Nonlinear dynamics of proton beams with hollow electron lens in the CERN high-luminosity LHC D. Mirarchi, R. B. Appleby, R. Bruce, M. Giovannozzi, A. Mereghetti, S. Redaelli and G. Stancari Eur. Phys. J. Plus, 137 1 (2022) 7 Published online: 13 December 2021 DOI: 10.1140/epjp/s13360-021-02201-5