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TY - CONF AU - Kaltchev, D. ED - Liu, Lin ED - Byrd, John M. ED - Neuenschwander, Regis T. ED - Picoreti, Renan ED - Schaa, Volker R. W. TI - Two-Dimensional Beam-Beam Invariant with Applications to HL-LHC J2 - Proc. of IPAC2021, Campinas, SP, Brazil, 24-28 May 2021 CY - Campinas, SP, Brazil T2 - International Particle Accelerator Conference T3 - 12 LA - english AB - Long-range beam-beam interactions represent the most severe limitation on the performance and achievable luminosity of circular collider. The paper presents a two-dimensional nonlinear Courant Snyder Invariant derived to first order in the beam-beam perturbation and based on the two-dimensional coefficients in the Fourier expansion of the Beam-beam Hamiltonian. Its validity in case of HL-LHC lattices with realistic beam-beam setup is verified with MadX tracking. PB - JACoW Publishing CP - Geneva, Switzerland SP - 3301 EP - 3304 KW - optics KW - resonance KW - closed-orbit KW - lattice KW - luminosity DA - 2021/08 PY - 2021 SN - 2673-5490 SN - 978-3-95450-214-1 DO - doi:10.18429/JACoW-IPAC2021-WEPAB280 UR - https://jacow.org/ipac2021/papers/wepab280.pdf ER -