Laser-produced plasmas with electron densities less than or comparable to the critical density are used in many applications of high-energy-density physics related to the creation of bright X-ray sources,1 acceleration of charged particles,2 and laser imprint mitigation in inertial fusion experiments.3,4 However, the plasma critical density, at which the electron plasma frequency is equal to the laser frequency, corresponds for optical lasers to a mass density of 3–30 mg/cm³, which is much lower than the typical density of bulk materials. Solid porous materials (foams) are well suited for reaching electron densities of fully ionized homogenized plasmas below the critical density (undercritical foams). Several techniques for production of low-density foam have been developed.5 Foam targets are relatively inexpensive, produce small amounts of debris, and are suited for mass production. However, they are fragile, and the effect of porous structure on plasma formation is poorly understood.

The technique of additive manufacturing (AM) using two-photon laser polymerization6 opens new perspectives for using foams in laser–plasma interaction studies.7 Laser-printed AM foams have a controllable, regular structure and higher rigidity,8 and they can be free-standing, allowing for much better diagnostic access.9 However, the thickness of structural elements and the pore size in AM foams are an order of magnitude larger than those in chemically produced foams of the same average density. Such foams have been much less studied,10,11 and the role of pore size in foam homogenization has not yet been investigated.

In this paper, we report experimental studies of laser interaction with three types of foams of approximately the same average density but produced with different techniques and having very different internal structures. The foam ionization and heating are characterized using three complementary X-ray diagnostics, and the experimental results are compared with the results of numerical simulations performed with the recently developed foam homogenization hybrid ablation–expansion model.12

The experiment was conducted on the PALS laser facility,13 delivering pulses with energy 600 J and duration 300 ps at a wavelength of 1.3 μm. In this experiment, the laser light was converted to the third harmonic, and so the critical density was larger than the average foam density. Therefore, fully ionized targets were optically transparent to the laser. The beam was focused on the target with an f/2 lens and a random phase plate at normal incidence. The laser energy on target was up to 190 J. The intensity distribution on the target can be represented as a superposition of two Gaussian functions, with 50% of the total energy contained in a circle of 120 μm full width at half maximum (FWHM) and 90% of the energy encircled in 500 μm FWHM.14 The average intensity in the 120 μm circle was 3 × 10¹⁵ W/cm², while the average intensity over the focal spot was up to 3 × 10¹⁴ W/cm². The laser pulse had an approximately Gaussian temporal profile with a duration of about 300 ps FWHM.

Three types of foam targets were studied:

1. 1.Plastic targets made of trimethylolpropane triacrylate (TMPTA, C₁₅H₂₀O₆) aerogel had an average density ρ_av ≃ 10 mg/cm³, thickness 600 μm, pore size l_pore ≃ 1 μm, and wire-like solid elements of diameter d_s ≃ 0.1 μm and density ρ_s ≃ 1 g/cm³ [Fig. 1(a)]. They were doped with 8 wt. % chlorine for the plasma diagnostics with X-ray spectroscopy. This type of material has been used at PALS in several experiments,15,16 and its properties are known. The foam was placed into a steel washer of inner diameter 1 mm with a lateral slit that served either for X-ray spectroscopy or, in another set of shots, for X-streak measurements of ionization wave propagation [Fig. 2(a)]. Copper foil of thickness 7–8 μm was attached to the rear side of the foam for hot-electron imaging using Cu Kα emission.
2. 2.Graphene targets of average density ρ_av ≃ 7–8 mg/cm³ had thickness 700–800 μm and pore size l_pore ≃ 2 μm [Fig. 1(b)].17 The solid elements were made from high-density carbon (HDC) of density 2.3 g/cm³ in the form of folded foils of irregular shape and thickness about 20 nm. The foam was free-standing, with copper foil attached to the rear side.
3. 3.Although supercritical AM foams were used in the previous experiments,11,18 we used undercritical laser-printed AM targets with average density ρ_av ≃ 8.5 mg/cm³, thickness 600 μm, diameter 950 μm, and a regular octet truss structure with beams of diameter d_s = 2 μm and density 1.2 g/cm³ (CHO) [Fig. 1(c)].8 The average distance between beams was about 20 μm. The target was free-standing thanks to a “cage” consisting of a thick frame of two rings connected by four rods [Fig. 2(c)] printed around the foam structure outside the laser–target interaction region. Copper foil of thickness 7 μm was attached to the rear side of the foam for X-ray imaging [Fig. 2(b)]. For comparison, several shots were performed with solid targets: planar copper foil, polypropylene plastic foil with copper foil attached at the rear side, and Saran (polyvinyl chloride, C₂H₃Cl) plastic foil.

