We present a kinetic simulation of the plasma formed by photoionization in the intense flux of an extreme ultraviolet lithography (EUVL) light source. The model is based on the particle-in-cell plus Monte Carlo approach. The photoelectric effect and ionization by electron collisions are included. The time evolution of the low density argon plasma is simulated during and after the EUV pulse and the ion-induced sputtering of the coating material of a normal incidence collector mirror is computed. The relation between the time and position at which the ions are created and their final energy is studied, revealing how the evolution and the properties of the sheath influence the amount of sputtered material. The influence of the gas pressure and the source intensity is studied, evaluating the behavior of Ar+ and Ar2+ ions. A way to reduce the damage to the collector mirror is presented.