The dependence of the laser cooling force on velocity is strongly non-linear and consists of two narrow peaks associated with co- and counter-propagating laser beams. Under these conditions a single intrabeam scattering event can knock a particle out of the cooling range. This creates large non-Gaussian tails in the distribution function for longitudinal velocity. A theoretical model describing single and multiple intrabeam scattering is considered. A detailed analysis of the scattering and its comparison with experimental data for the ASTRID storage ring are performed.