Abstract The stochastic acceleration of subrelativistic electrons from a background plasma is studied to find an explanation of the hard X-ray emission detected from the Coma cluster. We show that the temporal evolution of the electron distribution functions has, at its final stationary stage, a rather specific form determined by the interactions with charged background particles and electromagnetic fluctuations. These distribution functions cannot be described by simple exponential or power-law expressions. A broad transfer region is formed by Coulomb collisions at energies between the Maxwellian and power-law parts of the distribution functions. In this region the radiative lifetime of a single quasi-thermal electron differs greatly from the lifetime of the distribution function as a whole. This solves the problem of rapid cluster overheating by nonthermal electrons (Petrosian, 2001): while Petrosian's estimates are correct for nonthermal particles they are inapplicable in the quasi-thermal range.
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