*3.2. Pressure Measurement*

Figure 7 presents a comparison of the rear free-velocity profile of the aluminum target in the water-confined regime at 2.7 GW/cm<sup>2</sup> measured with VISAR with the values obtained by simulation. The velocity profile presented two peaks corresponding respectively to the first and second occurrences of the shock wave at the rear surface of the target.

On the front shock, an inflection of the velocity corresponded to the elastic precursor at 38 m/s which equates to a Hugoniot limit *PH* of 0.312 GPa. We could calculate the dynamic yield stress using the following formula [26]:

$$
\sigma\_0^{\text{Dyn}} = P\_H \frac{1 - 2\nu}{1 - \nu}.\tag{2}
$$

This calculation yields 0.179 GPa, which is in agreemen<sup>t</sup> with value previously determined in Table 1 [22]. The simulation agreed very well with the experiments for both peaks. The corresponding maximum plasma pressure, denoted as *Pmax*, was 3.252 GPa. Simulation showed a negative peak (25 m/s) at the end of release at 300 ns. This corresponds to effects in relation with the edge of the spatial profile [27], which are very sensitive to pressure gradients.

**Figure 7.** Simulated and experimental rear free-velocity profiles of a water-confined laser shot on 1-mm-thick aluminum at 2.7 GW/cm<sup>2</sup> with a laser spot diameter of 3 mm.

From the simulation, the maximum pressure of plasma *Pmax* could be related to the maximum velocity of the first peak (*vmax*) measured by VISAR, as shown in Figure 8:

$$P\_{\text{max}}\text{(GPa)} = -0.01456 v\_{\text{max}}\text{(m/s)}^2 - 20.075 v\_{\text{max}}\text{(m/s)} - 29.246.\tag{3}$$

Compared to previous results [18], this includes shock-wave attenuation depending on the incident pressure and target thickness.

Figure 9 presents typical rear free-velocity profiles at 2.7 GW/cm<sup>2</sup> for water as well as acrylate and PDMS polymeric confining materials. Figure 9 focuses on the first occurrence of the laser shock wave. The global shape was similar for the three materials: both the inflection on the shock front due to elastic precursor and the FWHM (55 ns) were alike. Some differences were highlighted in the end of the relaxation in relation to edge effects. However, maximum velocities *vmax* were different, showing 237 m/s, 217 m/s, and 187 m/s for water, acrylate, and PDMS respectively. From rear free-velocity profiles, corresponding *Pmax* values were calculated from the incident power densities ranging from 0.22 GW/cm<sup>2</sup> to 12.50 GW/cm2. They are gathered in Figure 10 for water, acrylate, and PDMS.

For the three confining materials, the data can be separated in two parts. In the first part, pressure increased with the incident power density, and in the second part the pressure saturated due to the detrimental effect of plasma breakdown of the material confinement [28]. The power density for which the breakdown limits the plasma pressure of a confining material is called the breakdown threshold. These are reported with maximum pressure in Table 3.

The acrylate and water confinements exhibited the same pressures up to 2.3 GW/cm2. At higher intensities, the acrylate produced slightly higher pressures, respectively 6.5 GPa at 6.02 GW/cm<sup>2</sup> and 6.4 GPa at 6.53 GW/cm2. The breakdown threshold was 7 GW/cm<sup>2</sup> for both confinements, and saturating pressures were produced at 7.6 GPa for the acrylate confinement and 7 GPa for water.

**Figure 8.** Maximum pressure of the plasma extracted from simulation as a function of the maximum velocity developed by the laser shock process depending on the rear free-surface velocity obtained with VISAR measurement.

**Figure 9.** Velocity profiles with a laser focal diameter of 3 mm, an incident power density of 2.7 GW/cm2, and a 1-mm-thick aluminum target for water, acrylate, and PDMS confinements.

**Figure 10.** Pressure measurements obtained from the rear free-surface velocity measured with VISAR for the three different confinements: water, acrylate, and PDMS.

As expected with its optical transmission, the PDMS confinement exhibited pressures that were slightly lower than water and acrylate confinements, respectively 4.25 GPa at 3.50 GW/cm2, 4.90 GPa at 3.75 GW/cm2, and 4.98 GPa at 3.50 GW/cm2. The breakdown threshold was also lower at 4.7 GW/cm2, producing a maximum pressure of 4.6 GPa.

The chemical composition of the polymers can influence the breakdown threshold. Following this, the higher optical absorption of the PDMS favored material damage initiation compared to the acrylate confining medium. In fact, polymer damage was observed regardless of the polymer confinement used when high laser intensities were applied, typically when going higher than 3 GW/cm<sup>2</sup> for the acrylate confinement, which seemed to be perfectly transparent except for the laser energy loss at the interfaces. With growing damages, plasma breakdown can initiate on defects, thus lowering the breakdown threshold. The confined plasma composition is a mix, coming from the contribution of the aluminum target and the polymer confinement material through ablation and plasma heating, respectively [29]. Maximum plasma pressures were also higher than previously published by Berthe in [18,30]. The difference could be due to the better laser spatial profile obtained by using a DOE and the simulation of rear free-surface velocity on the range of incident power density instead of using a constant attenuation. The present results clearly indicate the capability of polymers to reach pressures equivalent to water confinement. However, efforts must be made concerning the adhesion and mechanical properties of polymers for LSP configuration using high repetition rate shot without coatings by varying chemical composition and manufacturing parameters.

**Table 3.** Breakdown thresholds and maximum pressures extracted from Figure 10.

