Experimental setup

The experiments (see Fig. 1a) were performed on the GEKKO-LFEX laser facility at the Institute of Laser Engineering in Osaka University. The target (see Methods section for more details) used in the experiments consisted of a solid Cu contained CH sphere31 and a CH (parylene) coating layer, which aimed to prevent the Cu atoms from directly interacting with the lasers. Twelve 526-nm GEKKO-XII (GXII) lasers, with an energy of 200 J per beam and a pulse duration of 1.6 ns in full width at half maximum (FWHM), were used to uniformly compress the target. A typical pulse shape of GXII lasers is shown in Fig. 1b, with t = 0 ns defined as 2.0 ns prior to the peak power. According to our benchmarked 2D radiative hydrodynamic simulation (see Methods section), a peak areal density (ρR) of ~0.06 g cm−2 can be achieved at 2.6 ns (Fig. 1b) under these experimental configurations. In joint shots (see Table 1 for detailed experimental parameters), the short pulse (1.5 ps in FWHM) LFEX laser was injected in the equatorial plane at different times around the peak compression (2.6 ns), generating a forward moving fast electron beam. It was focused 230 μm ahead of the target center (Fig. 1a), which corresponded to ~0.5 n c (n c = 1021 cm−3 for the LFEX laser) as predicted by the simulation. The generated fast electrons transported through the compressed target, colliding with the Cu atoms and exciting Kα emission. The spatial distribution of the Cu Kα emission was recorded by a narrow-band (5 eV) Cu-Kα imager; while the total Cu Kα photon number was measured by a calibrated planar highly oriented pyrolytic graphite (HOPG) crystal spectrometer. Fast electrons escaping from the target were measured by electron spectrometers (ESMs) at different directions. An x-ray streak camera (XSC) served to detect the temporal and spatial evolutions of the target self-emission (the thermal emission in photon energy range of 1–10 keV), based on which the 2D radiative hydrodynamic code (FLASH, ref. 32) was benchmarked.

Fig. 1: Experimental setup, laser power and areal density. a Target parameters, the LFEX laser and detectors. A Cu-Kα imager and a HOPG crystal spectrometer are used to detect the 2D image and the spectrum of the Cu Kα emission, respectively. Three electron spectrometers (ESMs) are used to measure the energy spectra of the escaping fast electrons at different directions. An X-ray streak camera (XSC) functions to detect the target self-emission. b Experimentally measured beam power of GXII lasers (black) and simulated target areal density (blue) as a function of time. The LFEX injection times (2.2 ns, 2.6 ns, and 4.6 ns) in joint shots are marked by red arrows. Full size image

Table 1 Experimental parameters of the joint shots. Full size table

A solid sphere rather than a conventional shell was used because of two reasons. First, a mass-equivalent solid sphere is more hydrodynamically stable than a shell during the compression under the current conditions of the GXII lasers33,34, thus promising a denser core at the peak compression with a very good shot-to-shot reproducibility. Second, the core temperature at the peak compression in a sphere target is lower than that in a shell target, facilitating the detection of fast electron transport by the stimulated Cu Kα emission, because the high temperature could shift the Cu Kα line outside the narrow bandwidth of the Kα imager, leading to signal diminishing in the core region16,35.

Apart from the joint shots, where both the GXII lasers and the LFEX laser were applied, some GXII-only shots were also performed by switching off the LFEX laser. In the GXII-only shot, the Kα imager measured the target self-emission in the detectable photon energy range, as well as the Cu Kα emission stimulated by the GXII-produced suprathermal electrons; while in the joint shot, additional Cu Kα emission due to the LFEX-produced fast electrons was observed. By comparing the results between the GXII-only and joint shots, the fast electron induced Cu Kα images were obtained. Applying the same method to the HOPG results, one obtained the total Cu Kα photon numbers produced by the fast electrons.

