Particle reacceleration by compressible turbulence in galaxy clusters:
  effects of reduced mean free path
  Direct evidence for in situ particle acceleration mechanisms in the
inter-galactic-medium (IGM) is provided by the diffuse Mpc--scale synchrotron
emissions observed from galaxy clusters. It has been proposed that MHD
turbulence, generated during cluster-cluster mergers, may be a source of
particle reacceleration in the IGM. Calculations of turbulent acceleration must
account self-consistently for the complex non--linear coupling between
turbulent waves and particles. This has been calculated in some detail under
the assumption that turbulence interacts in a collisionless way with the IGM.
In this paper we explore a different picture of acceleration by compressible
turbulence in galaxy clusters, where the interaction between turbulence and the
IGM is mediated by plasma instabilities and maintained collisional at scales
much smaller than the Coulomb mean free path. In this regime most of the energy
of fast modes is channeled into the reacceleration of relativistic particles
and the acceleration process approaches a universal behaviour being
self-regulated by the back-reaction of the accelerated particles on turbulence
itself. Assuming that relativistic protons contribute to several percent (or
less) of the cluster energy, consistent with the FERMI observations of nearby
clusters, we find that compressible turbulence at the level of a few percent of
the thermal energy can reaccelerate relativistic electrons at GeV energies,
that are necessary to explain the observed diffuse radio emission in the form
of giant radio halos.
