactors.