A particle-in-cell simulation with Monte Carlo collisions was developed to study ion extraction from a capacitively-coupled argon plasma through a grid. A one-dimensional simulation of the plasma reactor was coupled with a two-dimensional simulation of the sheath region over a grid hole. The 13.56 MHz power applied to the plasma was pulsed 50 µs ON and 50 µs OFF. A dc bias voltage was applied in the afterglow (power OFF fraction of the cycle), to raise the plasma potential and expel ions out of the plasma through the grid. The electron temperature decayed rapidly in the afterglow, minimizing spatial variations of the plasma potential and allowing a nearly mono-energetic ion beam to be extracted. Due to the absence of plasma moulding over the grid holes, the beam was highly directional with an angular spread decreasing with increasing dc bias. The applied dc bias also set the beam energy. Simulation predictions were in good quantitative agreement with measurements. The ion beam could be neutralized by grazing angle collisions on a set of parallel neutralization plates downstream of the extraction grid, to produce a highly directional and nearly mono-energetic neutral beam.