The origin of relativistic particles that generate the observed synchrotron radio emission in the Intra-Cluster-Medium (ICM) of galaxy clusters is one of the most mysterious problems in our understanding of these complex systems. Recent advances from observations and theory suggest that turbulence, generated during cluster-cluster mergers, has a major impact on the acceleration of relativistic particles in the ICM. We propose a 2-year project to develop advanced cosmological numerical simulations to model self-consistently the acceleration of cosmic-rays in the turbulent ICM and the resulting non-thermal emission on cluster scales, radio halos. Our simulations will provide a significant step forward in the field and yield direct predictions for radio telescopes. They will shed light on the origin of the observed radio emission and the important issue of the interplay between thermal and non-thermal components in galaxy clusters. Upcoming european projects like the LOFAR telescope are expected to discover thousands for radio halos and are going to directly benefit from our project. This promises a golden age of discoveries in this field and make our proposed project particularly timely.