Experimental results

Figure 2a displays a typical target self-emission recorded by the XSC in experiments, which indicates compression of the target surface up to 3 ns. This compression process is well reproduced by the simulated target self-emission obtained from the benchmarked FLASH code, as shown in Fig. 2b, c. This good agreement between the simulation and the experiment validates the reliability of the FLASH code in predicting the hydrodynamic behavior of the target. The predicted density and temperature profiles at the injection times of the LFEX laser are shown in Fig. 3, while the predicted history of the areal density is shown in Fig. 1b. These results indicate that, because of the laser ablation, a shock is launched in the target, which moves inward until 2.6 ns, forming a high-density shell surrounding the target center (see Fig. 3a). At 2.6 ns, the target reaches its peak compression, resulting in a core with a radius of ~70 μm. The areal density and the density at the target center at this moment correspond to 0.057 g cm−2 and 20 g cm−3, respectively. After 2.6 ns, the target starts to decompress, reaching a size of ~120 μm in half width at half maximum at 4.6 ns. The laser ablation produces a hot (~2 keV) and large density gradient scalelength (~60 μm at the critical density surface for the LFEX laser, see Supplementary Fig. 1 and Supplementary Discussion for more details) coronal plasma around the time of peak compression (e.g., 2.2 ns and 2.6 ns). While at 4.6 ns, the coronal temperature drops below 50 eV due to the termination of the GXII lasers; the density gradient scalelength decreases to ~15 μm due to the decompression of the target.

Fig. 2: Temporal and spatial evolution of the target self-emission. a Experimentally measured and b simulated target self-emission for a typical shot (#41266). The positions of the wings, marked with crosses and lines in a, b, respectively, are plotted in c as a function of time. Here, the positions of the wings are defined as the positions of the peak emission at each side of the target. Full size image

Fig. 3: Simulated density and temperature profiles at different times. Radial distributions of a mass densities of both the whole target (solid) and the Cu atoms (dashed) and b electron temperatures from FLASH simulations at different times: 2.2 ns (blue), 2.6 ns (green), and 4.6 ns (red). Since the inner Cu contained sphere is coated by a CH layer, the size of the Cu contained region is always smaller than the target size, being ~60 μm (2.2 ns), ~50 μm (2.6 ns), and ~100 μm (4.6 ns) in radius, respectively. The density gradient scalelengths at the critical density surface (r ~ 160 μm) for the short pulse LFEX laser are, respectively, ~60 μm (2.2 ns), ~60 μm (2.6 ns), and ~15 μm (4.6 ns). Full size image

The fast electron induced Cu Kα images at different times are shown in Fig. 4a–c, while the corresponding Cu Kα photon numbers measured by the HOPG spectrometer are listed in Table 1. Figure 4a–c reflects directly the fast electron transport in a compressed target at different evolution phases. The size of the emission region decreases from 2.2 ns to 2.6 ns and then increases thereafter, corresponding, respectively, to the compressing (from Fig. 4a, b) and decompressing (from Fig. 4b, c) phases of the target.

Fig. 4: Cu Kα images induced by fast electrons as a function of LFEX injection time. a–c Fast electron induced Cu Kα images measured in experiments when the LFEX laser is injected at 2.2 ns, 2.6 ns, and 4.6 ns, respectively. The background attributable to the drive lasers, which is measured in the GXII-only shot (see Supplementary Fig. 2), has been subtracted. d–f Simulated Cu Kα images induced by fast electrons at the corresponding LFEX injection times. The details of the simulation are described in the text. In both measured and simulated images, the LFEX laser is injected from the left side, as marked in a and d. The white dashed circles represent the original size of the target. g–i Horizontal (left) and vertical (right) lineouts across the target center from experiments (black) and simulations (red) at the corresponding times, respectively. Full size image

At 2.2 ns, 0.4 ns before the peak compression, most of the Cu Kα emission is produced in the inward-moving shocked region due to its much higher density of Cu atoms than the rest region, as shown in Fig. 3a. The asymmetry (stronger emission on the upstream (left) side) shown in Fig. 4a is caused by the injection of the fast electrons from the LFEX entrance side. Due to the intrinsic angular divergence and energy deposition, the density of fast electrons decreases as they propagate from left to right, so that the Cu Kα intensity decreases accordingly.

