Propagation of ultra-high energy protons in regular extragalactic magnetic fields

We study the proton flux expected from sources of ultra high energy cosmic rays (UHECR) in the presence of regular extragalactic magnetic fields. It is assumed that a local source of ultra-high energy protons and the magnetic field are all in a wall of matter concentration with dimensions characteristic of the supergalactic plane. For a single source, the observed proton flux and the local cosmic ray energy spectrum depend strongly on the strength of the field, the position of the observer, and the orientation of the field relative to the observer's line of sight. Regular fields also affect protons emitted by sources outside the local magnetic fields structure. We discuss the possibility that such effects could contribute to an explanation of the excess of UHECR above $5.10^{19}$ eV, and the possibility that sources of such particles may be missed if such magnetic fields are not taken into account.