The origin of the microgauss magnetic fields in galaxy clusters is one of the outstanding problems of modern cosmology. We have performed three-dimensional particle-in-cell simulations of the nonrelativistic Weibel instability in an electron-proton plasma, in conditions typical of cosmological shocks. These simulations indicate that cluster fields could have been produced by shocks propagating through the intergalactic medium during the formation of large-scale structure or by shocks within the cluster. The strengths of the shock-generated fields range from a few nanogauss in the intercluster medium to a fraction of a microgauss inside galaxy clusters. Further amplification of these fields by sheared turbulent motions and gas accretion in clusters may be expected. Thus, cluster fields may be explained without resorting to the amplification of a primordial field.
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