Ellis R. Owen, Kinwah Wu, Yoshiyuki Inoue, Tatsuki Fujiwara, Qin Han, Hayden P. H. Ng

Cosmological filaments, galaxy clusters, and galaxies are magnetized reservoirs of cosmic rays (CRs). The exchange of CRs across these structures is usually modeled assuming that they remain charged and magnetically confined. At high energies, hadronic interactions can convert CR protons to neutrons. This physics is routinely included in air-shower and ultra-high-energy (UHE) CR propagation Monte Carlo simulations used for composition studies but is rarely treated explicitly in propagation models of CR transport and exchange between magnetized reservoirs. CR neutrons are not affected by magnetic fields and can propagate ballistically over kpc-Mpc distances before decaying back into protons, with relativistic time dilation extending their effective decay length. We show how such charged-neutral switching modifies CR confinement and escape in four representative environments: a Milky Way-like galaxy, a starburst galaxy, a galaxy cluster, and a cosmological filament. By solving the transport of a confined CR proton population in each structure using a diffusion/streaming propagation approach with hadronic pp and p$γ$ interactions, and treating neutron production and decay as a stochastic Poisson ''jump'' process, we find that neutron-mediated steps can allow additional CR escape from large-scale cosmological structures at energies where charged-particle transport alone would predict strong CR confinement and attenuation in ambient radiation fields. These effects imply a qualitative shift in how ultra-high-energy CRs are transferred from embedded sources into filaments and voids once intermediate neutron propagation is considered, with consequences for the partitioning of CRs across the large-scale structure of the Universe.