Porous materials, also known as foams, have a non-trivial internal structure, constituted by randomly arranged solid parts, which can be filaments or membranes, separated by empty spaces. These materials have a wide range of application in the laser-plasma interaction experiments. They are used for the study of equations of stateand shockwaves, for increasing the efficiency of absorption of laser energy and of its conversion into X-rays, as bright neutron sources and to enhance electron acceleration by short laser pulses.

In the direct drive schemefor Inertial Confinement Fusion (ICF), foams with an average density larger than the critical density for the given laser wavelength, also named overcritical, have been suggested to be employed as absorbers for the fusion capsule, being able to increase the ablation loading on the target surface. Foams of subcritical density showed the ability of smoothing spatial inhomogeneities of the laser profile and have been suggested as liners in the indirect drive scheme for ICF to delay the closing of the entrance holes of the hohlraum and to improve the capsule drive.

The peculiarity of laser-produced plasma in a porous material is the nonequilibrium nature of its state associated with the homogenization process. In these materials, the absorption of the laser energy occurs volumetrically at the homogenization depth, leading to a higher absorption efficiency in comparison with a solid target constituted by a homogeneous material. Despite the many experiments performed in the last decades and the actual experimental interest about laser-foam interaction, the experimental behavior of the inhomogeneous plasma generated by the laser in the porous material is still not well established in all its aspects, and numerically simulating the laser interaction with the foam is still a challenging task.

Recently, effective analytical and numerical models have been developed and implemented in existing hydrodynamic codes for laser-plasma interaction for reproducing the features of laser-foam interaction and energy transport in a reasonable computational time. In particular, the MULTI-FM code has been recently developed by the authors of this work and it is based on the use of limiters for the thermal conductivity and pressure gradient which depend on the homogenization degree of the plasma.

The experimental and theoretical study of the light reflection from laser-produced plasmas of foams is of primary importance for understanding the physics of laser interaction with partly-homogenized plasmas as well as the directions of foam applications in ICF target design.

In the work published on High Power Laser Science and Engineering, Vol. 9, Issue 3(M. Cipriani, S. Yu. Gus'kov, F. Consoli, et al. Time-dependent measurement of high-power laser light reflection by low-Z foam plasma[J]. High Power Laser Science and Engineering, 2021, 9(3): 03000e40), the authors reported about the time-dependent measurement of the total laser light reflected during the irradiation of overcritical foam targets at ABC laser facility in the Centro Ricerche Frascati of ENEA (Italy). ABC is a Nd-glass:phosphate laser, able to deliver two counterpropagating infrared (λ = 1054 nm) beams with a duration of 3 nanoseconds and energy per beam up to 100 J, for a maximum intensity on the target of ~10¹⁵ W/cm². In these experiments, one beam was employed with an intensity of about 10¹⁴ W/cm². The targets were made of free-standing polystyrene foams with a density of 10 mg/cm³ and pores with an average size of 40 mm. Additional targets made by solid, homogeneous polystyrene were also used for comparison. The authors also implemented in the MULTI-FM code an algorithm to reproduce the light reflection process in the non-homogeneous plasma. The reflection is regulated by the homogenization state of the plasma, being therefore self-consistent with the plasma evolution.

A render of the interaction of a high-power laser pulse with a foam target, showing the trapping of the laser light in the inhomogeneous plasma and the reflection of a small fraction of the incident light towards the laser propagation direction.

The signals of the reflected light collected in the experiments with foam targets were characterized by a lower amplitude compared with the ones obtained from solid targets. This is one of the main results of the paper. The absorption efficiency of the thick overcritical-foam target was measured to be up to 90% for the first harmonic of a nanosecond Nd-based laser. The second main result is the observation, only in the case of foam targets, of oscillations in the amplitude of the signal, which have been interpreted as the manifestation of the homogenization of the laser-produced foam plasma. The same features resulted from the numerical simulations performed with the MULTI-FM code, which were in very good agreement with the experimental data, indicating a way of investigating the internal behavior of the foam plasma by a detailed time-dependent analysis of the laser light reflected from the target. Moreover, the oscillations in the reflected light in the simulations dumped in correspondence with the complete homogenization of the foam plasma, which was realized after 2 nanoseconds from the beginning of the irradiation.

Dr. Mattia Cipriani from the Centro Ricerche Frascati of ENEA said that "Given the good agreement between simulations and experimental data, the careful time-dependent experimental analysis of the reflected laser light from a foam target, combined with an ad-hoc numerical model, could be used to obtain a reasonable estimate of the homogenization time of the foam plasma, whose measure is still a very challenging task".

The results of this work can be extended by varying the parameters of the foam targets, in terms of pore size and average density. This kind of parametric scan will be fundamental to further investigate the possibility of estimating the homogenization time of the laser-generated plasma from the analysis of the reflected light. In such experimental program, the measurement of the transmitted light, in addition to the reflected light, will contribute to extending the measure of the absorption efficiency of the foam samples over a wider range of target characteristics, allowing to further test the reliability of the numerical model of the MULTI-FM code. By adding a spectral resolution to the time-dependent reflected light, it will be also possible to determine the role of parametric instabilities in the reflection process and in the plasma evolution.