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Numerical methods have been used to study the filling of the energy-phase plane and the evolution of the beam during capture time. Beam shapes and distribution of particle densities can thus be obtairrd at various instants in phase and median planes. The results are meant to be used in studying space charge effects during injection.doi:10.1063/1.2946365 fatcat:ik3yokd4crfi7apz7thz652oaa