Equation-of-State Measurement of Dense Plasmas Heated With Fast Protons

Using an ultrafast pulse of mega-electron-volt energy protons accelerated from a laser-irradiated foil, we have heated solid density aluminum plasmas to temperatures in excess of 15 eV. By measuring the temperature and the expansion rate of the heated Al plasma simultaneously and with picosecond time resolution we have found the predictions of the SESAME Livermore equation-of-state (LEOS) tables to be accurate to within 18%, in this dense plasma regime, where there have been few previous experimental measurements.

Figure 1

A two foil, vacuum spaced target for proton heating. A 100 J, 500 fs pump laser is focused to a $10\mu \mathrm{m}$ spot from the left onto the $17\mu \mathrm{m}$ source foil. Protons generated from the source back surface traverse the $400\mu \mathrm{m}$ vacuum gap, heating the $2\mu \mathrm{m}$ Al sample layer. The support frame was etched from a Si wafer. The mirror finish of the Al sample allows clean reflection from the back surface. The probe reflected at 15° from normal, while the SOP imaged the sample surface at 15° above the plane, allowing the proton spectrum to be measured from the normal direction.

Figure 2

Raw images from our two time-resolved diagnostics. (a) An SOP image, showing both OTR and thermal emission. The OTR is offset $200\mu \mathrm{m}$ spatially from the proton heating center, consistent with a target-normal trajectory for the protons and electrons traveling in the laser direction. (b) A raw CPI image, showing a disturbance that starts in the middle of the time window viewed. This image is Fourier analyzed along horizontal lineouts to extract phase and reflectivity.

Figure 3

Comparison of SOP and CPI data from the same shot using HYADES simulations with SESAME EOS 3718 (solid curves) and LEOS (dashed curves) models. (a) A lineout of the SOP measured brightness temperature, with OTR removed, and the simulated signal achieved using a rough fit to the proton spectrum as an energy input to HYADES, scaled to best fit the SOP data for the two EOS models. The simulation curves overlap here and continue to match the SOP data beyond 100 ps. (b) Points show lineout of expansion velocity measured by the CPI on the same shot; lines show calculated expansion from the simulations.