Faraday rotation and synchrotron emission from extragalactic radio sources give evidence for the presence of magnetic fields extending over ~Mpc scales. However, the origin of these fields remains elusive. With new high-resolution grid simulations we studied the growth of magnetic fields in a massive galaxy cluster that in several aspects is similar to the Coma cluster. We investigated models in which magnetic fields originate from primordial seed fields with comoving strengths of 0.1 nG at redshift z=30. The simulations show evidence of significant magnetic field amplification. At the best spatial resolution (3.95 kpc), we are able to resolve the scale where magnetic tension balances the bending of magnetic lines by turbulence. This allows us to observe the final growth stage of the small-scale dynamo. To our knowledge this is the first time that this is seen in cosmological simulations of the intracluster medium. Our mock observations of Faraday Rotation provide a good match to observations of the Coma cluster. However, the distribution of magnetic fields shows strong departures from a simple Maxwellian distribution, suggesting that the three-dimensional structure of magnetic fields in real clusters may be significantly different than what is usually assumed when inferring magnetic field values from rotation measure observations.
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