Self-confinement of low-energy cosmic rays around supernova remnants
  Supernova remnants have long been considered as a promising candidate for
sources of Galactic cosmic rays. However, modelling cosmic-ray transport around
these sources is complicated by the fact that the overdensity of cosmic rays
close to their acceleration site can lead to self-confinement, that is the
generation of turbulence upon which these particles scatter. Such a highly
non-linear problem can be addressed by numerically solving the coupled
differential equations describing the evolution in space and time of the
escaping particles and of the turbulent plasma waves. In this work, we focus
essentially on the propagation of cosmic rays from supernova remnants in the
warm ionized and warm neutral phases of the interstellar medium and propose an
extended framework to take into account also the effect of energy loss relevant
for cosmic rays of energy below 10 GeV. Interestingly, the diffusion
coefficient of low-energy cosmic rays could be suppressed by up to 2 orders of
magnitude for several tens of kiloyears after the escape from the shock. The
cosmic-ray spectrum outside the supernova remnant flattens below 1 GeV at a
sufficiently late time reminiscient of the spectral behaviour observed by
Voyager. We also find the grammage accumulated around the source to be
non-negligible, with important implications for precision fitting of the
cosmic-ray spectra.
