Grammage of cosmic rays in the proximity of supernova remnants embedded in a partially ionized medium

Aims. We investigate the damping of Alfven waves generated by the cosmic-ray resonant streaming instability in the context of cosmic-ray escape and propagation in the proximity of supernova remnants. We study in particular whether the self-confinement of cosmic rays in the vicinity of sources can appreciably affect the grammage. Methods. We considered ion-neutral damping, turbulent damping, and nonlinear Landau damping in the warm ionized and warm neutral phases of the interstellar medium. For the ion-neutral damping, the most recent damping coefficients were used. Results. We show that ion-neutral damping and turbulent damping effectively limit the residence time of cosmic rays in the proximity of the source, so that the grammage that is accumulated near sources is found to be negligible. In contrast to previous results, this also occurs in the most extreme scenario in which ion-neutral damping is less effective, namely in a medium consisting only of neutral helium and fully ionized hydrogen. The standard picture, in which cosmic-ray secondaries are produced during the whole time that cosmic rays spend in the Galactic disk therefore do not need to be revised substantially.