As all three foams were made of plastic materials and had similar average electron densities, the basic differences influencing the laser–foam interaction were the cell size and cell topology. The basic parameters of the foams are summarized in Table I.

The four diagnostics deployed in the experiment are shown in Fig. 3. A soft X-ray streak camera was used to measure the velocity of ionization front propagation. It was positioned in the target plane perpendicular to the laser axis and received the target emission in the spectral range of 1–10 keV through the washer slit.

The macroscopic parameters of the plasma created inside the foam were measured using an X-ray spectrometer equipped with a mica crystal spherically bent to a radius of 150 mm. The spectrometer was aligned to simultaneously cover spectral ranges of 4.3–4.55 and 3.44–3.64 Å in the fourth and fifth diffraction orders, respectively, and measured the diagnostically important emission lines of highly ionized Cl atoms Heα_y (4.467 Å, intercombination line) and Heδ/Lyβ (3.523/3.534 Å).19 Owing to geometric restrictions inside the interaction chamber, the spectra were observed at an angle of 69° from the laser axis, recorded on Fuji BAS MS imaging plates (IPs), and digitized using an absolutely calibrated GE Amersham Typhoon scanner with pixel size of 25 μm.20

The spectrometer configuration was optimized to provide high spectral and spatial resolution for the detector positioned at the Rowland circle. The characteristics of the chosen experimental geometry with spatial demagnification of 0.59 were checked by a ray tracing procedure,21 including the detailed reflection curve of the bent crystal, the real source dimensions, and the pixel size of the detector used, i.e., the parameters likely to affect spectral resolution. Although the effect of the source size was negligible, the intrinsic spectral resolution of the spectrometer (λ/Δλ ≃ 10 000) was reduced to 1300, owing to the IP resolution of about 53 μm.20 The spatial resolution along the laser axis also dropped to 97 μm (as recalculated with respect to the source normal and taking into account the spectrometer demagnification and the angle of the spectral observation).

The recorded signal was recalculated to an intensity scale with respect to a variable crystal reflectivity and transmission through protective filters. The wavelength scale was calibrated using the calculated dispersion relation of the experimental geometry and cross-checked via tabulated dominant transitions of H- and He-like Cl.

Doppler broadening of the Heα_y line was interpreted in terms of the ion temperature,22 whereas the intensity ratio of Heδ/Lyβ transitions evaluated using the collisional–radiative code FLYCHK23 was used to infer the electron temperature.

