hand, our analysis confirms that the choice of $L_c$ does not have a large effect on the statistical properties of EP propagation or the distribution of the hitting-points on the disk (see Appendix \[s:Lc\]). Likewise, it is possible that $L_c$ depends to some extent on the stellar rotation velocity, though by the same argument we do not expect the short rotation period ($4$ days) as compared to the Sun would significantly affect the results.

Since EPs in our simulations sample a relatively small region ($\sim 0.1$ AU), we assume that $L_c$ is uniform within the simulation box; in future work this condition will be relaxed. The chosen $L_c$-values ensure that the EPs are resonant within the turbulent inertial range (see Fig. \[Pspectrum\]) during their propagation, namely $$k_{\rm min} r_g({\mathbf x})/2\pi = r_g({\mathbf x})/L_c < 1,$$ where $r_g ({\mathbf x}) = p_\perp c/ e B_0 ({\mathbf x})$ is the gyroradius for an EP with momentum (or velocity) perpendicular to the unperturbed and space-dependent magnetic field of the T Tauri star, $B_0 ({\mathbf x})$, given by $p_\perp = m v_\perp \gamma$ (or $v_\perp$), $m$ is the EP mass, the Lorentz factor is $\gamma = 1/ \sqrt{1-(v/c)^2}$ with $c$ being the speed of 