  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.