An absolutely calibrated hard X-ray imager was used to measure the time-integrated Cu Kα₁ emission produced by hot electrons in copper foil attached to the rear side of the foam. The two-dimensional spatially resolved images of the Cu Kα₁-emitting area were recorded at a magnification M = 1.73 using a quartz (422) crystal spherically bent to a radius of 380 mm. This combination of Cu Kα₁ emission (1.5406 Å) with the crystal interplanar spacing 2d = 1.5414 Å resulted in quasi-normal incidence and quasi-monochromatic diffraction, providing minimal distortion of the recorded images. The hot-electron-induced X-ray emission was observed in the horizontal plane at an angle of 27.6° from the foam surface using the IP, and the recorded images were again scanned with a pixel size of 25 μm. The IP-limited spatial resolution related to the Cu foil surface was 66 μm in the horizontal direction and 30 μm in the vertical direction. Recorded Cu Kα₁ fluxes were recalculated with respect to the emission from the target using the ray-traced transfer function of the imager21 and then related to the incident hot-electron dose using the code GEANT424 combined with the averaged Livermore Monte Carlo model25 and assuming a characteristic hot-electron energy of 30–50 keV, hot-electron generation of 300 μm in front of the irradiated target surface, and a parallel hot-electron flux toward the target. The details of the design and performance of the imager can be found in Ref. 26.

In several shots, a short-pulse optical probe was applied to measure the transmission before and after the laser shot through TMPTA foam without a copper layer. A Ti:sapphire laser pulse of duration 70 fs and energy 165 μJ converted to the second harmonic (wavelength 405 nm) was used as a probe. It was focused at an angle of 30° to the target normal to a focal spot of 165 μm. The probe intensity on the target was below the foam damage threshold. The transmitted probe light was measured in the near and far fields, thus providing information about density fluctuations. Preset synchronization between the sub-nanosecond and femtosecond lasers had a relatively large jitter of ∼100 ps, but the measured delay had a significantly better accuracy of about 10 ps.

Laser interaction with low-density porous materials differs in many respects from interaction with bulk materials. Density homogenization of a porous microstructure is a complex multistage process. Laser energy is first absorbed by electrons via the inverse bremsstrahlung mechanism, and electrons initiate expansion of the solid elements. Two main regimes of interaction are identified. Nearly uniform heating of the whole volume of very thin solid foam elements with thickness less than the laser skin depth leads to volume expansion, whereas gradual ablation dominates for thicker solid elements. Most of the absorbed laser energy is transferred to ion kinetic energy during the expansion. The empty pores are gradually filled by the foam material. When the flows of the foam material collide at the pore boundaries, the ion kinetic energy is converted to ion thermal energy via ion viscosity. Thus, the ion temperature may exceed the electron temperature until the slow process of electron–ion relaxation equilibrates the temperatures. The region of foam homogenization gradually moves into the depth of an undercritical foam.

Figure 4 shows typical X-ray streak images for the three foam targets of different structures; similar results with an accuracy of about 10% were obtained for four TMPA targets, six graphene targets, and three AM targets, since the we had only six AM targets for the whole experiment. The X-ray emission is most intense for the chlorine-doped TMPTA foam, the signal maximum for the 3D graphene target is 2.5 times smaller, and that for the AM target is 1.6 times smaller. The emission starts from the region of laser initial penetration into the target below the target front surface, indicated by the dashed line. The initial laser penetration depth is ∼40 μm for the TMPTA foam, while it is approximately twice as large for the AM target and three times as large for the graphene target. The initial laser penetration depth depends strongly on the size and shape of the foam filaments. It is expected that the laser will penetrate deeper in the case of AM foams with larger pores than for the small pores of TMPTA foams. Although a smaller initial penetration is expected for the closed-pore structures, the observed deeper laser penetration into the graphene foam is tentatively explained by laser transmission through very thin graphene structural elements.

We define the ionization front position (the oblique solid line in Fig. 4) at the level of ∼2%–3% of the signal maximum. It is evident that in spite of the different structures of the foams used, the ionization front velocity is approximately the same for all three and depends essentially on the average target density and laser intensity. It is about 400 μm/ns for the TMPTA target and 450 μm/ns for the AM and graphene targets. However, there is a difference in the position of maximum X-ray emission, which remains near the target surface for TMPTA, but moves inside for the graphene and AM foam. This absence of a maximum X-ray emission displacement indicates a higher laser absorption in the nearly homogenized undercritical TMPTA plasma.

