light in vacuum.

The parallel diffusion coefficient, $\kappa_\parallel$, in turbulence with the assumed power-spectrum can be calculated using quasi-linear theory [@Jokipii:66; @Earl:74; @Giacalone.Jokipii:99]; the resulting space-dependent mean free path $\lambda_\parallel ({\mathbf x}) = 3 \kappa_\parallel ({\mathbf x}) / v$ reads $$\lambda_\parallel ({\mathbf x}) \simeq 4.8 (r_g({\mathbf x})/L_c)^{1/3} L_c/\sigma^2
\label{lambda}$$ up to mildly relativistic (i.e., a few GeV) energy protons, where $$\sigma^2 = (\delta B ({\mathbf x}) /B_0 ({\mathbf x}))^2
\label{sigma}$$ is the power of the space-dependent fluctuation $\delta B$ relative to $B_0$. In our simulations, we will assume $\sigma^2$ independent of space throughout the simulation box (see Appendix \[s:sigma\] for the physical justification). Thus, $\lambda_\parallel ({\mathbf x})$ drops in the proximity of the T Tauri star as $\lambda_\parallel ({\mathbf x}) \propto L_c^{2/3} / B_0^{1/3}({\mathbf x})$ due to the increase of $B_0 ({\mathbf x})$; in a more realistic approach, such a drop is even faster due to the decrease of $L_c$ not accounted for in this work. For 1 GeV protons and $\sigma^2 = 0.1$, $\lambda_\parallel \ll 10 R_{\star}$; this value is further reduced if $\sigma^2$ approaches unity. Typically $\lambda_\parallel$ is smaller than the grid-cell size ($0.36 R_\star$), ensuring a sufficient number of scatterings within a single cell.

In addition to 