Surface structure on diamond foils generated by spatially nonuniform laser irradiation

Here we report on the effects of material strength factors on the generation of surface structure due to nonuniform laser irradiation. The influence of material strength on the generation of perturbation on a diamond surface subjected to nonuniform laser irradiation was experimentally investigated. Our previous investigations suggested that stiffer and denser materials reduce surface perturbation due to spatially nonuniform laser irradiation, which was reproduced well by calculations with multi-dimensional hydrodynamic simulation code. In this work, we found that local fractures due to yield strength failure are generated by high degrees of irradiation non-uniformity. A characteristic crack-like surface structure was observed, which was not reproduced by the 2D simulation code calculations at all. The 2D simulations showed that the pressure at the diamond surface locally exceeds the Hugoniot elastic limit due to nonuniform irradiation, implying the potential for development of surface perturbations. We also measured the areal-density distribution of perturbations for single-crystal diamond and diamond with a thin high atomic number (high-Z) coating on its surface. The experimental results imply that the combination of a stiff material and thin high-Z coating can suppress the solid-strength effects caused by large irradiation non-uniformity. The knowledge given here is applicable to inertial confinement fusion target design, laser material processing, and universal problems involving solids and high-energy-density plasmas.

In the case of diamond, the shock physics is more complicated compared with conventional ICF capsule materials (e.g., plastic), due to its tightly bound crystalline structure in combination with an ultrahigh melting temperature, and the existence of the phase transition to BC8 24,25 at ultrahigh pressure. The existence of a solid or partially melted diamond ablator during the ICF implosion phase can provide microstructures that seed hydrodynamic instabilities 18,26,27 . Using a strong shock that completely melts the diamond or keeping within the coexistence regime is necessary in order to suppress distortions of the shock front due to anisotropy in the sound velocity in crystals 18 . The anisotropy of diamond is indeed a concern for the ICF application, but recent experiments at NIF have demonstrated that this can be mitigated by using an optimized laser pulse profile 21 . Although the diamond with its high stiffness is becoming a candidate ablator material, brittle materials such as diamond can easily cleave due to dynamic stress along certain crystallographic planes 28,29 . In the case of direct-drive inertial confinement fusion, in particular, nonuniform laser irradiation would lead to local fracture on the brittle material surface. However, there has been no previous work done on material strength issues due to nonuniform irradiation so far.
In this paper, we report on the effects of material strength against dynamic stress on the surface perturbation due to spatially nonuniform laser irradiation. An understanding of the effects of solid strength under laser irradiation is also important in the basic physical process of laser material processing and the early phases of inertial confinement fusion. We carried out measurements of the areal density of perturbations due to non-uniform laser irradiation with the face-on x-ray backlighting method, which is a standard technique in hydrodynamic instability experiments 4,6 . In this study, we present perturbation areal-density data and their analysis, as well as calculations of perturbation areal density and amplitude with the two-dimensional hydrodynamic simulation code PINOCO-2D 30 . We analyzed the effects of irradiation nonuniformity and high-Z coating on the areal density of perturbations in diamond foils. All the results from the experiments and simulations suggest that material strength factors affect the surface perturbation due to nonuniform laser irradiation. In the Methods section, details of the experimental method and specifications for measurements of the areal density of perturbations are described.

Results
Measurements of perturbation areal-density growth with face-on backlighting technique. The experiments were conducted using the GEKKO-XII Nd: glass laser facility at the Institute of Laser Engineering, Osaka University 31 . An overview of the experimental setup and typical stacked pulse shape are shown in Fig. 1. The diamond foils were irradiated with the second harmonic laser emission (wavelength: 0.527 μm). The stacked pulse with time delays between the beams consists of one beam for the foot pulse at an intensity of ~4.0 × 10 12 W/cm 2 , and a subsequent pulse with two beams for the main drive pulse, at an intensity of ~10 14 W/cm 2 (see Fig. 1(b)). Figure 2(a) shows the spatial pattern of the foot pulse at the target surface. Foot pulses had irradiation nonuniformity (perturbation intensity/average intensity ~40%), in order to generate a surface perturbation due to nonuniform irradiation. The wavelength λ of the perturbation intensity variation was λ ~ 100 μm as shown in Fig. 2(b). Perturbations were observed on the target via amplification due to Rayleigh-Taylor instability (RTI) growth using the main drive beams, because the imprinted perturbations were typically too small for detection 15 .