Similar ionization front velocities for similar interaction conditions and foams with different pore sizes and topologies were reported in Ref. 27. From the data provided there, we estimate front velocities of 470 and 420 μm/ns for laser intensities of 10¹⁵ and 10¹⁴ W/cm², respectively, in the case of a SiO₂ foam with small pores and density 8 mg/cm³. A front velocity of 410 μm/ns is estimated for an agar foam with large pores and average density 9 mg/cm³ for a laser intensity of 10¹⁵ W/cm². These data also show a weak dependence of front velocity on pore size.

The speed of the expansion front indicated in Fig. 4 by the dashed line is ∼200 μm/ns for the TMPTA and graphene targets, while it is higher, ∼350 μm/ns, for the AM target. A comparison with hydrodynamic simulations performed with the FLASH code28 with a subgrid module12 indicates that these expansion velocities correspond to a plasma with density ∼30% of the critical density.

Since the plasma expansion velocity in vacuum is larger than the ion acoustic velocity, we conclude that the ionization and heat front velocities are both supersonic during the laser pulse. This high-speed ionization is a specific feature of laser interaction with undercritical materials.29,30 Supersonic propagation of the heat wave is essential when a foam layer is used for laser smoothing and imprint reduction.31

The laser penetration into the foam is limited by the pulse duration. It is about 180 μm for the TMPTA foam and up to 270 μm for the AM and graphene foams. The slowing down of the ionization front is due to laser absorption in the downstream plasma, limiting the energy flux supporting ionization. The apparently more rapid slowing of the ionization wave for the TMPTA target can be explained by less laser energy reaching the front owing to higher laser absorption in the nearly homogenized undercritical plasma. Hot plasma created behind the ionization front lives for ∼1 ns after the end of the laser pulse. It then expands and cools down.

The laser–foam interaction was simulated in a two-dimensional geometry using the hybrid model described in Ref. 12. The model utilized the ablation-dominated interaction regime, which matched experimental data for previous experiments with similar small-pore foams. The results are in a general agreement with the experimental heat-wave propagation data for all three types of foams. The simulated heat-wave propagation velocities are about 470 and 520 μm/ns for the TMPTA and graphene foams, respectively. For the AM foams, the simulation results show a similar velocity of ∼460 μm/ns, but the initial penetration of 120–150 μm is larger than in the experimental X-ray streak image. More detailed simulations are needed to account for the complicated laser spatial profile and shape of the foam elements. In the present simulations, the laser intensity distribution is modeled by a single Gaussian beam with 200 μm FWHM, and the foam structural elements are cylindrical in form, which is suitable for TMPTA and AM foams, but may not be appropriate for the graphene foam with its sheet-like, closed-pore microstructure.

Spectral measurements were performed only with the TMPTA targets, since the other targets were not doped. The emission was spatially and spectrally resolved. A typical spectrum is shown in Fig. 5. The ratio of the chlorine Lyβ to Heδ lines provided an estimate of the electron temperature, which decreases slowly from 900 eV at a depth of 90 μm to about 800 eV at 225 μm inside the target. The electron density was not measured. It is estimated from hydrodynamic simulations to be at a level of (2–3) × 10²¹ cm⁻³ because of plasma expansion behind the ionization front. Owing to the low density of the chlorine doping, the target is optically thin for the emission lines used for diagnostics.

The ion temperature was deduced from the Doppler broadening of the Cl Heα_y intercombination line, which is known to have only a small contribution from other broadening mechanisms.22,32 The ion temperature estimated from the width of the intercombination chlorine Heα_y line is about 3.8 keV for a laser pulse energy of 200 J, and it decreases to 2.5 keV for a lower laser energy of ∼100 J. Broadening of the intercombination line due to the Doppler shift by the lateral plasma motion at the laser beam edges was estimated from our numerical simulations and is negligible. As the angle of observation is not exactly parallel to the target surface, the Doppler shift due to varying longitudinal motion of plasma can lead in principle to a broadening of the intercombination line, but our simulations lead to the conclusion that this is also negligible.

