Proton fluxes, ﹩J({E}^{{\prime} })={v}^{2}f(v)/{m}_{p}﹩, are presented as functions of energy, ﹩{E}^{{\prime} }﹩, in the plasma reference frame. Panel (a): hybrid-simulation-derived distributions of thermal protons (blue circles) and PUIs (red circles) downstream of the TS. The fitted double-κ distributions for both populations are shown with the thin lines. Panel (b): example of the evolved VDFs deep in the IHS along the V1 LOS (symbols), compared with the corresponding thermal-proton and PUI VDFs from simulation B obtained using the TS VDF model without loss or injection due to charge exchange (thin blue and red lines, respectively). Panel (c): streamline lengths. Panel (d): the convective times from the TS to the radial point on the LOS.