We are dealing with the problem of the charge distribution within an i
nsulator (present application: SiO2) which is bombarded by a narrow el
ectron beam. The electron trajectories within the sample are simulated
via a single diffusion Monte-Carlo method. A mathematical model is pr
oposed for the potential and the charge density. The development of an
electric field, a potential and the broadening of the incident beam a
re taken into account. These two last distributions appear to have a p
rominent effect. It is shown that the charge distribution tends to a d
ouble layer; the shape and thickness of positive and negative distribu
tions are given.