Abstract
Recent advances on gamma-ray observations from SuperNova Remnants and
Molecular Clouds offer the possibility to study in detail the properties of the
propagation of escaping Cosmic Rays (CR). However, a complete theory for CR
transport outside the acceleration site has not been developed yet. Two
physical processes are thought to be relevant to regulate the transport: the
growth of waves caused by streaming instability, and possible wave damping
mechanisms that reduce the growth of the turbulence. Only a few attempts have
been made so far to incorporate these mechanisms in the theory of CR diffusion.
In this work we present recent advances in this subject. In particular, we show
results obtained by solving the coupled equations for the diffusion of CRs and
the evolution of Alfven waves. We discuss the importance of streaming
instabilities and wave damping in different ISM phases.
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