At 2.6 ns, a small emission region with a side-to-side diameter of ~100 μm is observed (see Fig. 4b), which agrees well with the diameter (100 μm) of the Cu contained region at the time of peak compression predicted by the FLASH simulation (see Fig. 3a). The weak emission at this time could be explained possibly by three factors. First, the core subtends a small solid angle (~0.2π) from the fast electron source, leading to a reduction in the population of fast electrons that can hit the core. Second, the large target opacity due to the high areal density results in an intensity decay of the Cu Kα emission. Third, the enhancement of the core temperature (see Fig. 3b) shifts and broadens the Cu Kα line, reducing the detection efficiency of the narrow-band Kα imager35. It is worth noting that this is the direct observation of the fast electron transport through a high-density core. With this result and the Cu Kα photon number given by the HOPG spectrometer, the energy deposited in the core by the fast electrons can be estimated, which will be discussed later.

At 4.6 ns, the target has decompressed to a large size (see Fig. 3a) and a water-drop-like Cu Kα image is observed (see Fig. 4c), which clearly reveals the angular divergence of the fast electrons. By taking advantage of this spatial feature in the Cu Kα image, the divergence angle of the fast electrons can be estimated. In contrast, at 2.2 ns and 2.6 ns, the Cu contained regions are so small that the shapes of the Cu Kα images are primarily dependent on the target geometry rather than the spatial distribution of fast electrons, making it impossible to estimate the divergence angle of fast electrons at these times.

Laser-to-core energy coupling efficiency

The energy deposited by fast electrons is inferred by taking advantage of the fact that the fast electrons deposit their energy and excite Cu Kα emission concomitantly when passing through the Cu contained plasma16,19. In principle, as long as the plasma conditions and the cross-section of Cu Kα emission are known, the measured Cu Kα emission, including its absolute intensity and spatial features, allows one to derive the information of the fast electron beam, which is usually characterized by an exponential distribution for the energy spectrum and by a Gaussian distribution for the angular divergence. With the derived information, the deposited energy can be estimated based on the collisional stopping power. Following this idea, a code named eTrans in 2D cylindrical geometry has been developed to simulate the transport and energy deposition of a fast electron beam, as well as its excitation of the Cu Kα emission in a given plasma (see Methods section).

In our experiments, the short pulse laser had to pass through a long density scalelength coronal plasma before reaching the critical density surface (see Fig. 3a); as a result, an additional high-temperature component in the fast electrons would be produced in the underdense region, as observed in both experiments36 and simulations37. Therefore, in our eTrans simulations, the input fast electron beam consisted of two components with different slope temperatures (T 1 and T 2 , with T 1 < T 2 ). Each component was further parameterized by its own divergence angle (θ 1,2 , in FWHM) and population (N 1,2 ). Because the T 2 -component was energetic enough to escape from the target and be detected by the ESMs, its parameters (T 2 , θ 2 , and N 2 ) were obtained by fitting the experimental data, as listed in Table 2. The estimated total energy of this T 2 -component (E 2 ) was just several joules, corresponding to a few percentages of the LFEX laser energy (\(\eta_{L\rightarrow {T_2}}\)). As a result, the proportion (η Kα ) of the Cu Kα photons excited by this T 2 -component was less than 1% in the experimentally measurements. It meant that the Cu Kα photons measured in experiments and hence the deposited energy resulted dominantly from the T 1 -component. Theoretically, T 1 , θ 1 , and N 1 could be obtained by fitting the measured Cu Kα emission. However, the small size of the Cu Kα emission in our experiments (see Fig. 4) revealed limited spatial features, making it difficult to derive T 1 and θ 1 . All we could obtain were simply the upper limit of T 1 and the lower limit of θ 1 (see Supplementary Fig. 5 and Supplementary Discussion for more details). Therefore, T 1 and θ 1 were chosen as free parameters in the eTrans simulations, while N 1 was determined by matching the simulated Cu Kα photons with the experimental data. Fortunately, as will be shown below, within a large parameter domain of interest (e.g., 0.5 MeV ≤ T 1 ≤ 3 MeV and θ 1 ≥ 30° for the t LFEX = 2.6 ns case), the simulated Cu Kα emission and hence the deposited energy depended strongly on N 1 while weakly on T 1 and θ 1 , which therefore allowed us to estimate the deposited energy even with lack of exact T 1 or θ 1 .

