Introduction

Energetic electron beams produced by the laser-plasma interaction are useful sources for particle acceleration1, novel radiation2, medical therapy3, the formation of warm dense matter of interest in planetary science4,5 and astrophysics6,7, and particularly the development of high-gain laser-driven inertial confinement fusion (ICF)8,9.

Conventionally, laser-driven ICF is supposed to be achieved via the central hotspot approach. By compressing a deuterium-tritium (D-T) fuel shell either directly with laser beams or indirectly with laser-produced X-rays, a high-temperature hotspot is formed, igniting the nuclear fusion reactions and then burning the surrounding high-density fuel by α-particle heating10. This hotspot is formed at the target center by accurately timed shock waves10, which thereby requires excellent spherical compression symmetry for the ignition, large driver energy and little mixing of surrounding cold fuel into the hotspot. In recent experiments performed on the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory11, fuel gain exceeding unit has been demonstrated12, indicating a landmark step towards ignition. However, ignition has not been achieved so far in this central hotspot approach.

As an alternative approach, fast ignition13 separates the hotspot formation from the compression phase by taking advantage of an additional energetic electron beam, therefore relaxing the requirements of compression symmetry and driver energy. Specifically, the fuel shell is compressed isochorically to a high areal density, and then a fast (relativistic) electron beam produced by an ultra-intense laser (UIL) is injected to rapidly heat the compressed fuel, creating a hotspot13. Due to the isochoric compression, this approach allows more fuel to be compressed, thus promising a higher gain than the central hotspot approach.

A key issue in this fast ignition approach is the energy coupling efficiency from the UIL to the compressed core13. One solution is to introduce a guide cone into the fuel shell in order to keep the UIL path free from the surrounding plasmas and bring the intrinsically divergent fast electrons close (~50 μm) to the core. The early experiments8,9 performed in this cone-in-shell scheme at the Institute of Laser Engineering (ILE) in Osaka University reported a coupling efficiency of 15–30%, which was, however, demonstrated to be an optimistic result by the subsequent experiments. Lower coupling efficiencies of ~1.6% and (3.5 ± 1.0)% were, respectively, inferred in the follow-up experiments14 on the same facility at ILE and in the experiments15 performed on the OMEGA Laser Facility at the Laboratory for Laser Energetics (LLE). Improvement of the coupling efficiency requires detailed information about the spatial transport of the fast electrons, which motivated the more recent experiments conducted on OMEGA by Jarrott et al.16,17. Energy deposition of fast electrons in the compressed cone-in-shell target was spatially identified by exploiting the Kα emission from a Cu tracer doped in the fuel shell. The results suggested that the coupling efficiency was limited by the intrinsic properties of the fast electron source, which not only had a large divergence angle but also was far away from the core due to preplasma filling the cone. In subsequent optimized experiments with a wider cone tip and a high-contrast short pulse, the coupling efficiency was improved to 7% (ref. 16), making this cone-in-shell scheme a promising way for fast ignition. Further optimization of the experiments has been proposed by creating a collimated electron beam with magnetic fields produced either externally18,19 or using an engineering target20,21.

Another unique solution to improve the coupling efficiency is the super-penetration scheme22,23,24, proposed based on the original idea of FI, where two successive short pulse UILs are injected into the pre-compressed fuel core: the first UIL producing a low-density plasma channel through the coronal region, while the second, guided by the preformed channel, acting as an ignitor pulse to generate the fast electrons. The idea of the super-penetration scheme is to apply effects such as relativistic self-focusing25, relativistic induced transparency26 and hole-boring27 to the ignitor pulse, so that it can propagate into the overcritical region (where ne > nc, with ne and nc, respectively, being the local electron density and the classic critical density), minimizing the transport distance of the fast electrons to the core and hence improving the coupling efficiency. Due to the absence of the cone in the target, the cone-induced issues, such as implosion symmetry breakage, preplasma filling in the cone16, and mixing of cone material into the fuel core28 could be avoided in this super-penetration scheme. Because of its simplicity, this scheme appears even advantageous for a future laser fusion reactor. With a planar target, recent experiments on OMEGA have demonstrated the formation of a plasma channel up to overcritical density under fast-ignition-relevant conditions29 and observed collimated fast electrons on the channel axis30, rather promising to achieve fast ignition with this super-penetration scheme.

