In the present work we focus on the interplay between stochastic acceleration of charged particles and radiation processes in a region of turbulent magnetized plasma, setting the framework for an ‘one-zone’ radiation-acceleration model for Gamma-Ray Burst (GRB) afterglows. Specifically, we assume that the particle distribution is isotropic in space and treat in detail the particle propagation in the momentum-space. The electron distibution is modified by the acceleration, synchrotron and Synchrotron Self-Compton (SSC) radiation and escape processes. The magnetic field as well as the particle injection rate are functions of time as measured in the comoving frame of the blast wave. In order to study the dynamical evolution of this system, we numerically solve the time-dependent Fokker-Planck equation for the electron distribution and present the obtained particle and photon spectra of an indicative example.
