The ultra-high energy cosmic ray sources are most likely extragalactic. For the commonly invoked luminosities of the potential sources, the electric current associated with escape flux of cosmic ray may be very large. The plasma instabilities associated with the cosmic ray streaming create magnetic perturbations that can scatter particles, forcing them to diffuse rather than stream freely, as usually assumed. The non-resonant branch of the streaming instability is excited if the level of the background magnetic field is below its saturation value $B_{sat} \sim 10$ nG, in agreement with actual bounds. We investigate the growth of the instability and its effect on the particle's transport close to the source. We argue that, for typical values assumed for the source parameters, cosmic rays of energy $E < 10^{17}$ eV are confined in the source proximity, and the cosmic ray spectrum propagating in the Universe is suppressed below this energy.