In this article, we report on the integral fast ignition experiments with the super-penetration scheme, which are performed by injecting a short pulse UIL into a spherically compressed target. The transport and energy deposition of fast electrons in the compressed core plasmas are directly observed through the Cu Kα emission induced by fast electrons when interacting with the Cu tracer. An energy coupling efficiency of (0.8 ± 0.3)% from the UIL to the low-density (~0.06 g cm−2) core plasma at the time of peak compression is obtained based on the measured Cu Kα photons. Key factors for achieving higher coupling efficiency are identified with the support of 2D particle-in-cell (PIC) simulations for the future ignition experiments. It indicates that the energy coupling efficiency can be improved up to 12% by optimizing the key factors in future ignition-scale plasmas.

Results

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 nc (nc = 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.
figure 1

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.

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Table 1 Experimental parameters of the joint shots.
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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.
figure 2

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.

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Fig. 3: Simulated density and temperature profiles at different times.
figure 3

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).

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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.
figure 4

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.

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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 (T1 and T2, with T1 < T2). Each component was further parameterized by its own divergence angle (θ1,2, in FWHM) and population (N1,2). Because the T2-component was energetic enough to escape from the target and be detected by the ESMs, its parameters (T2, θ2, and N2) were obtained by fitting the experimental data, as listed in Table 2. The estimated total energy of this T2-component (E2) was just several joules, corresponding to a few percentages of the LFEX laser energy (\(\eta_{L\rightarrow {T_2}}\)). As a result, the proportion (ηKα) of the Cu Kα photons excited by this T2-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 T1-component. Theoretically, T1, θ1, and N1 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 T1 and θ1. All we could obtain were simply the upper limit of T1 and the lower limit of θ1 (see Supplementary Fig. 5 and Supplementary Discussion for more details). Therefore, T1 and θ1 were chosen as free parameters in the eTrans simulations, while N1 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 ≤ T1 ≤ 3 MeV and θ1 ≥ 30° for the tLFEX = 2.6 ns case), the simulated Cu Kα emission and hence the deposited energy depended strongly on N1 while weakly on T1 and θ1, which therefore allowed us to estimate the deposited energy even with lack of exact T1 or θ1.

Table 2 Parameters of T2-component fast electrons.
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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, T1 = 1 MeV and θ1 = 40° were used for the T1-component fast electrons, while the plasma parameters were from the FLASH simulations. It indicated that the Cu Kα images were weakly dependent on T1, as long as T1 > 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 θ1, as long as θ1 > 20°. While for 4.6 ns, the comparison between experimental data and simulation results indicated that θ1 = 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 T1 and θ1 in the domain of interest (0.5 MeV ≤ T1 ≤ 3 MeV and θ1 ≥ 30°, see Supplementary Discussion) to estimate the laser-to-core energy coupling efficiency (ηL→core). Here, ηL→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 T1 and θ1, the population (N1) and hence the total energy (E1) of T1-component fast electrons were obtained, which allowed the calculation of the laser-to-electron energy conversion efficiency (ηL→e = (E1 + E2)/ELFEX), as summarized in Fig. 5a. In most of the cases, ηL→e was physically reasonable, at the level of ≲30%. While in some cases with θ1 ≥ 90°, unphysically large values (e.g., ≥50%) of ηL→e were derived, indicating that either T1 or θ1 was overestimated in these cases. We note that this overestimation of T1 or θ1 did not affect the estimation of ηL→core. As shown in Fig. 5b, ηL→core depended weakly on T1 and θ1 when T1 > 1 MeV and θ1 > 60°, respectively. In the parameter domain of interest (0.5 MeV ≤ T1 ≤ 3 MeV and θ1 ≥ 30°), ηL→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), ηL→core = (0.8 ± 0.3)%.

