Measurement of the equation of state of solid-density copper heated with laser-accelerated protons

We present equation of state (EOS) measurements of solid-density copper heated to 5–10 eV. A copper sample was heated isochorically by hydrogen ions accelerated from an adjacent foil by a high intensity pulsed laser, and probed optically. The measured temperature and expansion are compared against simulations using the most up-to-date wide range EOS tables available.

Figure 1

Schematic of experimental layout. Laser is incident at 45°; FDI probe angle is 9.46°; SOP viewing angle is 22.5°; Thomson measures ions in source target normal direction.

Figure 2

Brightness temperature versus time for the six models with the same heating profile, as derived from the measured ions of a specific shot. XEOS results are shown for two different definitions of Z* being used to calculate the dielectric function for the Helmholtz equation.

Figure 3

Measured and simulated brightness temperature (a) and expansion rate (b). Measurements (black curves and points) are taken in the central region of heating. One simulation is given for each of six models, where the energy inputs are individually scaled such that the peak BT matches that of the measurement. Measured expansion and the derivative of the smoothed curve are shown, along with the determination of final velocity.

Figure 4

Final expansion velocity vs brightness temperature for measurements and simulations. Curves show simulations using various equation of state models. Each measured data point represents a single shot, with error bars based on the estimated certainty of each measurement. For QEOS, individual simulations are shown as dots to show the maximum deviations from the curve.