Cosmic ray nonlinear processes in gamma-ray sources

The interaction of cosmic ray (CR) particles (protons, nuclei and electrons) with matter determine the main processes of high energy gamma-ray (GR) generation through neutral pions decay and bremsstrahlung emission. On the other side, the acceleration and propagation of these particles is mainly determined by nonlinear processes of CR in GR sources: the influence of CR pressure on plasma dynamics; the influence of kinetic stream instability on the small-scale magnetic structure of plasma (generation of Alfven wave turbulence, etc.). The Alfven wave turbulence influences the CR propagation and acceleration, i.e. the distribution of CR pressure and, therefore, the distribution of matter. These effects are nonlinear and it is necessary to consider self-consistent problems. First, we will consider the expected distribution of local and outer CR particles and the matter distribution in some types of GR sources, by taking into account CR nonlinear processes. Second, we will estimate the expected GR intensity generated by local and outer CR for outer and inner observers.