Impulse coupling enhancement of aluminum targets under laser irradiation in a soft polymer confined geometry

In the field of impact studies, the investigation of the structural response caused by strong solicitations is an active area of research. In particular, the study of momentum transfer during these shocks has many applications. For example, blast loading experiments¹ can be used to gain insight into the failure of structures or their response to seismic solicitations.² Another area of study involving momentum transfer is hypervelocity impacts, generally coupled with the analysis of the debris produced by the impacts.^3,4 Those researches are linked to applications such as ballistic protections and planetary defense^5,6 and demonstrated promising results, notably those recently obtained from the DART spacecraft impact on the asteroid Dimorphos.⁷ 

Other space applications include Laser Ablation Propulsion (LAP) and debris deorbiting.⁸ The former aims to use a laser beam to propel small spacecrafts, while the latter uses lasers attached to satellites to shoot debris and give them enough momentum to alter their trajectory and deflect them out of important orbits, eventually disintegrating as they re-enters the atmosphere.

The experiments were performed on the HERA laser platform located at LULI.³⁰ The pulse duration used for the shots was 15 ns at full width at half maximum (FWHM) with a top-hat pulse and a wavelength of 1053 nm. The energy of the shots ranged from 19.6 to 204.2 J with a spot diameter of 30 mm, producing laser intensities ranging from 0.2 to 1.9 GW/cm $2$⁠. These low intensities ensured that no breakdown plasma was produced during the laser–matter interaction. Before the shots, a qualitative assessment of the laser spot was obtained with burn paper and showed an overall good homogeneity of the energy distribution (see Fig. 1).

Prior to the pendulum experiments, preliminary shots were performed on 200  $μ$m thick pure aluminum targets upon which acrylate confinement was apposed. The laser spot size used was 30 mm, the same as the one used for the pendulum experiments. To characterize the shots, velocity interferometer system for any reflector (VISAR) and PDV measurements have been used.³⁰ The resulting backface velocity profiles were then used to calibrate the simulations (see Sec. IV). VISAR measurements are based on the Doppler effect and collect the reflected light from a probe laser aimed at the back of a moving target. The wavelength of the probe laser is shifted proportionally to the velocity of the moving target. The signal is then injected into a Michelson interferometer with two arms, one of which is delayed by a reference of known length. The interaction between the two arms of the interferometer then allows a backface velocity profile to be extracted.^31,32 PDV principle is described in Sec. II B.

For each laser shot, the energy and temporal pulse profile were controlled using a pre-calibrated calorimeter and a photodiode, respectively, both placed on energy leaks. An example of a typical temporal pulse profile is given in Fig. 2.

The profile is represented as the intensity (a.u.) as a function of time in ns, in this case for a 103 J on target laser pulse. The FWHM of this particular shot is 16.1 ns with a well defined top-hat shape. The figure shows the experimental acquisition, as well as a moving average of the profile later used for the simulation of the shot. This was done in order to reduce potential numerical problems during the simulations while not impacting the results.

The targets used were 6061-T6 aluminum plates (⁠ $75×75×2$ mm) machined to provide a 30 mm diameter by 2 mm height stud in the center. The confinement used for the laser–matter interaction was a 1 mm thick acrylate tape. The confinement was cut to the same diameter as the stud to cover it completely. This provided better control of the area affected by the confined interaction and also ensured that the confinement was ejected during the shock, effectively setting the pendulum in motion during the experiments. Another advantage of using a large laser spot was that the momentum transfer was mainly uniaxial, allowing better simulations with our mono-dimensional code.

The complete pendulum assembly is shown in Fig. 4. It consists of a pendulum frame to which several materials have been attached. In order, from the center of the pendulum to the outside exposed to the laser pulse, the materials used were: steel plates to increase the weight of the whole assembly so that pendulum deflection was not too great, Divinycell foam used to dampen the shockwave and allow easier and better PDV measurements, and finally, the 6061-T6 targets on which the confinement was applied. The same material was placed on the side opposite to the incident laser pulse to balance the pendulum and have a center of mass perpendicular to the ground when the pendulum was at rest.

