Model-Independent Equation of State Measurements for Proton-Heated Warm Dense Matter

Determining the equation of state (EOS) in the warm dense matter (WDM) regime is challenging for both theoretical models and experimental techniques. However, accurate EOS data in this regime is crucial for advancing knowledge in fields ranging from astrophysics to high energy density physics. We present experimental measurements of the release isentrope for aluminum and diamond, using isochoric proton heating and streaked X-ray radiography at the OMEGA EP facility. We developed a model-independent analysis method employing a neural network (NN) to extract the pressure-density isentrope directly from the measured radiographs. The NN approach allows for reliable extraction even with increased noise and reduced resolution. Results for aluminum are in good agreement with theoretical predictions, while preliminary data for diamond suggest possible differences that merit further investigation. These findings provide benchmarks for EOS models and motivate the extension of such measurements to a broader range of materials.