Cosmic rays in galaxy clusters and their non-thermal emission
  Radio observations prove the existence of relativistic particles and magnetic
field associated with the intra-cluster-medium (ICM) through the presence of
extended synchrotron emission in the form of radio halos and peripheral relics.
This observational evidence has fundamental implications on the physics of the
ICM. Non-thermal components in galaxy clusters are indeed unique probes of very
energetic processes operating within clusters that drain gravitational and
electromagnetic energy into cosmic rays and magnetic fields. These components
strongly affect the (micro-)physical properties of the ICM, including viscosity
and electrical conductivities, and have also potential consequences on the
evolution of clusters themselves. The nature and properties of cosmic rays in
galaxy clusters, including the origin of the observed radio emission on
cluster-scales, have triggered an active theoretical debate in the last decade.
Only recently we can start addressing some of the most important questions in
this field, thanks to recent observational advances, both in the radio and at
high energies. The properties of cosmic rays and of cluster non-thermal
emissions depend on the dynamical state of the ICM, the efficiency of particle
acceleration mechanisms in the ICM and on the dynamics of these cosmic rays. In
this review we discuss in some detail the acceleration and transport of cosmic
rays in galaxy clusters and the most relevant observational milestones that
have provided important steps on our understanding of this physics. Finally,
looking forward to the possibilities from new generations of observational
tools, we focus on what appear to be the most important prospects for the near
future from radio and high-energy observations.
