The ion distribution function is calculated as a function of time, sel
f-consistently with the electrostatic potential in two spatial coordin
ates for a pulsed sheath experiment. Such pulsed sheaths are used for
a variety of purposes, including modification of material surfaces. Th
e accuracy of the model is established by comparing the time varying i
on density with experimental measurements. Additionally, the first rep
orted prediction of the ion velocity distribution in this kind of puls
ed sheath is given. This is important because the velocity distributio
n of the ions striking the surface determines how the surface material
is modified.