Aims. This paper introduces a kinetic code that simulates gamma-ray burst (GRB) afterglow emission from the external forward shock and presents examples of some of its applications. One interesting research topic discussed in the paper is the high-energy radiation produced by Compton scattering of the prompt GRB photons against the shock-accelerated electrons. The difference between the forward shock emission in a wind-type and a constant-density medium is also studied, and the emission due to Maxwellian electron injection is compared to the case with pure power-law electrons.

Methods. The code calculates the time-evolving photon and electron distributions in the emission region by solving the relativistic ki- netic equations for each particle species. For the first time, the full relativistic equations for synchrotron emission/absorption, Compton scattering, and pair production/annihilation were applied to model the forward shock emission. The synchrotron self-absorption ther- malization mechanism, which shapes the low-energy end of the electron distribution, was also included in the electron equation. Results. The simulation results indicate that inverse Compton scattering of the prompt GRB photons can produce a luminous 􏰀TeV emission component, even when pair production in the emission region is taken into account. This very high-energy radiation may be observable in low-redshift GRBs. The test simulations also show that the low-energy end of a pure power-law distribution of electrons can thermalize owing to synchrotron self-absorption in a wind-type environment, but without an observable impact on the radiation spectrum. Moreover, a flattening in the forward shock X-ray light curve may be expected when the electron injection function is assumed to be purely Maxwellian instead of a power law. The flux during such a flattening is likely to be lower than the Swift/XRT sensitivity in the case of a constant-density external medium, but a wind environment may result in a higher flux during the shallow decay.