Supernova remnants are expected to contain braided (or stochastic) magnetic fields, which are in some regions directed mainly perpendicular to the shock normal. For particle acceleration due to repeated shock crossings, the transport in the direction
of the shock normal is crucial. The mean squared deviation along the shock normal is then proportional to the square root of the time. This kind of anomalous transport is called sub-diffusion. We use a Monte-Carlo method to examine this non-Markovian transport and the acceleration. As a result of this simulation we are able to examine the propagator, density and pitch-angle distribution of accelerated particles, and especially the spectral properties. These are in broad agreement with analytic predictions for both the sub-diffusive and the diffusive regimes, but the steepening of the spectrum predicted when changing from diffusive to sub-diffusive transport is found to be even more pronounced than predicted.
We present a model of the spectra of gamma-ray emitting blazars in which a single homogeneous emission region both emits synchrotron photons directly and scatters them to high (gamma-ray) energy before emission (a ``synchrotron self-Compton or SSC mo
del). In contrast to previous work, we follow the full time dependent evolution of the electron and photon spectra, assuming a power-law form of the electron injection and examine the predictions of the model with regard to variability of the source. We apply these computations to the object Mkn 421, which displayed rapid variability in its X-ray and TeV emission during a multiwavelength campaign in 1994. This observation strongly implies that the same population of electrons produces the radiation in both energy bands. By fitting first the observed quiescent spectrum over all 18 orders of magnitude in frequency, we show that the time dependence of the keV/TeV flare could have been the result of a sudden increase in the maximum energy of the injected electrons. We show also that different types of flare may occur in this object and others, and that the energy band most sensitive to the properties of the acceleration mechanism is the X-ray band.