Table 2 Parameters of T 2 -component fast electrons. Full size table

Examples of the simulated Cu Kα images are shown in Fig. 4d–f, with their horizontal and vertical lineouts plotted in Fig. 4g–i together with the corresponding experimental data. In these simulations, T 1 = 1 MeV and θ 1 = 40° were used for the T 1 -component fast electrons, while the plasma parameters were from the FLASH simulations. It indicated that the Cu Kα images were weakly dependent on T 1 , as long as T 1 > 0.1 MeV. For 2.2 ns and 2.6 ns, due to the small size of the Cu contained region, these images were also weakly dependent on θ 1 , as long as θ 1 > 20°. While for 4.6 ns, the comparison between experimental data and simulation results indicated that θ 1 = 30°–40° (see Supplementary Fig. 4 and Supplementary Discussion). These simulated Cu Kα images well reproduced the experimental data, including the sizes of the emission region, the relative intensities at different times, and features such as the asymmetry at 2.2 ns and the water-drop-like shape at 4.6 ns. This good agreement in the Cu Kα emission between simulation and experiment once again justified the reliability of the FLASH simulation. At 2.6 ns, the simulation indicated that the target opacity and the detection efficiency of the Kα imager did play important roles in the weak Cu Kα emission, leading to intensity reduction by factors of 27% and 23%, respectively, at the image center.

At the time of peak compression (2.6 ns), a series of eTrans simulations were performed by scanning T 1 and θ 1 in the domain of interest (0.5 MeV ≤ T 1 ≤ 3 MeV and θ 1 ≥ 30°, see Supplementary Discussion) to estimate the laser-to-core energy coupling efficiency (η L→core ). Here, η L→core is defined as the ratio of the energy deposited by fast electrons inside the core (70 μm in radius, see Fig. 3a) to that of the LFEX laser. For each pair of T 1 and θ 1 , the population (N 1 ) and hence the total energy (E 1 ) of T 1 -component fast electrons were obtained, which allowed the calculation of the laser-to-electron energy conversion efficiency (η L→e = (E 1 + E 2 )/E LFEX ), as summarized in Fig. 5a. In most of the cases, η L→e was physically reasonable, at the level of ≲30%. While in some cases with θ 1 ≥ 90°, unphysically large values (e.g., ≥50%) of η L→e were derived, indicating that either T 1 or θ 1 was overestimated in these cases. We note that this overestimation of T 1 or θ 1 did not affect the estimation of η L→core . As shown in Fig. 5b, η L→core depended weakly on T 1 and θ 1 when T 1 > 1 MeV and θ 1 > 60°, respectively. In the parameter domain of interest (0.5 MeV ≤ T 1 ≤ 3 MeV and θ 1 ≥ 30°), η L→core = (0.83 ± 0.23)% was obtained, which corresponded to an energy of 3.5 ± 1.0 J deposited inside the core. Note that our eTrans simulations were constrained by the total Cu Kα photon number, which had an accuracy of ±30% in measurement. By taking this additional uncertainty into account (added in quadrature), η L→core = (0.8 ± 0.3)%.