Fig. 5: Simulated results for the tLFEX = 2.6 ns case.
figure 5

Simulated (a) laser-to-electron energy conversion efficiency (ηL→e) and (b) laser-to-core energy coupling efficiency (ηL→core) as a function of the slope temperature (T1) and the divergence angle (θ1) of the T1-component fast electrons. These simulations are constrained by matching the simulated Cu Kα photons with the experimental measurement. ηL→e increases rapidly as T1 and θ1 increase. ηL→core depends weakly on T1 and θ1 when T1 > 1 MeV and θ1 > 60°, respectively. For the LFEX intensity in the experiments, ~3.7 × 1018 W cm−2, the slope temperature given by the ponderomotive scaling27 is ~0.5 MeV, as marked by the dashed line. In the domain of [0.5 MeV,3.0 MeV] × [30°, +∞), ηL→core = (0.83 ± 0.23)%.

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Discussion

We figured out that the laser-to-core energy coupling efficiency could be improved by optimizing the implosion and super-penetration performances, because it was limited by two aspects in experiments reported here. One aspect was the low areal density (ρR ~ 0.06 g cm−2) of the core, which resulted from the low driver energy (~200 J beam−1) and the target preheat caused by the driver-produced suprathermal electrons38. The kinetic energy of fast electrons optimal for heating a core of 0.06 g cm−2 ranges from 200 keV to 500 keV. When electrons with a slope temperature of ~1 MeV were transmitting through a core of this areal density, only ~10% of the energy could be deposited16; in contrast, 40–50% of the energy could be deposited for an areal density of 1.3 g cm−2 (ignition level attainable in the NIF-scale, corresponding to an optimal electron energy ranging from 2 MeV to 5 MeV). The other aspect was the low energy carried by the fast electrons to the core region. Taking T1 = 1 MeV as an example, our eTrans simulations indicated that only 26–39 J energy was transported to the core region, corresponding to 6–9% of the LFEX energy (423 J), as shown in Fig. 6. This low energy could be limited by three factors. (i) The laser-to-electron energy conversion efficiency (ηL→e) might be very low (e.g., ηL→e = 10% at θ1 = 40°, dashed lines in Fig. 6), which could be a result of spending too much energy in forming the plasma channel or creating laser and electron filaments30, leaving little energy to produce fast electrons. (ii) The fast electrons might have a very large divergence angle (e.g., θ1 = 75° at ηL→e = 30%, dash-dotted lines in Fig. 6), which could be caused by beam filamentation, laser hosing and channel bifurcation39 when the LFEX laser was propagating through the long scalelength coronal plasmas. (iii) The fast electron source might be far away from the core. Previous experiments29,30 showed that the plasma channel created by a 10 ps high-intensity (~1019 W cm−2) laser stopped in the underdense region (0.6nc), probably due to beam filamentation and plasma pileup in front of the channel.

Fig. 6: Energy carried by fast electrons for the tLFEX = 2.6 ns case.
figure 6

The fraction of the LFEX energy (ηhit, blue squares, left axis) carried by fast electrons that are capable of hitting the core and laser-to-electron energy conversion efficiency (ηL→e, red dots, right axis) are plotted as a function of the divergence angle (θ1) of the T1-component fast electrons. In these simulations, T1 = 1 MeV and the calculated Cu Kα photons are set to match the experimental measurement. Only 6–9% of the LFEX energy is transported to the core region, indicating a low ηL→e (as marked by the dashed lines), or a large θ1 (as marked by the dash-dotted lines) in the fast electrons, or a large distance from the fast electron source to the core.

