10^{16}\left(\frac{B_0}{10^{8.5}{\rm G}}\right)\left(\frac{\Omega}{10^3{\rm s^{-1}}}\right)^{2}\left(\frac{R}{10^{6}{\rm cm}}\right)^{3}\left(\frac{V}{10^7{\rm cm\ s^{-1}}}\right)^{-1} {\rm cm},$$ where $V$ is the velocity of a MSP. Due to the assumption of the energy equipartition, the strength of the magnetic field is $$B_{\rm bow}=\left(\frac{2L_{\rm sd}}{cR^2_{\rm bow}}\right)^{1/2}\sim 50\left(\frac{V}{10^7{\rm cm\ s^{-1}}}\right) \mu {\rm G}.$$ The ratio of the Larmor radius of electrons/positrons to the bow shock radius is $$\frac{r_{\rm g}}{R_{\rm bow}}\sim 0.5 \kappa^{-1}.$$ The fact that $r_{\rm g}/R_{\rm bow}$ is close to unity supports that electrons/positrons may escape from the bow shock region. Therefore, in the case of $\kappa\sim 1$, high-energy electrons/positrons can escape with an efficiency of order unity [@B08; @BA10]. Even if we consider the case of $\kappa \gg 1$, the synchrotron loss can be estimated by using eqs. (11), (14) and (16) as $$\frac{\Delta\varepsilon_e}{\varepsilon_e}\sim 9\times 10^{-4}\left(\frac{B_0}{10^{8.5}{\rm G}}\right)^2 \left(\frac{\Omega}{10^3{\rm s}^{-1}}\right)^4\left(\frac{R}{10^6{\rm cm}}\right)^6\left(\frac{V}{10^7{\rm cm\ s^{-1}}}\right).$$ Therefore, we can conclude again that the radiative energy loss of electrons/positrons in the pulsar wind nebula is not so large.

Diffusion in Interstellar medium
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The observed electron/positron spectrum after the propagation in ISM is obtained by solving the diffusion equation $$\frac{\partial}{\partial t}f(t,r,\varepsilon_e)=D(\varepsilon_e)\nabla^2 f+\frac{\partial}{\partial \varepsilon_e}\left( P(\varepsilon_e)f \right) +Q(t,r,\varepsilon_e),$$ where $f(t,r,\varepsilon_e)$ is the energy distribution function of electrons/positrons, $D(\varepsilon _e)=D_0(1+\varepsilon_e/3{\rm GeV})^{\delta}$ is the diffusion coefficient, $P(\varepsilon_e)$ is the 