Diffusive shock acceleration in extragalactic jets

We calculate the temporal evolution of distributions of relativistic electr ons subject to synchrotron and adiabatic processes and Fermi-like accelerat ion in shocks. The shocks result from Kelvin-Helmholtz instabilities in the jet. Shock formation and particle acceleration are treated in a self-consi stent way by means of a numerical hydrocode. We show that in our model the number of relativistic particles is conserved during the evolution, with no need of further injections of supra-thermal particles after the initial on e. From our calculations, we derive predictions for values and trends of qu antities like the spectral index and the cutoff frequency that can be compa red with observations.