PUI transport with adiabatic (left-hand panels) and magnetic (right-hand panels) energy changes: the normalized PUI velocity distribution f2U²r/3Q as a function of normalized PUI speed (with w = U) and heliocentric distance (and, thus, of time): from bottom to top the curves are for r/r₀ = 1.2, 1.6, 2.0, 4.0, 8.0 and 29 (approximating the asympotic shape). The three rows are the diffusion coefficients D = 5  D_F(r,v), D = D_F(r,v), and D = 0.2  D_F(r,v). The symbols in the right middle panel illustrate that the very weak distance dependence of the square bracket term in Eq. (6) has no effect on the solution.