Porous materials (foams) are attracting growing interest among those in the high-energy-density physics community working with lasers. Under extreme conditions of high laser intensities and high pressures, in contrast to homogeneous materials, foams are capable of accumulating large amounts of free energy in small-scale turbulent flows, which is relevant to many applications, including inertial confinement fusion,1,2 bright sources of particles and radiation,3 and modeling of dynamic processes in astrophysics. The technology of foam fabrication has evolved rapidly, and in addition to chemical polymerization,4 new methods based on nanomaterial structuring5 and additive manufacturing via two-photon polymerization6 have opened up new avenues for foam applications in high-energy-density physics.

However, the processes of foam transformation in plasma under such extreme conditions of high pressure, high temperature, and high laser intensity are poorly understood, and modeling foams as homogeneous materials of equivalent average density results in significant errors. Such a simplistic approach ignores the physics at the microscopic (pore-size) scale: ablation of structural elements of subwavelength size under the laser irradiation, large-angle laser scattering, generation of vorticity under the interaction of the foam’s structural elements with a shock, corrugations of the shock front, small-scale density fluctuations, etc. These processes depend strongly on the method of foam fabrication, the pore size, and the shape and material of the structural elements. In addition to its practical importance, an understanding of microscopic foam properties will shed light on fundamental features of turbulence that can be studied under controlled conditions.

It is essential to investigate the excitation and evolution of plasma turbulence under intense laser irradiation and strong shock pressures, develop theoretical models making connections between microscopic turbulent flows and macroscopic foam properties, and understand how microscopic structures affect macroscopic responses. There are three directions along which this work can proceed:1.Experimental studies of foam dynamics under intense laser irradiation and strong shocks on laser facilities. A new generation of high-repetition-rate laser facilities, such as ELI,⁷ will allow the establishment of the large database needed for statistical analysis, optimization of foam performance, and validation of theoretical models.2.Development of techniques for the fabrication of foams with desirable properties and in the large quantities needed for high-repetition-rate experiments. Foam targets have already been demonstrated to be of interest for the study of laser–plasma interactions with chemically fabricated⁸ and laser-printed^1,9 foams (see Fig. 1).3.Development of microscopic data-informed models of foams. Such models specific to foam fabrication technology can be implemented in radiation hydrodynamics codes ready for use in high-energy-density applications.¹⁰

Each of the research directions listed above presents significant challenges and requires the development of original and innovative approaches. Experimental data concerning foam properties under extreme conditions are limited to a few publications covering a restricted domain of parameters, with a limited number of diagnostics and with imposed foam structures.11 It is therefore necessary to develop a more regular and coherent approach consisting of diagnostics providing information about macro- and microscopic foam properties and comparing porous materials with different and controlled microscopic structures produced using various technologies.

Macroscopic properties of foam ionization and homogenization can be studied by measuring the X-ray emission from the ionization front and with a two-VISAR technique aiming to diagnose the propagation of two subsequent shocks with different delays: one propagating through a cold material and the other propagating behind the first and through a partially homogenized foam. Microscopic foam properties can be characterized by X-ray spectroscopy of dopants and side-view radiography, providing information about electron and ion temperatures, amplitude and size of density fluctuations, and, possibly, microscopic flow velocities using UV and X-ray Thomson scattering. These diagnostics will provide for the first time information about the quantity of free energy stored in the foam-produced plasma and its partition between turbulent flows and temperature disequilibrium.

In addition to chemical methods of foam fabrication, some new techniques have been developed. They include the use of carbon nanotubes, fabrication of nanowires in a regular or stochastic arrangement, and additive manufacturing of porous structures.9,12 Compared with traditional methods, these new techniques open the way to the use of a wide range of materials and promise new functionalities such as high mechanical stability, ability to withstand tensile stress, and resistance to extreme irradiation conditions. However, the dynamic properties of these new materials are largely unknown, and their fabrication is limited to small quantities. There is an evident need to build links between material structure, fabrication technology, including new methods of foam doping and coating, and plasma properties under extreme conditions. Eventually, it will be possible to design materials with desirable properties and develop techniques for mass production of foams.

The data acquired in experiments will be used for the development and validation of theoretical models of foam interaction with intense laser radiation and foam dynamics under strong mechanical loads. Instead of direct modeling of porous materials, which is time-consuming and limited to small volumes, subgrid models of a single-pore response to laser radiation and strong shocks are under development. Both dry and wetted foams are of interest for applications and need to be considered. The microscopic processes to be investigated include deformation and ablation of structural elements, formation of ambient plasma, density homogenization, and energy partition between micro- and macroscopic flows. Such subgrid models coupled to radiation hydrodynamic codes will provide an accurate and predictive description of foam properties in experiments.

Two foam configurations are of particular interest:1.Underdense foams, which have an average density smaller than the critical density and are therefore transparent to laser radiation after homogenization, are of interest for laser imprint smoothing in inertial confinement fusion, charged particle acceleration, and the creation of bright X-ray sources.2.Higher-density, overdense foams, which are exposed to laser-driven shocks and radiation fluxes, are promising for use in innovative target designs in inertial confinement fusion, since they are more resistant to hydrodynamic instabilities.

The challenges to be faced concern the assessment of ion overheating in foam-produced plasmas, the quantity of kinetic energy stored in microscopic flows, and homogenization time. Macroscopic characteristics such as shock propagation velocity and plasma temperature obtained in experiments will be used to tune and validate theoretical models and numerical codes. Combining theory and experiment will make it possible to design foams with the specific properties needed for particular applications.

Acknowledgment. This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.