The Surprising Role of Equation of State Models In Electrically Exploding Metal Rod MHD Simulations

The fundamental limits of high-current conduction and response of metal conductors to large, fast current pulses are of interest to high-speed fuses, exploding wires and foils, and magnetically driven dynamic material property and inertial confinement fusion experiments. A collaboration between the University of Nevada, Reno, University of New Mexico, and Sandia National Laboratory has fielded an electrically thick (R ~ 400-μm > skin-depth) cylindrical metal rod platform in a Z-pinch configuration driven by the Sandia 100-ns, 900-kA Mykonos linear transformer driver 1 . Photonic Doppler velocimetry (PDV) measuring the expansion velocity of the uncoated surface of aluminum rods 2 was used to benchmark equation of state (EOS) and electrical conductivity models used in magnetohydrodynamics simulations using the Los Alamos National Laboratory (LANL) code FLAG 3 . The metal surface was found to expand along the liquid-vapor coexistence curve in density-temperature space for 90 ns of the rod’s expansion for both tabular EOSs with Van der Waals loops and with Maxwell constructions under the vapor dome. As the slope of the coexistence curve varies across EOS models, the metal surface in simulation was found to heat and expand at different rates depending on the model used. The expansion velocities associated with EOS models were then compared against the PDV data to validate the EOS used in simulations of similar systems. Here, the most recent aluminum EOS (SESAME 93722) 4 was found to drive a simulated velocity that best compared with the experimental data due to its relatively steep coexistence curve and high critical point.