Definition of all possible cases for the radiative regime and the distribution of electrons in the plane γ₀ vs γ_self. The Lorentz factors γ_m and γ_c are indicated by red and green solid lines either in the fast-cooling regime with γ_m > γ_c (left) or in the slow-cooling regime with γ_m < γ_c (right). The black solid line in the left panel corresponds to γ₀ = γ_self. The two Lorentz factors ${\widehat{\gamma }}_{\mathrm{m}}$ (red) and ${\widehat{\gamma }}_{\mathrm{c}}$ (green) are plotted in dashed lines. In some regions, additional Lorentz factors relevant to identify the radiative regime are also plotted: ${\stackrel{\sim }{\gamma }}_{\mathrm{m}}$ (red dotted line) and ${\stackrel{\sim }{\gamma }}_{\mathrm{c}}$ (green dotted line). The regions where there is no impact of the SSC cooling on the distribution of electrons are shaded in orange (${\widehat{\gamma }}_{\mathrm{m},\mathrm{c}}<{\gamma }_0<{\gamma }_{\mathrm{c}}$) and blue (${\gamma }_0<{\widehat{\gamma }}_{\mathrm{m},\mathrm{c}}$). This diagram allows to identify all possible orderings of γ₀, γ_m, γ_c, ${\widehat{\gamma }}_{\mathrm{m}}$, ${\widehat{\gamma }}_{\mathrm{m}}$ defining all possible radiative regimes. The corresponding limits for γ_self are indicated by vertical black dashed lines. All the possible cases are listed in Table B.1 (fast cooling) and B.2 (slow cooling). In practice, several cases have the same breaks and slopes for f(x) and h(x) and can therefore be treated simultaneously in the numerical implementation of the model. This allows to group (F1,F2,F3,F4,F5), (F8,F13,F14), (F9,F15,F16), (F10,F17), (F20,F21), (F22,F23), (S1,S2,S3,S4,S5,S6,S7), (S8,S9), (S10,S12,S13) and (S11,S14).