Phenomenology of Ultra-High Energy Cosmic Rays Self Confinement in Cosmic Filaments

We discuss the self-induced confinement of ultra-high-energy cosmic rays near their sources, as driven by the excitation of the Non-Resonant Streaming Instability in the intergalactic medium. For a standard source spectrum, the current associated with the escaping UHECRs excites perturbations through Non-Resonant Streaming Instability, leading to Bohm diffusion in self-generated nG-scale fields. This process forms magnetized cocoons around powerful UHECR sources, significantly delaying particle escape. For rigidities below 1 EV, the confinement time exceeds the age of the Universe, naturally suppressing the low-rigidity flux of escaping cosmic rays. We present a phenomenological model that accounts for the UHECR prolonged confinement near sources over cosmological timescales, showing how this mechanism may explain the hard UHECR spectra needed to match the spectrum and composition observations from the Pierre Auger Observatory and Telescope Array. Finally, we quantify the diffuse neutrino contribution from confined protons, which exceeds the standard cosmogenic neutrino background in the 100 PeV energy range, and compare it against current IceCube, Auger, and KM3Net constraints.