On the production of very high energy beamed gamma-rays in blazars
  The variable flux of TeV gamma-rays detected from Mkn 421 and Mkn 501 requires the presence of high energy electrons, which could in principle produce large numbers of electron/positron pairs, leading to an electromagnetic cascade. We point out that this scenario can be avoided if electrons are accelerated to high energy rectilinearly, rather than being injected isotropically into a blob, as in most of the models of the GeV gamma-ray emission. By balancing linear acceleration by an electric field against inverse Compton losses in the radiation field of the accretion disk we calculate the emitted spectra and find the conditions which must be fulfilled in order to exclude the development of electromagnetic cascades during acceleration. Assuming these to be fulfilled, we show that the maximum possible photon energy is approximately $10M_8^{2/5}\,$TeV, where $M_8$ is the mass of the central black hole in units of $10^8\,\msolar$. In addition we compute the optical depth to absorption of TeV photons on a possible isotropic scattered component and on the observed nonthermal radiation (in the case of Mkn 421) and find that TeV photons can escape provided the nonthermal X-rays originate in a jet moving with a Lorentz factor of around 8. 
W. Bednarek (MPI Kernphysik, Heidelberg and University of Lodz,   Poland), J.G. Kirk and A. Mastichiadis (MPI Kernphysik, He...