We study the damping of Alfvén waves generated by the cosmic ray resonant streaming instability
as due to ion-neutral damping, turbulent damping and non linear Landau damping, in the warm
ionized and warm neutral phases of the interstellar medium. We do so in the context of the cosmic
ray escape and propagation in the proximity of supernova remnants. For the ion-neutral damping,
state-of-the-art damping coefficients are used, where the momentum transfer and charge exchange
cross sections between various species of ions and neutrals are computed in detail or measured.
We investigate whether the self-confinement of cosmic rays nearby sources can appreciably affect
the grammage. In fact, if this is the case, the standard picture, in which CR secondaries are
produced during the whole time spent by cosmic rays throughout the Galactic disk, should be
deeply revisited. We show that the ion-neutral damping and the turbulent damping effectively
limit the residence time of cosmic rays in the source proximity, so that the grammage accumulated
near sources is found to be negligible, contrary to what was previously suggested.