A first-order analytical investigation on emittance evolution of relativistic space-charge dominated beams

The evolution of both correlated emittance and slice emittance due to nonlinear space-charge force of relativistic cylindrical beams in a general photoinjector beamline are investigated analytically in first-order approximation and based on envelope analysis, in order to clarify the relation between the evolution of the two kinds of emittance. The first-order analysis shows that slice emittance due to transverse nonlinear space-charge force and correlated emittance have similar behavior in a general photoinjector if energy spread is neglected and phase space wave breaking does not happen. Furthermore, the two kinds of emittance have the same dependence on propagating distance for specific initial-phase space. As another result of the first-order analysis, the evolution of the two kinds of emittance in drift space can be depicted analytically as a function of only the propagating distance and several parameters determined by the initial-phase space. The analytical expressions predict that two emittance compensation points exist when some constraints on the initial-phase space are fulfilled, which may correspond to the well-known double emittance minimum phenomenon often observed in simulations of photoinjectors. Parmela simulations are carried out to verify the analytical results and are in good agreement to the analytical results.