  The recent discoveries of several reliable events of high energy cosmic rays
at an energy above 10^20 eV raise questions about their path through the nearby
universe. The two analyses of the Haverah Park data set and the Akeno data set
appear to have an inconsistent pattern. Both data sets showed some measure of a
correlation with the supergalactic plane, the locus of cosmologically nearby
galaxies, radio galaxies and clusters of galaxies. We need a reasonable model
of the true intergalactic magnetic field. Using recent cosmological simulations
of structure formation in the universe, we estimate the magnetic fields which
correspond to the upper limits in the Rotation Measure to distant radio
sources. We estimate that the magnetic field strength in supergalactic sheets
and filaments may be in the range of 0.1 to 1 muG. If such strengths are
realized inside our Local Supercluster, this opens up the possibility to focus
charged particles in the direction perpendicular to the supergalatic plane,
analoguously but in the opposite direction to solar wind modulation. If
focusing exists, it means that for all particles captured into the sheets, the
dilution with distance d is 1/d instead of 1/d^2. This means in effect, that we
may see sources to much larger distances than expected sofar. This effect is
relevant only for energies for which the possible distances are smaller than
the void scale of the cosmological galaxy distribution, in the range possibly
up to 100 Mpc.
