Combined influence of beamstrahlung and coupling impedance on beam energy spread and length in future lepton colliders

A semianalytical model has been developed to study a combined effect of beamstrahlung due to beam-beam interaction and beam coupling impedance in the future lepton colliders CEPC and FCC-ee. This model allows evaluating an impact of the coupling impedance on the bunch length and energy spread in collision. The model is benchmarked against numerical simulations. Analytical estimates for the supercolliders are presented.