  There is now firm evidence that the ICM consists of a mixture of hot plasma,
magnetic fields and relativistic particles. The most important evidences for
non-thermal phenomena in galaxy clusters comes from the diffuse Mpc-scale
synchrotron radio emission (radio halos) observed in a growing number of
massive clusters (Feretti 2003) and from hard X-ray (HXR) excess emission
(detected in a few cases) which can be explained in terms of IC scattering of
relativistic electrons off the cosmic microwave background photons
(Fusco-Femiano et al. 2003). There are now growing evidences that giant radio
halos may be naturally accounted for by synchrotron emission from relativistic
electrons reaccelerated by some kind of turbulence generated in the cluster
volume during merger events (Brunetti 2003). With the aim to investigate the
connection between thermal and non-thermal properties of the ICM, we have
developed a statistical magneto-turbulent model which describes the evolution
of the thermal and non-thermal emission from clusters. We calculate the energy
and spectrum of the magnetosonic waves generated during cluster mergers, the
acceleration and evolution of relativistic electrons and thus the resulting
synchrotron and inverse Compton spectra. Here we give a brief description of
the main results, while a more detailed discussion will be presented in a
forthcoming paper. Einstein-De Sitter cosmology, $H_o=50$ km
$s^{-1}$$Mpc^{-1}$, $q_o=0.5$, is assumed.
