Fig. 5: Summary plots of the XPCI-enabled density and speed measurements performed in this work.

a Decay of shock density ratio with time. This plot compiles together the simulated XPCI results which best fit experiment (black circles) as a function of time relative to plasma initiation; horizontal error bars indicate an assumed shock speed uncertainity (estimated from the parabolic fit in Fig. 3) of  ± 10%, and vertical error bars indicate the range of density ratios which produce simulated XPCI shock profiles which would still fall within the upper and lower quartiles of the expimerental average shock profile (Fig. 4b). By fitting the thermodynamic model from Equation (3) to these points (solid black curve), we conclude that α = ~ 3% of the event’s total stored energy is expressed as excess internal energy behind the shock. This same model for alternate values of α are shown (dashed black curves) to roughly illustrate uncertainty. The blue curve and shaded area highlight the timescale of significant energy input to the system, as measured via electrical diagnostics. b Hugoniot states in the ρ₂--v_shock plane, showing how values estimated from this work’s XPCI data and diffraction model (black) compare to normal shock thermodynamic relations in heptane both with (green) and without (red) the cavitation bubble compression effect. Vertical error bars (ρ₂/ρ₁) match those of Fig. 5a, and horizontal error bars (v_shock) assume a simple  ± 10% uncertainty. The blue datapoint corresponds with the X-ray diffraction model fit result from Fig. 4.