High-Energy Cosmic Ray Self-Confinement Close to Extra-Galactic Sources

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 approximate to 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 approximate to 2 x 10(8)lambda(10) (L44B-101/2)-B-1/4 GeV, where B-10 is the field in units of 0.1 nG, lambda(10) is its coherence lengths in units of 10 Mpc, and L-44 is the source luminosity in units of 10(44) erg/s.