  We study the evolution of magnetized clusters in a cosmological environment
using magneto-hydro dynamical simulations. Large scale flows and merging of
subclumps generate shear flows leading to Kelvin-Helmholtz instabilities,
which, in addition to the compression of the gas where the magnetic field is
frozen in, further amplify the magnetic field during the evolution of the
cluster. Therefore, well-motivated initial magnetic fields of
$<B^2>^{1/2}=10^{-9} {\rm G}$ reach the observed $\sim\mu{\rm G}$ field
strengths in the cluster cores at $z=0$. These magnetized clusters can be used
to study the final magnetic field structure, the dynamical importance of
magnetic fields for the interpretation of observed X-Ray properties, and help
to constrain further processes in galaxy clusters like the population of
relativistic particles giving rise to the observed radio halos or the behavior
of magnetized cooling flows.
