the charged particles can also diffuse across the magnetic field lines due to the collisions between the charged particles that gyrate around the lines, since a collision will alter a particle’s velocity and make it to gyrate around another field line. The Fermi energy of the electrons in the case we are discussing is much higher than the energy interval between adjacent Landau levels of the electrons, we thus adopt the classical descriptions to estimate the diffusion rate. Folowing [@niu89], the diffusion coefficient $D_{\rm c}$ is approximately given by the square of the mean distance travelled (which is of the order of the Larmor radius $\rho_{\rm L}={mvc 
\over eB}$) divided by the mean free flight time $\tau_{\rm F}$, which is of the order of $ \tau_{\rm F}\sim {m^2 v^3 \over\pi e^4 n}$ (derived from eq.\[2.55\] or \[2.65\] of [@niu89], assuming that light elements dominate in the atomsphere). Thus the diffusion rate is $D_{\rm c}\sim \rho_{\rm L}^2/\tau_{\rm F} \sim {\pi c^2 e^2 n\over B^2 v}$. Let’s estimate the electron diffusion rate first. For the bottom density $\rho_{\rm b}\sim 5.8 \times10^5 {\rm g~cm^{-3}}$, the electron number density is $n_{\rm b}\sim \rho_{\rm b}/(2u)\sim 10^{29} {\rm cm^{-3}}$, the Fermi energy is $\sim 10^{-5}B_{12}^{-2} n_{\rm 