Abstract
1. Introduction
The equation of state (EOS) of carbon at high pressures is a subject of interest for several branches of science, including astrophysics, material science, and applied engineering (first of all including fusion research). In particular, a very important point (in particular for the explanation of large magnetic fields of giant planets such as Uranus and Neptune) is the existence of a metallic phase of carbon[
A well-known experimental method to measure the EOS is based on the impedance mismatch technique and consists in measuring the shock velocity of two different materials (test and reference) at the same time. The shock-wave measurements are realized by a streak camera recording the emission from the rear side of the shocked target. Using time-resolved imaging, we can experimentally determine the times of the shock arrival for each part of target (see Figure
One of the critical points of this method is the effect of the temporal profile of the high-power pulse. Indeed, an ideal shock can be produced only with a high-power flat-top laser pulse, and the analysis of the effect of the real temporal profile of a high-power laser in experiments is important, because it can be a substantial contribution to the total experimental error. The aim of the present work was to realize a set of simulations for Gaussian pulses with different durations and to analyse the effect on the calculation of shock velocities.
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2. Simulations
For the realization of simulations we have used the hydrocode MULTI (multigroup radiation transport in multilayer foils)[
We have tested four Gaussian laser profiles with the same peak intensity () and full width at half maximum (FWHM) durations , and 600 ps. Gaussian profiles were calculated by (see Figure
3. Results and discussion
Figure
If the rise-time of the Gaussian pulse is small ( from Figure
Simulations done for show that instead the shock has the time to become stationary in the steps (the difference is indeed the same for the two steps) but not for base. In this case the shock velocity cannot simply be calculated as .
4. Conclusion
On the basis of hydro simulations, we can conclude that, with the considered laser intensity ( and target design, it is necessary to have the duration of the Gaussian pulse not longer 300 ps. In the opposite case, the shock does not have the time to become stationary before the shock breaks out of the base. These results can be extrapolated to pulses with any shape by saying that the pulse rise-time should be less than 150 ps. Depending on target thickness, the pulse rise-time required will be different; however, the method described here is general.
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