Magneto-turbulent cosmic ray acceleration in galaxy clusters

The aim of this paper is constructing a magneto-turbulent model for the radio halo. Energy of the cosmic ray electrons is gained through a number of pitch angle scattering by Alfven waves. We evaluate the energy spectrum of the turbulent Alfven waves reproducing the observed radio spectrum of the Coma radio halo. We find that the index of the energy spectrum of the turbulent Alfven waves is 2.8, and the energy density for the acceleration is five orders of magnitudes smaller than that of the large-scale-field which is supposed to be similar to 1 muG.