Left panels: time evolution of the observer frame photon spectrum (top panel) and electron distribution (bottom panel) resulting from relativistic Maxwellian electron injection in a constant-density ISM. The radiation processes are synchrotron emission/absorption, Compton scattering and pair production/annihilation. The simulation parameters are E₀ = 10⁵²erg, n₀ = 1 cm^-3, ϵ_e = 10^-2, ϵ_B = 10^-4 and Γ₀ = 200, and the redshift is z = 1. The Maxwellian injection function has the temperature T′ ~ ϵ_eΓm_pc²/k. Right panels: evolving particle distributions in the case of a power-law electron injection with s = 2.5. The other parameters are the same as in the simulation with Maxwellian injection.