Comparison of the semi-analytical approximation of the function g(γ), see Eq. (35), shown as a black line with numerically obtained values. Small red dots denote the simulation series “G” with varying adiabatic index; each red dot represents a single simulation. Larger blue dots denote values derived by fitting the scaling of the stand-off distance with the non-linearity parameter for a variety of different simulation series shown in the top panel of Fig. 13; each blue dot represents such a fit value to a full simulation series. See main text for details of the derivation.