The simulations were performed using the mono-dimensional Lagrangian hydrocode ESTHER. This code is used for the simulation of the laser–matter interaction and shock propagation in target in the direct or confined regime and for a wide range of laser intensities, pulse durations, or wavelengths. The validity of the code has already been established for a range up to 500 GW/cm $2$ with laser parameters close to the one used in this study.²⁸ The code incorporates laser propagation through matter by solving the Helmholtz equation. Palik’s tables³⁵ are used to determine the index of refraction for the solid part, while the Lorentz plasma model is used for the plasma part.³⁶ The hydrodynamics of the cells are simulated by tracking their position and solving the conservation equations for mass, momentum, and energy in finite volumes. Two equations of state (EoS) were used to calculate the overall behavior of the cell stack to determine the optimal one for our experiments. The first set of calculations was performed with a SESAME-tabulated equation of state (EoS No. 3720) from Los Alamos National Laboratory, which has already been used for simulations of 6061-T6 aluminum alloys.²⁹ The second set of calculations used the Bushman–Lomonosov–Fortov (BLF) equation of state^37,38 to represent the cell stack. The mechanical properties were described by the Steinberg–Cochran–Guinan model.³⁹  Figure 5 shows the geometry of a material stack as modeled in ESTHER. The mesh has been refined at the interface between the aluminum and the confinement to better capture the laser–matter interaction.

The confinement used in the simulations was a 1 mm layer of water. The choice was motivated by the fact that the acrylate confining layer used is not fully characterized, whereas water has well defined parameters and the simulation of confined interactions using it has been performed several times successfully.^28,40 Running the simulations with water confinement while performing the experiments with an acrylate confinement is comparable since the performance of the two has already been compared pressure-wise and gave the same results when the backface velocity of the shocked target was measured by Velocity Interferometer System for Any Reflector (VISAR)^31,32 during previous work.^23,24 Moreover, calculations of the losses by reflection give a difference of $≈2$% between the energy lost in water and an acrylate tape^41–43 while considering the losses at the interface air/confinement by Fresnel reflectivity coupled with the losses in the bulk of the confinements with a thickness of 1 mm. The experiment was simulated for 2  $μ$s to capture all of the momentum developed by the interaction. This choice was based on preliminary simulations which showed that all the momentum was imparted to the pendulum in this time frame in the range of laser parameters used in this study.

In order to precisely assess the beam homogeneity, shots were realized with a 30 mm laser diameter on 200  $μ$m thick confined targets. The free surface velocity was then extracted by placing VISAR and PDV probes at different locations of the target hit by the laser spot. Figure 6 presents the different locations used and the backface velocity profiles associated with each one for a 107 J shot.

The four backface velocity profiles presented are all similar, and the three peaks visible at 178, 255, and 330 ns represent the shockwave going back and forth in the material with a constant velocity. For all the profiles, the peaks are appearing at the same time. Probe number 1 displays an overall velocity lower than the other acquisition, which could be explained by a small inhomogeneity in the energy distribution of the laser spot. The reproductibility of the measurement using either VISAR or PDV gives us good confidence in the setup accuracy for the experiment.

These measurements are in agreement with the qualitative energy distribution deduced from the burn paper shown in Fig. 6(a). The beam intensity was probably a bit lower in the red area in the left side of the burn paper shown, but unfortunately no VISAR or VH probe was located there.

To complete the previous measurement, the ejection angle of the confinements used during the shots was calculated from camera acquisitions of the experiments. The angle was calculated using ImageJ software.⁴⁴  Figure 7 shows the images taken for a laser shot at 103 J with an interval of 30.3  $μ$s between each image.

The first image shows a moment just after the laser pulse hits the target, during the formation of the plasma before its expansion. After that, the plasma starts to expand and disbonds the confinement from the target. The disbonding appears to be homogeneous, the small irregularities may be due to the cutting and applying of the confinements, but also and mainly to the fact that the energy distribution in the laser spot is not perfectly homogeneous (see Fig. 1). Despite that, the polymer confining layer is ejected practically horizontally in all the images.

