title: High-Energy Cosmic Ray Self-Confinement Close to Extra-Galactic Sources.
abstract: The ultrahigh-energy cosmic rays observed on the Earth are most likely accelerated in extra-Galactic sources. For the typical luminosities invoked for such sources, the electric current associated to the flux of cosmic rays that leave them is large. The associated plasma instabilities create magnetic fluctuations that can efficiently scatter particles. We argue that this phenomenon forces cosmic rays to be self-confined in the source proximity for energies E<E_{cut}, where E_{cut}≈10^{7}L_{44}^{2/3} GeV for low background magnetic fields (B_{0}≪nG). For larger values of B_{0}, cosmic rays are confined close to their sources for energies E<E_{cut}≈2×10^{8}λ_{10}L_{44}^{1/4}B_{-10}^{1/2} GeV, where B_{-10} is the field in units of 0.1 nG, λ_{10} is its coherence lengths in units of 10 Mpc, and L_{44} is the source luminosity in units of 10^{44} erg/s.
authors.affiliation: INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy.|Gran Sasso Science Institute (INFN), Viale F. Crispi 6, 60100 L'Aquila, Italy.
authors.forename: Pasquale
authors.initials: P
authors.lastname: Blasi
authors.affiliation: INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy.
authors.forename: Elena
authors.initials: E
authors.lastname: Amato
authors.affiliation: Gran Sasso Science Institute (INFN), Viale F. Crispi 6, 60100 L'Aquila, Italy.
authors.forename: Marta
authors.initials: M
authors.lastname: D'Angelo