A large ratio of ion-to-electron temperature is a characteristic feature of laser-ionized foam plasmas.22 However, the measured ratio T_i/T_e ≃ 3–4 is larger than in previously reported measurements. A ratio T_i/T_e = 2 was derived22 from X-ray spectroscopy for chlorine-doped agar foam of density 2 mg/cm³ and a ratio T_i/T_e ≃ 1.5 in 2 mg/cm³ SiO₂ foams was estimated33 from stimulated Brillouin scattering (SBS) reflectivity. This difference could be attributed to the higher average density of the TMPTA foams.

An estimate of average temperature (resolved along the target depth) was obtained from simulations by averaging over time and lateral plasma size. To ensure that only the domain containing sufficiently ionized plasma was included, we considered a weighted average where the weight function was the emissivity of the intercombination line for the average T_i or the emissivities of Heδ and Lyβ lines for the average T_e. In the case of a laser pulse of energy 180 J, the average electron temperature is 0.9 keV for the TMPTA foams. The spatial profile of the electron temperature is slightly steeper than in the experimental data, and the average electron temperature from our simulations is T_e = 1050 eV at a depth of 90 μm and 700 eV at 225 μm. The average ion temperature is ∼3.5 keV.

Even though the spectroscopy was not employed for the AM and graphene foams because of the absence of chlorine doping, we can calculate the emissivity-weighted temperatures to estimate the effective temperatures in these targets. The estimated electron and ion temperatures for AM foam are 0.8 and 4 keV, respectively. The ion temperature has approximately linear profile, decreasing from T_i = 7 keV at the target surface to 1 keV at a depth of 300 μm inside the target. This is different from the TMPTA foams, where the ion temperature profile is more uniform and the maximum is T_i ≃ 4.5 keV. For graphene foams, the electron temperature T_e = 0.9 keV is comparable to that of the TMPTA foams. The ion temperature T_i ≃ 5.2–5.5 keV is higher because of the higher average ion charge Z of the target material. An approximate relation between electron and ion temperatures T_i ≃ ZT_e can be derived from the simulation results.

The probe laser pulse was used to measure foam homogenization under the action of the main laser pulse on TMPTA targets with copper foil removed. Other targets were not used in this experiment. It was expected that foam ionization and homogenization would affect the transmission of the probe and its angular divergence. Each target was exposed twice to the probe pulse: first before the main laser pulse and then after it with a delay varied in the range of 0.4–1.5 ns. Figure 6 shows two images taken in the far field for a TMPTA foam of thickness 250 μm. As can be seen in Fig. 6(a), there is rather low transmission through a cold foam, ∼10⁻⁴, and the near-field image is hidden in the noise. This far-field image shows the same angular divergence of 0.3° as the incident probe beam. We attribute such a strong attenuation to the diffuse scattering of the probe in foam. The extinction coefficient is estimated in Sec. IV using Mie theory.

The transmitted probe light after the main laser pulse [Fig. 6(b)] shows three distinct features: first, the transmission is increased by a factor of 20; second, the angular divergence of the transmitted light is increased by a factor of 10; and third, the probe beam has deviated vertically out of the plane of incidence by about 2.5°. This near-field image of the transmitted probe beam has a shape and diameter similar to those of the calibration pulse without any target. These observations are strong manifestations of dramatic changes in the foam state induced by the main pulse.

