Table 5: Summary of the typical cut-off in z and r directions beyond where a cosmic ray cannot originate. The sole parameters that determine these cut-offs are L (halo size) and/or $\chi _{\rm w}\equiv r_{\rm w}/L$ - related to the convective wind $V_{\rm c}$ via $r_{\rm w}=2K/V_{\rm c}$, or $r_{\rm loss}$ related to the effective life-time for positrons and electrons.
Cut-off Escape-dominated Convection-dominated Losses-dominated
  ( $\chi_{\rm w}\gg1$) ( $\chi_{\rm w}\ll1$) ($e^-e^+\ga$ GeV)
Halo L $L^*\approx 3K/V=3r_{\rm w}/2$ $ \approx 5r_{\rm loss}$
Radial $\min(R,3L)$ $\min(R,3L^*)$ $ \approx 5r_{\rm loss}$


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