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The nonlinear space charge effect of bunched beam in linac is one of theimportant factors that induces the emittance growth due to the conversion of thefield energy to kinetic energy. Using a cylinder model of space charge in a linac,we derive the internal energy for a bunched beam with some nonuniform spacecharge distributions, such as Gaussian, waterbag and parabolic distributions inboth the longitudinal and transverse directions. And the emittance growth causedby these nonuniformities is worked out.
The nonlinear space charge effect of bunched beam in linac is one of theimportant factors that induces the emissiontance growth due to the conversion of thefield energy to kinetic energy. Using a cylinder model of space charge in a linac, we derive the internal energy for a bunched beam with some nonuniform spacecharge distributions, such as Gaussian, waterbag and parabolic distributions inboth the longitudinal and transverse directions. And the emittance growth caused by these nonuniformities is worked out.