Hot electrons detected with an X-ray imager were produced in laser interactions with the plasma behind the ionization front and revealed the excitation of parametric instabilities: stimulated Raman scattering or two-plasmon decay.34 Laser shots on a bare copper foil provided a reference value of hot electron dose of ∼0.1 J for a laser energy of ∼180 J. The size of the Kα₁ emission spot shown in Fig. 7(d) is ∼260 μm FWHM, which is twice that of the laser focal spot. The energy of hot electrons and the size of the emission spot are consistent with data from other experiments on PALS.26

Kα₁ emission from the TMPTA target is shown in Fig. 7(b). It has a smaller size compared with a bulk copper target [Fig. 7(d)], and the emission intensity is 20 times smaller. It corresponds to a dose of hot electrons of less than 5 mJ. An even smaller Kα₁ signal is observed in shots on graphene targets [Fig. 7(a)], but the spot diameter is ∼1.5 times greater. This strong suppression of hot-electron production is not yet understood. It may be related to the rapid expansion of homogenized plasma behind the ionization front such that the density drops below quarter critical density, which is 1.4 × 10²¹ cm⁻³. However, it is significantly lower than the maximum achievable plasma density of 3.2 × 10²¹ cm⁻³, and this hypothesis needs confirmation with a direct measurement of plasma density behind the ionization front.

Kα₁ emission from the AM target is shown in Fig. 7(c). It is remarkably different from the other images. First, the size of the emission spot is increased almost threefold to 700 μm; second, the hot-electron dose of 0.08 J is almost the same as in a bare copper target. This observation is confirmed in three consecutive shots with a variation of hot-electron dose by a factor of 2.

This experiment on laser pulse interaction with foams of similar average density but different structures provides new information about the homogenization and heating of underdense foams. In spite of large differences in the pore size and thickness of structural elements, the velocity of ionization front propagation is quite similar for all three foams. It is in the range of 400–450 μm/ns for our interaction conditions, with the lower limit corresponding to TMPTA foams. The results for propagation of the ionization front are in agreement with numerical simulations performed using a radiation hydrodynamics code, including a subgrid model of foam ionization and heating developed in Ref. 12. Compared with a simulation for a homogeneous material of the same average density, the ionization front velocity in foams is reduced by a factor of 2. The basic conclusion that ionization wave propagation speed is only weakly dependent on pore size is in agreement with Ref. 27, where similar propagation velocities were measured at similar laser intensities and foam densities.

Moreover, AM foams show an anomalously high level of hot-electron production, which is more than an order of magnitude higher than in the two other foams. This can be attributed to the incomplete homogenization of AM foams and a strongly inhomogeneous density distribution because the thickness of the AM struts is an order of magnitude larger than the thickness of structural elements in the other two foams.

Laser interaction with TMPTA aerogel foams has been characterized by two other diagnostics: X-ray spectroscopy and probe transmission. The measured ion temperature is approximately three to four times higher than the electron temperature. This is a consequence of laser-driven ablation of structural elements, which is a common feature of all foams and has been reported in other experiments.22 Such an anomalous ion-to-electron temperature ratio may modify the excitation of parametric instabilities, in particular, suppression of the SBS reported in Ref. 33.

In contrast to the probe transmission experiment16 with low-density cellulose triacetate (TAC) foams, which are transparent, the TMPTA foams studied here are opaque. The measured transmission of 10⁻⁴ corresponds to an extinction coefficient h ≃ 370 cm⁻¹. This is consistent with the Mie theory expectation. The foam can be considered as an agglomeration of wires of diameter d_s ≃ 100 nm, which is smaller than the probe laser wavelength λ_p = 405 nm. The dielectric permittivity of plastics in the optical domain, ϵ ∼ 3, is real with a very small imaginary part. This corresponds to the scattering of incident light characterized by a factor Q_sca, the ratio of the scattering cross section to the geometrical cross section.35 Its value for the TMPTA parameters and for incidence normal to the cylinder is Q_sca = 1.7 for polarization perpendicular to the cylinder axis and 0.6 for the parallel polarization. For a qualitative estimate, it is sufficient to take the average value Q_sca ≃ 1 and incorporate the geometrical cross section σ_g into the scattering cross section. Then, for TMPTA foam, σ_g = d_sl_pore ≃ 10⁻⁹ cm², the density of scattering centers is the inverse of the pore volume, ns=lpore−3≃1012 cm⁻³, and the extinction coefficient h = σ_gn_s ≃ 10³ cm⁻¹ is in qualitative agreement with the measured value. A similar estimation gives a much smaller extinction coefficient for the AM foam h ∼ 50 cm⁻¹, which is also in agreement with the observed partial target transparency.

