Stochastic acceleration and nonthermal radiation in clusters of galaxies

We calculate the distribution of electrons in clusters of galaxies, which results from thermalization processes in the presence of stochastic acceleration due to plasma waves. We show that the electron distribution can deviate from a Maxwell-Boltzmann distribution because of the effect of the stochastic energy gain, provided that waves can be sustained against damping. The bremsstrahlung emission of the nonthermal tail of electrons can result in a flux of hard X-rays that is compatible with the ones recently detected in some clusters of galaxies.