Non-linear Diffusion of Cosmic Rays Escaping from Supernovae Remants in the Cold Partially Neutral Atomic and Molecular Phases

Cosmic rays (CRs) emitted by supernovae remnants (SNRs) have a non-negligible impact over the turbulent dynamic of our galaxy. We will discuss a model of CR propagation in the weakly ionized environments of SNRs based on the cosmic rays cloud (CRC) model developed by Malkov et al. (2013) and Nava et al. (2016). It consists in solving two transport equations simultaneously : one for CR pressure and one for the Alfven waves energy density where CR are initially confined in the SNR shock. CR trigger a streaming instability and generate slab-type resonant Alfven modes. The self-generated turbulence is damped by ion-neutral collision and non-correlated interaction with Alfven modes generated at large scales. We show that CR leaking in cold dense phases as Cold Neutral Medium (CNM) and Diffuse molecular Medium (DiM) can still be confined over distances of a few tens of parsecs from the CRC center for a few kyrs. At 10 TeV CR diffusion can be suppressed by two or three order of magnitude compared to the diffusion coefficient derived from direct CR observations. This effect results from a reduced ion-neutral collision damping in the decoupled regime. We discuss the grammage accumulated by particles around CR sources in partially ionized media.