Abstract

A simple model of cosmic ray electron acceleration at the jet boundary yields a power law particle energy distribution of ultra-relativistic electrons with an energy cut-off growing with time, and, finally, a growing particle bump at the energy where energy gains equal radiation losses. For such electron distribution, in tens-of-kpc scale jets, we derived the observed time-varying spectra of synchrotron and inverse Compton radiation, including Comptonisation of synchrotron and cosmic microwave background photons. Slowly varying spectral index along the jet in the ‘low frequency’ spectral range is a natural consequence of boundary layer acceleration. Variations of the high energy bump of the electron distribution can give rise to anomalous behaviour in the X-ray band in comparison to the lower frequencies.