Stochastic Acceleration and Non-Thermal Radiation in Clusters of Galaxies

We calculate the distribution of electrons in clusters of galaxies, resulting 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, due to the effect of the stochastic energy gain, provided waves can be sustained against damping. The non-thermal tail of electrons can generate as bremsstrahlung emission a flux of hard X-rays compatible with the ones recently detected in some clusters of galaxies.