The nonlinear space charge effect of bunched beam in linac is one of the important factors that induces the emittance growth due to the conversion of the field energy to kinetic energy. In this paper, using a cylinder model of space charge in linac, we derived the internal energy for a bunched beam with some nonuniform space charge distributions, such as Gaussian, waterbag and parabolic distributions in both longitudinal and transverse directions. And the emittance growth caused by these nonuniformities is worked out.
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