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A fully self-consistent extension to the SSC model with particle
acceleration due to shock
and stochastic acceleration (Fermi-I and Fermi-II-Processes
respectively) in a twozone-SSC model, i.e. two spatially homogenous
and isotropic emitting spheres, is presented. The emphasis lies on the
influence of the implemented acceleration processes on the electron
spectra in the twozone-SSC model. We find that shock acceleration in
competition with radiative synchrotron losses of the electrons leads
to falling powerlaw electron spectra depending only on the ratio of
the timescale of the catastrophic electron escape losses and the
intrinsic acceleration timescale itself. Whereas stochastic processes
leading to the exponential cutoff at high electron energy regimes and
to rising powerlaw specta at small electron Lorentz-factors $gamma$
thus explaining recent observational data e.g. from PKS2155 observed
by FERMI in Aug/Sept 2008. Concluding the validity of the implemented
hard-sphere approximation of the plasma instabilities and the limits
of such a simple acceleration model (only two well known acceleration
mechanisms) for a highly relativistc jet system shall be discussed.
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