to $\sim 30 \%$ for $R_s = 8 R_{\star}$. Since the path-length to stop an EP is much smaller than the thickness of the disk, once a particle hits the surface of the disk we assume that its kinetic energy is converted instantaneously into ionization of the disk gas.

Numerical Method {#nummeth}
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In a series of numerical experiments, we consider a population of energetic charged test-particles (protons) gyrating in a turbulent magnetic field described as follows. We assume a three-dimensional magnetic field of the form $${\bf B(x) = B}_0 ({\bf x}) + \delta {\bf B(x)},$$ where the large-scale component, ${\bf B}_0 ({\bf x})$, is the 3D magnetic field generated by the MHD simulations as calculated in @Drake.etal:17, and the random component ${\bf \delta B} = {\bf \delta B} (x, y, z)$ has a zero mean ($\langle \delta {\bf B(x)} \rangle = 0$) and a turbulence correlation length $L_c$. We assume an inertial range $k_{\rm min} < k < k_{\rm max}$, with $k_{\rm max}/k_{\rm min} = 10^2$, where $k_{\rm min} = 2\pi/L_c$ and $k_{\rm max}$ is the magnitude of the wavenumber corresponding to some dissipation scale marking the smallest scale of applicability of the ideal MHD. A broader inertial range 