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An analytical investigation of beamstrahlung-induced blow-up in Gaussian beams with arbitrary dimensions is presented, using various approximations for the strength of the hourglass effect and crab waist scheme. The results, applied to the FCC-ee resonances, are compared with simulations and previous calculations, and relative luminosity values are also calculated. The stability of resultant conformations are analysed to rule out the existence of a flip-flop phenomenon in the longitudinal plane analogous to the well-known transverse counterpart. Implications for the top-up injection procedures are discussed, and a phenomenological model is proposed to study the transverse-longitudinal coupling in the blowup dynamics.
Nguyen et al. (Sat,) studied this question.
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