Examples of raw streaked backlit images of the diamond and diamond with thin Cu coating (0.1 μm t ) foils for the foot pulse intensity ~4.0 × 10 12 W/cm 2 are shown in Fig. 3. The time origin (t = 0) was set as the time when the onset of the main drive pulse reached the half maximum, as shown in Fig. 1(b). Figure 3 also shows the lineouts for these targets. Time-integrated lineouts were obtained for the temporal resolution duration (~140 ps). The areal density of perturbations was obtained by fitting the convolutions of the resolution functions and sinusoidal perturbation functions to the raw lineouts, taking into account the x-ray absorption coefficient (at hν = 1.53 keV), which was calibrated with "cold" materials. This detail is described in the Methods section. From the lineouts for the diamond with irradiation non-uniformity ~10%, typical sinusoidal-like perturbations of the RTI growth can be seen in Fig. 3 (a). On the other hand, in Fig. 3 (b), the backlit image for the diamond with large irradiation non-uniformity of ~40% indicates a non-sinusoidal perturbation with "sharp" structure, which is different from the usual single-mode perturbation growth of the diamond observed for laser irradiation non-uniformity www.nature.com/scientificreports www.nature.com/scientificreports/ 10% 17 . Please note that the structure on the diamond surface is referred to as "crack"-like because we observed sharp grooves from the shadowgraph measurements. When a high-Z coating was present on the diamond, no sharp structure was observed as in Fig. 3 (c); instead, the non-uniformity was close to the typical sinusoidal perturbations of the RTI growth. Figure 4 presents plots of the temporal evolution of the areal density of perturbations for the diamond with laser irradiation ~40%, with the fundamental (λ: 100 μm) and second harmonic (λ: 50 μm) perturbation. In our previous work 17 , for diamond with irradiation nonuniformity ~10%, it was found that only the fundamental perturbation was observed, which was well-reproduced by the two-dimensional radiation hydrodynamic simulation code PINOCO-2D 30 . For the diamond with large irradiation non-uniformity of ~40%, however, the second harmonic component rises to the same level as the fundamental component at very early times, prior to onset of the foil acceleration: ~0.75 ns. Both fundamental and second harmonic components individually grow with their own growth rates. For the diamond with large irradiation nonuniformity of ~40%, ordinal imprinting generation and amplification are not observed, unlike previous studies of single spatial mode planar foil experiments 4,6 . Also shown are the results of calculation with the PINOCO-2D code, which do not reproduce the experimental result at all. The second harmonic component from the PINOCO-2D simulation is negligibly small compared with the fundamental component.
The temporal evolution of the areal density of perturbations for diamond with a Cu coating with irradiation non-uniformity of ~40% is also plotted in Fig. 4. The fundamental perturbation grew with time, which is in good agreement with the PINOCO-2D simulation result. The growth with time of the second harmonic perturbation is much smaller than that of the fundamental component after the foil acceleration time of ~0.5 ns (not shown here). Hence, a sinusoidal-like perturbation arises, as seen in Fig. 3(c).
Please note that the second harmonic components without Cu coating are antiphase from those with Cu coating. The second harmonic generation on the Cu-coated diamond is very typical Rayleigh-Taylor instability in the linear to non-linear growth regime, which is called bubble-spike generation. On the other hand, the perturbation shape on the diamond is not the bubble-spike shape but rather the "crack"-like structure, as illustrated in Fig. 4. This fact clearly shows that some hidden physics exists in the generation of imprinting perturbations on the diamond surface.

