Radial profile of χη (top panel), η_crit, the minimum η required for the strong diffusion regime (middle panel), and the maximum λ_CRF (bottom panel) for the galaxy clusters of different masses in hydrostatic equilibrium. Different colours stand for different halo masses as indicated in the top inset, either with a cored (solid lines) or with a non-cored profile (dashed lines). Grey horizontal lines demarcate the two regimes in χ (top panel) and gas that are CR-pressure dominated vs thermal pressure dominated (middle panel). η_crit, the minimum value required for χ < 1 increases with radius. By contrast, CR pressure profiles are expected to decrease with radius. It is therefore unlikely that χ < 1 at large radii, which means that CRs are unable to stabilise small-scale instabilities outside the cluster core.