| Summary: | Future hadron colliders aim at producing larger integrated luminosities by burning-off an increased fraction of the bunch particles. This burn-off removes particles unevenly in the bunch distribution generating an emittance growth. Analytical equations are derived describing the bunch distribution suffering luminosity burn-off and cooling from synchrotron radiation damping, far from the equilibrium emittance, and possibly including transverse collision offsets. This effect is evaluated for HL-LHC [G. Apollinari et al., Report No. CERN-2017-007-M, 2017], HE-LHC [A. Abada et al., Eur. Phys. J. Spec. Top. 228, 1109 (2019)EPJSAC1951-635510.1140/epjst/e2019-900088-6], and FCC-hh [A. Abada et al., Eur. Phys. J. Spec. Top. 228, 755 (2019)EPJSAC1951-635510.1140/epjst/e2019-900087-0.] and included into a step-by-step simulation of the physics fill, together with intrabeam scattering, to evaluate impact on performance.
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