Properties of the expansion of the CRC in the ISM. Left: evolution of the half-life time of the CRC as a function of its initial radius a in parsec units. Green, blue, red, and black solid lines refer to particle energies at 10, 10², 10³, and 10⁴ GeV. The black dashed line refers to the time evolution of the radius of the SNR front shock in the considered phase: WNM for the top figure, CNM for the middle one, and DiM for the bottom one. These plots have been obtained for Γ = 2.2. Right: evolution of the half-life time of the CRC derived from the left plots as a function of CR energy. The blue solid line refers to a CR energy spectral index of 2.2 while the red dashed line refers to a spectral index of 2.0. The gray zone corresponds to the no-wave propagation zone; it does not lead to any (a, t_1/2) solution.