The situation is completely different for the probe sent after the main pulse. This propagates through a high-temperature plasma with large-amplitude density fluctuations if homogenization is incomplete. The transmitted probe energy is reduced owing to inverse bremsstrahlung absorption, which is of the order of 70%–80% according to the measured electron temperature and hydrodynamic simulations.12 This is an order of magnitude larger than the measured transmission of less than 1%, owing to probe refraction and the fact that the focal spot is larger than the plasma size. Consequently, the probe beam edges are strongly absorbed in a colder plasma.

Scattering and deviation of the probe beam are related to plasma inhomogeneity. The expansion of hot plasma creates a large-scale density gradient, which causes refraction of the probe beam. According to geometrical optics, the probe beam is not deviated, but displaced by ∼60 μm if the plasma expansion is planar. The probe beam deviation is related to the curvature of the plasma density profile. The observed deviation of ∼2.5° corresponds to an angle of curvature ∼5°, which is consistent with the plasma density profiles obtained from hydrodynamic simulations.12

The angular spread of the probe beam is related to scattering on density fluctuations. The observed angular broadening of the order of 5° corresponds to scattering on density fluctuations with wavelengths ∼10 times the probe wavelength of 0.4 μm. These wavelengths are comparable to the pore size, but insufficient data are available for estimation of the amplitude of density fluctuations. Another source of density fluctuations may be related to the laser imprint. The size of speckles created in plasma by the main laser pulse smoothed with a random phase plate is of the order of 3 μm, which is comparable to the pore size. Identification of the origin of plasma density fluctuations, their relation to foam fabrication, and their evolution in time need further investigation.

A comparison of laser interaction with foams made of different materials and having different spatial structures has demonstrated unique features, some of which are yet to be understood. The velocity of propagation of the ionization front in the foam is slower than in a homogeneous material of the same average density. It depends weakly on the foam structure and pore size. The ion temperature in the plasma behind the ionization front is a few times larger than the electron temperature, which can lead to a significant decrease in reflectivity by SBS.33 Unfortunately, we did not measure the ion temperature in the laser-heated AM foam, and so its dependence on pore size has not been determined. An important effect is the strong suppression of hot-electron production in undercritical plastic foams with small pore sizes compared with solid targets. This effect was not expected and is not yet understood. On the other hand, the high hot-electron dose for AM targets, comparable to that for a bare copper target, suggests that solid elements in the AM foam were not completely ablated and homogenized under our interaction conditions. The strong dependence of hot-electron production on pore size requires further investigation. Unfortunately, we did not succeed in measuring the foam homogenization behind the ionization front. The probe beam was scattered on the plasma density modulations with characteristic scale comparable to the pore size and the size of the speckled structure imprinted by the main laser beam. Diagnostics more sensitive to small-scale density fluctuations need to be employed in the future experiments.

Acknowledgment. This research was supported by the Center of Advanced Applied Sciences (CAAS) Project No. (CZ.02.1.01/0.0/0.0/16019/0000778) from the European Regional Development Fund. It was also supported in part by the Czech Technical University in Prague Project No. SGS22/184/OHK4/3T/14. We acknowledge partial funding via EUROfusion Enabling Research Project No. AWP24-ENR-03-CEA-02 “Foams as a pathway to energy from high gain direct drive ignition,” within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Program (Grant Agreement No. 101052200—EUROfusion). The views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Commission. Our thanks also go to the Czech Ministry of Education, Youth and Sports (CMEYS) for funding the operation of the PALS facility (Grant No. LM2023068).