Left: steady-state solution for the flux, j_p(E) as a function of energy for different values of ℓ. Right: transported cosmic-ray flux, j_T(E), as a function of energy for different values of D₀ and ℓ. Note the different scales for the x- and y-axes of each panel. Without including the impact of energy losses and diffusion throughout the cloud, the resulting cosmic-ray flux would produce nonphysically high ionization rates.