**2. The Afterglow Model**

Afterglow emission refers to all the broad-band radiation observed from a GRB on longer timescales (minutes to months) as compared to the initial prompt radiation detected in hard X-rays [38,47,48]. Its temporal evolution is usually well described with simple decaying power-laws, in contrast with the short-time (<seconds) variability that characterizes the prompt emission [49–52]. These major differences place the emission region of afterglow radiation at larger radii (>10<sup>15</sup> cm), pinpointing its origin in the processes triggered by the interaction between the jet and the circumburst medium.

The expansion of the relativistic jet into the external medium is expected to drive two different shocks: the forward shock, running into the external medium, and the reverse shock, running into the jet. The shocked ejecta and the shocked external medium, separated by the contact discontinuity, are both sources of synchrotron radiation from the accelerated electrons [53]. Most of the detected radiation is interpreted as emission from ambient particles energized by the forward shock. Spectra and lightcurves are then shaped by the environment where the GRB explodes, which in turn is strictly connected to the nature of the progenitor. The other player that shapes the properties of afterglow radiation is particle acceleration at relativistic shocks, which is thought to proceed via diffusive shock acceleration, but for which the details of the underlying physics still remain poorly constrained. Moreover, the overall luminosity of the afterglow radiation depends on the energy content of the blast-wave. Such an amount is determined by how efficiently the prompt mechanism has dissipated and released part of the initial explosion energy. Following these considerations, it is evident how the study of afterglow radiation impacts on the general understanding of the GRB phenomenon: the progenitor and its environment, the nature and efficiency of the mechanisms responsible for prompt emission, the properties of the jet, and the micro-physics of relativistic shocks.

In this section, the physics involved in the afterglow scenario is presented, with a particular focus on the forward shock emission and on the radiative output expected at VHE. This section is organized as follows: we revisit the physics of the jet dynamical evolution in its interaction with the ambient medium (Section 2.1), the particle acceleration mechanism (Section 2.2) and the resulting radiative output and its spectral shape (Section 2.3).