Discussion
From the experimental results, the 2D hydrodynamic simulation calculations do not reproduce the experimental results when the irradiation non-uniformity is large, as shown above. In order to interpret these facts, we consider the effects of materials strength on the generation of surface perturbation due to nonuniform laser irradiation. From previous shock compression experiments, the Hugoniot elastic limits (HEL) of diamond are measured to be 80.1 (±12.4), 80.7 (±5.8) and 60.4 GPa (±3.3) for the <100>, <110>, and <111> orientations, respectively 32 . The elastic yield strength of diamond inferred from these measurements is 75 (±20) GPa 32 . In our experiments, pressure perturbations due to the foot pulse produce non-uniform stress, namely tensile stress and shear stress, in the diamond foils. In the regime beyond HEL pressures, slip and fractures, which are not taken into account in the hydrodynamic simulation code, may occur primarily on crystal planes 32,33 . As a result, non-sinusoidal perturbation would be generated at the diamond surface. Figure 5 shows the density and pressure distribution calculated by the PINOCO-2D code near the ablation front at early irradiation times. When the irradiation nonuniformity is large (40%), a compressed area exceeding the HEL or (elastic yield strength) of diamond locally appears as shown in Fig. 5(a). On the other hand, when irradiation nonuniformity is small (10%), most of the compressed area is over the HEL (Fig. 5(b)). The experimental data clearly indicate that the spatial perturbation is generated on the ablation surface (compression region), then the areal-density perturbation grows due to the Rayleigh-Taylor instability. Thus, the presence of crack-like structure in this experiment is not explained by cavitation nor spallation that occur when the pressure is released. At the pressure over the HEL, crystal is collapsed and transformed to plastic state which is movable like a fluid. On the other hand, crystal at elastic state is difficult to move. When the irradiation nonuniformity is large (40%), there appears two regions: elastic and plastic states on the diamond www.nature.com/scientificreports www.nature.com/scientificreports/ surface. Therefore, the mechanical local fracture due to elastic-plastic transition is the most probable interpretation for the generation of the crack-like structure.
We have also evaluated the effect of material strength using a thin high-Z coating that smooths the effects of irradiation non-uniformity or pressure perturbation. In previous multi-mode imprint experiments [13][14][15] , under initial low-intensity laser irradiation, the high-Z ablation layers were observed to expand and convert the initial nonuniform laser flux into uniform x-ray radiation, which uniformly ablates and accelerates the target. As the laser pulse shifts to higher intensities, the high-Z material burns away, and the target transitions to pure direct drive [13][14][15] . Figure 5(c) shows the pressure distribution for the non-uniform foot pulse irradiation (40%) for the diamond with a Cu coating. It is clear that pressure perturbation can be reduced by the high-Z coating compared to that without a Cu coating. That means local fracture at the surface is suppressed due to relaxation of the pressure perturbation. Hence the influence of material strength would be suppressed by the presence of a high-Z coating. As shown in Fig. 3, the crack-like structure, which is a non-sinusoidal perturbation, disappears for the samples coated by thin high-Z layers. This also suggests that the combination of diamond and high-Z coating are effective for suppression of the material strength effects due to large irradiation non-uniformity.
In conclusion, we have investigated the solid-strength effects on surface perturbation due to nonuniform laser irradiation when using diamond as an ablator material for ICF targets. When the irradiation non-uniformity is  large, a compressed area exceeding the HEL of diamond develops, showing a crack-like surface structure. The thin high-Z surface coating is effective in suppressing local fracture due to the large pressure perturbation. These findings are particularly closely related to the target physics at the early irradiation time regime in direct-drive ICF. In particular, the performance of laser implosion is sensitive to fracture of the brittle ablator due to nonuniform irradiation. The knowledge from this study is crucial to the understanding not only of ICF target physics but also laser-material interactions and laser material processing. Further investigations on more precise measurements and modeling would reveal the detailed physics of the structure on laser irradiated surface. Methods target samples and laser conditions. The targets comprised single-crystal diamond foils (Type-Ib, density: 3.51 g/cm 3 ) with a thickness of 13-16 μm 17 . The surface orientation of the single-crystal diamond was the (100) plane. The target foils were coated with Al of 0.05 μm thickness as a shield for shine-through inside of the foils in the very early irradiation time regime. Some of the diamond foils were surface-coated with Cu of 0.1 μm thickness in order to compare the smoothing effects on irradiation non-uniformity, which is described above in the Results and Discussion sections.
