A good understanding of the luminosity performance in a collider, as well as reliable tools to analyse, predict, and optimise the performance, is of great importance for the successful planning and execution of future runs. In this article, we present two different models for the evolution of the beam parameters and the luminosity in heavy-ion colliders. The first, Collider Time Evolution is a particle tracking code, while the second, the Multi-Bunch Simulation is based on the numerical solution of ordinary differential equations for beam parameters. As a benchmark, we compare simulations and data for a large number of physics fills in the 2018 Pb–Pb run at the CERN Large Hadron Collider (LHC), finding excellent agreement for most parameters, both between the simulations and with the measured data. Both codes are then used independently to predict the performance in future heavy-ion operation, with both Pb–Pb and p–Pb collisions, at the LHC and its upgrade, the high-luminosity LHC. The use of two independent codes based on different principles gives increased confidence in the results.

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The proton-lead runs of the LHC in 2012, 2013 and 2016 provided luminosity far beyond expectations in a diversity of operating conditions and led to important new results in high-density QCD. This has permitted the scope of the future physics programme to be expanded in a recent review. Besides further high-luminosity proton-lead (p–Pb) collisions, lighter nuclei are also under consideration. A short proton-oxygen run, on the model of the 2012 p-Pb run, would be of interest for cosmic-ray physics. Collisions of protons with argon, other noble gases and nuclei of lighter metals are also discussed. We provide an overview of the operational strategies and potential performance of various options. Potential performance limits from moving beam-beam encounters at injection and various beam-loss mechanisms are evaluated in the light of our understanding of the LHC to date.

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