Abstract: In this paper, the motion of the electron cloud in ideal long space-chargelens is studied. For the space-charge lens in a definite working condition, thestate of its electron cloud canbe described by three parameters: magnetic confin-ement factor, electron temperature and electron density in centre of lens. Theseparameters determine the size, shape and electron density distribution of electroncloud. Therefore, they also determine the electric field distribution and focusingproperties of lens. Numerical method is used for computation of electron densityand elcctric potential.