In the case shown in Fig. 7, the calculated ejection angle of the confinement was 3.8 $°$ from the eleventh frame, the last one in which the confinement was fully visible. The calculation was performed for each laser shot of the experimental campaign and gave an average ejection angle of 2.1 $°$⁠. The low value of this angle confirms the mono-dimensional aspect of the interaction thanks to the experimental configuration chosen.

The method described in Sec. II B was applied to extract the momentum and momentum coupling produced during each shot performed during the experimental campaign. The results are presented in Figs. 8 and 9 and compared with previous results with a similar setup but in the direct regime (i.e., without any confining medium and under vacuum).

Figures 8 and 9 show the momentum as a function of the laser pulse energy and the momentum coupling as a function of the $Iλ τ$ parameter, respectively. For both figures, the results are compared with experiments performed on a similar setup in previous campaigns,⁴⁵ where no confining layer was used to enhance the momentum imparted to the target material. In the specific case of Fig. 9, the results are also compared with the results from Rudder’s work.⁴⁶ 

In Fig. 8, both configurations follow a power law, the direct interaction fit is 2.0 $× 10 − 5 E 0.85$ while for the confined interaction it is 2.5 $× 10 − 3 E 0.80$⁠. The first point of the confined interaction at 19.6 J was not included in the fit because it marks the beginning of the vapor regime which does not follow a power law. The slope of the two fits is close, indicating that the same trend in momentum growth as a function of laser energy is followed by the confined and direct interactions. A factor of one hundred is observed between the direct and confined interactions, which can be explained by the significant increase in the pressure generated by a laser pulse, as well as the increased duration of the application of this pressure. All this induces a higher material velocity, which in turn leads to a higher momentum. In Fig. 9, the momentum coupling is plotted as a function of $Iλ τ$⁠. The same observations are made as in the previous figure, the same one hundred factor is observed as well as the same onset of the vapor regime (⁠ $Iλ τ$ = 400 W/m s $1 / 2$⁠) of the Phipps model. The results can be compared to those presented in Rudder’s work.^33,46 Although they use a direct regime setup, the laser parameters are similar and the trend observed at low $Iλ τ$ is the same as what is observed with confined shots. It is also interesting to note that this similarity in the $Iλ τ$ value, witness of the transition of the vapor regime to the plasma one, confirms the negligible aspect of the optical losses in the confinement.

Thus, confining the interaction with an acrylate polymer confinement does not induce changes in the vapor/plasma transition and the $Iλ τ$ range required to maximize $C m$ is the same as that observed for experiments without a confinement layer.

To calibrate the simulations, the backface velocity profile of a shot at 104 J on target on a 200  $μ$m pure aluminum sheet confined with a 1 mm thick acrylate tape was simulated. The acquisition of the velocity profile was realized with a VISAR. Two equations of state were used: the SESAME and the BLF one. The results of the simulations compared to the experimental shot are given in Fig. 10.

The 10% error margin of the VISAR is represented by the filled gray area, and the experiment is denoted by the full black line while the simulation results using the two EoS are represented by the red and blue lines.

The BLF EoS appears to be giving a slightly more accurate result compared to the SESAME EoS in terms of shockwave propagation velocity. However, the SESAME EoS better represents the velocity of the first peaks of the experimental velocity profile. Although both could be considered close to the experiments, the velocity given by the BLF EoS in longer time interval (⁠ $>500$ ns) follows more accurately the peak velocity of the experiment. From Eq. (11), one can see that to accurately calculate $I$ the peak velocity must be accurately predicted over a long time period. For this reason, the choice was made to use the BLF EoS for the comparison with the simulations.

A slight difference can be observed between the experimental and simulated rise and maximum velocity of the first peak. The difference in the rising of the first peak could be explained by the difference in surface absorption, as the value used in the EoS is for perfectly polished aluminum while the samples were not perfect. The maximum velocity difference can most likely be explained by the input fluence used in the ESTHER code. The value calculated from the experimental energy measurement is an average over the whole laser spot, looking at Fig. 6(a), one can see that the energy distribution is not homogeneous in our experiment. Areas of higher and lower power density are observed and probes numbered 2, 3, and 4 are located in an area of higher local fluence, which explains the maximum velocity difference between experiment and simulation.

