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Diffusion of cosmic rays at EeV energies in inhomogeneous extragalactic magnetic fields

Ultra-high energy cosmic rays can propagate diffusively in cosmic magnetic fields. When their propagation time is comparable to the age of the universe, a suppression in the flux relative to the case in the absence of magnetic fields will occur. In this work we find an approximate parametrization for this suppression for energies below $\sim$ Z EeV using several magnetic field distributions obtained from cosmological simulations of the magnetized cosmic web. We assume that the magnetic fields have a Kolmogorov power spectrum with the field strengths distributed according to these simulations. We show that, if magnetic fields are coupled to the matter distribution, low field strengths will fill most of the volume, making the suppression milder compared to the case of a constant magnetic field with strength equal to the mean value of this distribution. We also derive upper limits for this suppression to occur for some models of extragalactic magnetic fields, as a function of the coherence length of these fields.