We present a numerical model for particle-electron-
acceleration and radiation inside the body of an extragalactic jet. We
model the jet environment as a turbulent medium generating non-linear
structures (eddies and/or shocks) through a cascading process.
These structures act like in-situ accelerators for
the electrons, initially injected from the central engine.
Two types of acceleration processes are considered: second order Fermi
acceleration and shock drift acceleration depending on the velocity
of the non-linear structures encountered.
We study the modulation of the energy distribution
of electrons in such an environment, by incorporating synchrotron
radiation losses at the time intervals between successive interactions of
the particles with the turbulent structures. By performing a parametric
study with respect to the level of turbulent activity and the time
intervals between interactions, we calculate the
temporal evolution of the cut-off frequency of the synchrotron radiation
spectrum of the particles and discuss our results in connection to
recent observations.
keywords : Acceleration of particle - Shock waves - Turbulence - synchrotron radiation