disk–magnetosphere boundary, and cannot be calculated self-consistently in our simulations that do not include heating or the wind and magnetic field of the disk. Thus, the MHD instabilities generated at the disk–magnetosphere boundary [@Kulkarni.Romanova:08] are not reproduced here (see Sect. \[discuss\]). In Appendix \[s:disk\] we show that a thicker disk or a greater disk innermost radius do not qualitatively change our results. At much greater distances from the star, the vertical structure needs to be considered in more detail; we defer this more complex treatment to future work.

EPs are propagated within the circumstellar environment until their trajectories either intersect with the disk surface, or take them back to the stellar surface. The magnetic field of a T Tauri star is strongly curved and can be azimuthally wrapped, trapping EPs close to the star. As a consequence, the wind advection cannot efficiently drag EPs away from the star: the fraction of particles collapsing back onto the star, that in the stretched out Parker spiral field of the Sun is negligible, is significant and clearly larger for smaller injection radius, $R_s$. The fraction of particles escaping the simulation box is $< 10 \%$ for $R_s = 2 R_{\star}$, and grows up 