the solar wind at $1$ AU. Moreover, the turbulence in the circumstellar medium of a T Tauri star is likely to be much stronger than in the solar wind, due to the much more violent stellar activity. In our simulations we therefore considered values of $\sigma^2 $ in the range $0.01 -1.0$, to be compared with the steady solar wind at 1 AU where typically $\sigma^2 = 0.01$–$0.03$ [@Burlaga.Turner:76].

Since both $\kappa_\perp^{MFL}$ and $\kappa_\perp^{D}$ grow linearly in $\sigma^2$, we might expect a greater contribution to latitudinal and longitudinal spread due to cross-field diffusion than in the solar wind at a given $B_0$ [@Dresing.etal:12; @Fraschetti:16a; @Fraschetti:16b]. However, such an effect is outweighed by the steep scaling of $\kappa_\perp^{D}$ with $B_0$ in the T Tauri field, mentioned above.

Basic assumptions of the model {#assumptions}
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We assume that the stationary MHD wind solutions are a good approximation for the purposes of our study as both the large-scale magnetic field and the turbulence are stationary on the time-scale of EP propagation. The justification is that the typical EP propagation speed ($\simeq c$) greatly exceeds both the stellar rotation speed close the surface (approximately 25 km s$^{-1}$ for a rotation period of 4 days), 