The diamond foils were irradiated with the second harmonic laser emission (Wavelength = 0.527 μm) at an incident angle of 37.4°. The laser pulse consisted of one beam for the foot pulse and two beams for the main drive pulse, with time delays between the beams (Fig. 1(b)). The pulse shape was Gaussian with a 1.3 ns duration at full width at half maximum (FWHM). The laser pulse was focused on to the diamond foil to a spot with a size of ~600 μm (FWHM). The average intensity, I 0 , of the foot pulse was ~4 × 10 12 W/cm 2 . The peak intensity of the main drive was ~10 14 W/cm 2 . Intensity modulation δI of the foot pulse was introduced using a grid mask placed in front of the focusing lens, whereas the main drive was kept uniform. The spatial pattern and intensity distribution of the foot pulse on the target are shown in Fig. 2(a). The modulation wavelength on the target surface was 100 μm, with www.nature.com/scientificreports www.nature.com/scientificreports/ intensity non-uniformity δI/I 0 ~ 10% or ~40%. The higher spatial harmonic components (wavelength: 20-50 μm) in the imprint pulse were less than 10% of the fundamental wavelength (as shown in Fig. 2(b)).

Measurements of areal-density perturbation with face-on x-ray backlighting technique.
Perturbations were observed on the target via amplification due to the RTI growth using the main drive beams because the imprinted perturbations were typically too small for detection 17 . The areal-density perturbation growth was measured using a face-on x-ray backlighting technique. A backlight target (Zn) was irradiated to generate ~1.53 keV quasi-monochromatic x-rays coupled with a 6 μm-thick aluminum filter. Temporal evolution of the transmitted x-rays from the Zn backlight target through a diamond foil was imaged through a slit (10 × 50 μm 2 ) onto the CuI photocathode of an x-ray streak camera. The total magnification was ~25.9×, and the temporal resolution of the x-ray streak camera was ~140 ps. Data analysis. The spatial resolution was measured using a backlit grid image that took into account the analysis of the areal-density perturbation. The Au mesh (63.5 μm/period) was used to obtain the backlit grid image. The resolution function R(x) of the entire diagnostics system is given by the sum of two Gaussian functions as π σ ασ where α = 0.242, σ 1 = 4.881 μm, and σ 2 = 11.303 μm. The areal-density perturbations δ(ρl) were obtained by fitting the convolution of the resolution and a sinusoidal perturbation function to the raw lineouts, taking into account the x-ray absorption coefficient (μ = 660.9 cm 2 /g) for diamond. The raw lineouts function I(x) is expressed as where I 0 is the spatial intensity distribution of the backlight X-ray source, and δ(ρl) 1 and δ(ρl) 2 are perturbation amplitudes of the fundamental component and the second harmonic component, respectively. k (2π/perturbation wavelength) is the wave number of the raw lineouts. Fitting by convolution, considering the fundamental and second harmonic components, was in good agreement with the line profile. The trajectories of the irradiated foils were also determined using side-on x-ray backlighting in order to evaluate their basic hydrodynamics. Simulations were carried out using the two-dimensional (2D) radiation hydrodynamic code PINOCO-2D for comparison with the three experimental configurations. PINOCO-2D gives the arbitrary Lagrangian Eulerian (ALE) hydrodynamic for the radiation. This code includes hydrodynamic, flux-limited Spitzer-Härm thermal conduction 34,35 , nonlocal thermal equilibrium multigroup radiation transport, quotidian equation of state 36 , and ray-trace laser-energy deposition. For the EOS, we incorporated a multiphase EOS 37 , and a table of melting curves 38  Here, the x axis is perpendicular to the target surface, x a is the position of the ablation front, x r is the position of the rear surface, ρ(x,y) is density distribution in the target, and y p and y u are the perturbed and unperturbed y coordinates of the transverse direction, respectively. The ablation front x a and rear front x r are defined to be at 1/e of the peak density. In our calculation of perturbation areal density, the density distribution ρ(x,y) is considered as mentioned above.