(see Appendix \[s:sigma\]).

Test-particles are initialized in the fully twisted magnetic field and evolved according to the Lorentz force determined by the total magnetic field at the instantaneous particle position. The equation of motion numerically solved for particles with charge $e$ and mass $m$ moving with velocity ${\mathbf{v}} (t)$ in a magnetic field ${\mathbf{B}}({\mathbf{x}})$ is the Lorentz equation $$\frac{d{\mathbf{u}}(t)}{dt} =  {\mathbf{u}}(t)
\times{\mathbf{\Omega}}({\mathbf{x}})\;,
\label{lorentz}$$ where $${\mathbf{\Omega}}({\mathbf{x}})  = e {\mathbf{B}}({\mathbf{x}})/(mc\gamma)$$ with ${\mathbf{u}} (t) = \gamma {\mathbf{v}} (t)/c$ at the time $t$. The quantity ${\mathbf{\Omega}}({\mathbf{x}})$ in Eq.(\[lorentz\]) is given by $${\mathbf{\Omega}}({\mathbf{x}}) = {\mathbf{\Omega}}_0 ({\mathbf{x}})+\delta {\mathbf{\Omega}}({\mathbf{x}})$$ where $${\mathbf{\Omega}}_0 ({\mathbf{x}}) \equiv {e\over mc\gamma} {\mathbf{B}}_0 ({\mathbf{x}})   , \quad   \delta {\mathbf{\Omega}}({\mathbf{x}}) \equiv {e\over mc\gamma} \delta {\mathbf{B}} ({\mathbf{x}}).$$ in terms of the background magnetic field ${\mathbf{B}}_0$ and of $\delta {\mathbf{B}}$; we adopt a single realization of $\delta {\bf B}$ (see Appendix \[s:sigma\]).

The equation of motion \[lorentz\] is written in the local frame of the expanding plasma: the magnetic field transforms in a fluid in motion with velocity ${\mathbf{V}}$ as ${{\mathbf{B}}}_\parallel = {{\mathbf{B}}}'_\parallel$ and ${{\mathbf{B}}}_\perp = \Gamma({{\mathbf{B}}}'_\perp - {{\mathbf{V}}}/c \times {{\mathbf{E}}}')$ in the directions parallel (${{\mathbf{B}}}_\parallel$) and perpendicular (${{\mathbf{B}}}_\perp$) to ${\bf V}$, respectively, with $\Gamma = 1/ \sqrt{1-(V/c)^2}$. For a T Tauri wind $V/c \simeq 0.003$, $\Gamma \simeq 