Self-fields and forces as well as the local degree of space-charge neu
tralization in overcompensated electron beams are considered. The radi
al variation of the local degree of space-charge neutralization is ana
lysed. A novel model which describes the equilibrium potential distrib
ution in overcompensated beams is proposed and a method for computer s
imulation of the beam propagation is described. Results from numerical
experiments which illustrate the propagation of finite emittance over
neutralized beams are presented.