A Song of Shocks and Dynamo: Numerical Studies of a Galaxy Cluster
  Merger in the HIMAG Project
  With ENZO simulations run on the J\"ulich supercomputers, we have
investigated the evolution of magnetic fields in the largest cosmic structures
(namely galaxy clusters and filaments connecting them) with unprecedented
dynamical range. These simulations revealed the full development of the
small-scale dynamo in Eulerian cosmological magneto-hydrodynamical simulations.
The turbulent motions developed during the formation of clusters are energetic
enough to foster the growth of magnetic fields by several orders of magnitude,
starting from weak magnetic fields up strengths of $\sim \rm \mu G$ as
observed. Furthermore, shock waves are launched during cluster formation and
they are able to accelerate cosmic-ray electrons, that emit in the radio
wavelengths. Radio observations of this emission provide information on the
local magnetic field strength. We have incorporated, for the first time, the
cooling of cosmic-ray electrons when modelling this emission. In this
contribution, we present our advances in modelling these physical processes.
Here, we mostly focus on the most interesting object in our sample of galaxy
clusters, which shows the complexity of magnetic fields and the potential of
existing and future multi-wavelengths observations in the study of the weakly
collisional plasma on $\sim$ Megaparsecs scales.
