Allegra Firinu, Franco Vazza, Carmelo Evoli

The origin of ultra-high-energy cosmic rays (UHECRs) remains an open question. Extragalactic magnetic fields can modify their propagation and, at sufficiently low energies, suppress the observed flux through the magnetic horizon (MH) effect.} {We quantify the impact of the MH on the propagation of UHECR protons using cosmological simulations and a dedicated numerical framework that follows cosmic rays in a time-evolving background.} {We use \texttt{UMAREL}, a parallel code developed for this study, to propagate UHECR protons through a cosmological volume simulated with ENZO. The magnetic-field configurations are chosen to be consistent with recent radio constraints on magnetic fields in cosmic-web filaments. Unlike stationary approaches, we follow particle trajectories through a sequence of time-evolving snapshots and compare the resulting arrival properties with those in an unmagnetised reference model.} {We find that observationally motivated extragalactic magnetic fields progressively suppress the flux of arriving protons below \(E \lesssim 3 \times 10^{19}\,\mathrm{eV}\) through an effective Magnetic Horizon (MH). We estimate \(R_{\mathrm{MH}} \sim 50\,\mathrm{Mpc}\) for protons with \(E = 10^{18}\,\mathrm{eV}\) and \(R_{\mathrm{MH}} \sim 150\,\mathrm{Mpc}\) for protons with \(E = 10^{19}\,\mathrm{eV}\).} {The MH generated by extragalactic magnetic fields must be taken into account when modelling UHECR propagation and interpreting the spectrum observed in the local Universe.}