We study Cosmic Ray (CR) propagation in the weakly ionized environments of supernovae rem-
nants (SNRs). Our work is based on a Cosmic Ray Cloud (CRC) model developed by Malkov
et al. (2013) and Nava et al. (2016). We solve two transport equations simultaneously: one over
the CRs pressure and one for the Alfvén waves energy density. CRs are initially confined by the
SNRs shock. While escaping from their accelerator, CRs start to trigger the streaming instability
and produce slab-type resonant Alfvén modes. The self-generated turbulence is damped by ion-
neutral collision and by non-correlated interaction with Alfvén modes generated at large scale.
We show that CRs 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 orders of
magnitude. This effect results from a reduced ion-neutral collision damping in the low frequency
regime. We calculate the grammage of CR in these environements. We find both in single or
multi-phase set ups that at 10 GeV CNM and DiM media can produce grammage in the range
10-20 g/cm 2 in the CNM and DiM phases. At 10 TeV because of non-linear propagation the
grammage increases to values in the range 0.5-20 g/cm 2 in these two phases. We also discuss
preliminary calculations in inhomogeneous ISM combining two or three different phases where
we obtain the same trends. Finally, we discuss some improvements of the CRs diffusion code
: Increase of the dimensionnality of the problem, inclusion of perpendicular diffusion effects,
interstellar cloud ionization and gamma-ray emission.