Finally, the reasons for the disparities observed between the two EoS can also be of multiple origins. First, the solid–liquid transition is sharper with the BLF EoS while the SESAME EoS bridges the data before and after the said transition. This is shown in Fig. 11 where the pressure depending on the density of aluminum is represented for (a) the BLF EoS and (b) the SESAME EoS. Moreover, the liquid–vapor transition is also taken into account with BLF while not with SESAME. Finally, multiple parameters differ between the two EoS in their hot liquid model such as their Grüneisen and dilatation coefficient. Because of these reasons, the thermodynamic paths of the material submitted to energy deposition may slightly differ and, thus, explain the differences in the free surface velocities.

Figure 12 shows the momentum as a function of energy at the target surface for the experimental shots and for the ESTHER simulations. The experimental and simulated shots follow close trend lines: $Q∝ E 0.80$ for the experimental results and $Q∝ E 0.78$ for the shots simulated with the BLF equation of state. The fit was performed without considering the 19.6 J shot for the same reasons as stated in Sec. III B.

The comparison of both experimental and simulated results shows an average deviation of 10.0%. The first point on the plot at 19.6 J presents one of the highest deviation (14.5%). The other experimental shots presented a deviation comprised between 2.1% and 14.8%, with the highest being observed for 188 J shots. In this particular case, the variation seems to be linked to experimental factors and not to the code. Overall, the results seem to indicate that although accurate, the simulations are not able to completely represent the phenomena taking place at low laser energy such as the transition from the vapor to the plasma regime. It is also important to note that the low power density used for some shots (20–40 J, $I=0.2$–0.3 GW/cm $2$⁠) puts them at the limit of the validity range of the ESTHER code.

Figure 13 presents the momentum coupling as a function of the parameter $Iλ τ$ for the experimental and simulated results. The same observations can be made as for Fig. 12: the deviation between the experimental and simulated values increases as the $Iλ τ$ parameter decreases, highlighting the transition to the vapor regime at low $Iλ τ$ (⁠ $≈400$ W/m.s $1 / 2$⁠) for aluminum.

Ballistic pendulum experiments were performed on the HERA platform to calculate the momentum imparted to the pendulum by top-hat laser pulses with a 15 ns FWHM, a 1053 nm wavelength, and a 30 mm diameter laser spot size, using an acrylate polymer to confine the interaction. The momentum was evaluated using PDV and VISAR backface velocity measurements on the targets and showed results of one hundred times higher than those previously obtained using a direct interaction setup (i.e., without confinement and in vacuum). These results also followed the same trend as those presented in Rudder’s work⁴⁶ using a direct regime setup with similar laser parameters. To complete the study, the one-dimensional code ESTHER was used to simulate the experiments with two different equations of state and showed good agreement with the experimental results. The results showed an average deviation of 10.0% using the BLF EoS. The deviation increased as the laser pulse energy decreased, highlighting the difficulty in accurately representing the transition from vapor to plasma phase as described in the Phipps model¹⁵ with a mono-dimensional code and the current models. Future work will be focused on expanding the range of energy and $Iλ τ$ covered experimentally with direct and confined interaction and also on carrying out experiments with small laser spot configurations to better assess and understand the role of 2D effects on the momentum transfer phenomenon during laser shock experiments.

We would like to thank Laurent Berthe, Sophie Baton, Yann Rouchausse, and Julien Houy for their help and input throughout the design and realization of the experiments presented. More generally, we would also like to thank all the people at the Laboratoire d’Utilisation des Laser Intenses who have kindly helped us to operate the HERA platform.

The authors have no conflicts to disclose.

C. Le Bras: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). E. Lescoute: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). J-M. Chevalier: Data curation (equal); Formal analysis (equal); Investigation (equal); Resources (equal); Visualization (equal); Writing – review & editing (equal). G. Boutoux: Data curation (equal); Formal analysis (equal); Investigation (equal); Resources (equal); Visualization (equal); Writing – review & editing (equal). D. Hébert: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.