A self-consistent kinetic particle-in-cell model has been developed to describe a radiation driven plasma. Collisions between charged species and the neutral background are represented statistically by Monte Carlo collisions. The weakly ionized plasma is formed when extreme ultraviolet radiation coming from a pulsed discharge photoionizes a low pressure argon gas. The presence of a plasma close to optical components is potentially dangerous in case the ions that are accelerated in the plasma sheath gain enough energy to sputter the optics. The simulations predict the plasma parameters and notably the energy at which ions impact on the plasma boundaries. Finally, sputter rates are estimated on the basis of two sputtering models.