Numerically predicted critical decay indices for solar applications as a function of normalized apex height, plotted for different values of ε and ℓ_i. The plots here are chosen to be most applicable to solar conditions with an image current closure and toroidal current decay index of n_I = 0.5. (a) ﹩{n}_{\mathrm{cr}}^{}({z}_{\mathrm{ap}}/{x}_{{\rm{f}}})﹩ for different values of ε at fixed ℓ_i = 0.5. (b) ﹩{n}_{\mathrm{cr}}^{}({z}_{\mathrm{ap}}/{x}_{{\rm{f}}})﹩ for different values of ℓ_i at fixed ε = 0.5. The minimum value of z_ap/x_f where the MFR would pass below z = 0 is also shown for this plot.