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To identify the dominant factors responsible for the low energy carried to the core region, 2D PIC simulations (see Methods section) were performed for LFEX injection times at 2.6 ns and 4.6 ns. In these simulations, the LFEX parameters were from the experiments while the plasma conditions were from the FLASH simulations. The simulated results (see Supplementary Figs. 6–9 for more details) showed that strong laser filamentation and channel bifurcation took place in the tLFEX = 2.6 ns case, where the coronal plasma had a long density scalelength (~60 μm); as a result, the plasma channel stopped in the underdense region and the generated fast electrons were widely distributed in the transverse direction, as shown in Fig. 7. Because of the long density scalelength in this case, pulse depletion also played an important role in the reduced channel depth33. While for the tLFEX = 4.6 ns case, where the density scalelength in the coronal region is much shorter (~15 μm), the plasma channel arrived at the relativistic critical density (γnc, where γ is listed in Table 1) surface, and a much narrower electron beam was produced (see Fig. 7b, c). This narrow electron beam was supported by the experimentally inferred divergence angle of 30°–40° in FWHM (see Supplementary Discussion), indicating that a well collimated fast electron beam could be produced by interacting a high intensity laser with a short density scalelength plasma. These results demonstrated that, rather than the low ηL→e, the large divergence angle and long distance from the core of the fast electrons caused by the strong laser filamentation and channel bifurcation (see Fig. 7a) were the dominant reasons for the low energy transported to the core region at the time of peak compression (2.6 ns).

Fig. 7: Two-dimensional particle-in-cell simulation results.
figure 7

a, b Electron density profiles obtained 0.2 ps after the LFEX laser terminates are shown in a and b for cases of tLFEX = 2.6 ns and tLFEX = 4.6 ns, respectively. The horizontal axis denotes the distance from the target center. The white and red curves represent the classic critical density (nc) and relativistic critical density (γnc) surfaces, respectively, at the injection time of the LFEX laser. c Transverse distributions of time-integrated fast electron energies measured at r ~ −140 μm (1 μm beneath the rear surface of the plasma). These measurements only take into account the electrons with energy above 0.6 MeV. The red dots and blue squares are for the tLFEX = 2.6 ns and tLFEX = 4.6 ns cases, respectively. Their transverse distributions of the time-integrated laser energies multiplied by a factor of 0.1 are, respectively, plotted by red and blue dash-dotted lines as reference.

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These findings uncover the importance of applying an additional channeling pulse in this super-penetration scheme, because the plasma channel preformed by the channeling pulse not only helps to suppress the filamentation of the second heating pulse but also provides a short density scalelength plasma at the channel front. As demonstrated experimentally, by optimizing the experimental configuration, a plasma channel up to critical density surface can be created29,40. Besides, a magnetic field could be produced by the channeling pulse, collimating the fast electrons generated by the second pulse41. Therefore, a high laser-to-core energy coupling efficiency could be expected in this optimized double-pulse scheme. Given that the experimentally inferred laser-to-electron conversion efficiency is above 30% (ref. 42), if the fast electrons are well guided to the core region, a laser-to-core coupling efficiency of 3% could be expected for the 0.06 g cm−2 core plasma on the GEKKO-LFEX facility. While for the NIF-scale core plasma (1.3 g cm−2 in areal density), 40–50% of the energy of fast electrons could be deposited when they pass through the core16; therefore, a laser-to-core energy coupling efficiency of as high as ≳12% could be expected, which is comparable to that expected for the cone-in-shell scheme16. However, it is worth noting that, compared to the cone-in-shell scheme, this super-penetration scheme has a simpler experimental configuration and requires no external assistance for electron collimation, which are good advantages for the ignition experiment. Also due to the absence of the cone, multiple short-pulse beams incident from different directions (e.g., six orthogonal directions) can be applied in super-penetration scheme. Compared to the cone-in-shell scheme, this configuration either promises more energy coupled to the core by increasing the short-pulse beams or relaxes the engineering requirement of optical elements by reducing the intensity of each beam.

Methods

Target

The target used in the experiments consisted of two parts: an inner solid Cu contained CH sphere and an outer CH coating layer. The inner sphere with a diameter of 190 μm was made of Cu(II) oleate [Cu(C17H33COO)2]31, resulting in a Cu concentration of ~10% in weight; while the outer coating layer with a thickness of 30 μm was made of parylene. The densities in both parts were ~1 g cm−3. Our previous experiments in similar configurations indicated that, when a ~20 μm thick coating layer was used, plenty of suprathermal electrons produced by the drive (GXII) lasers were able to penetrate into the inner region, resulting in strong background Cu Kα emission38. Therefore, a thicker (30 μm) coating layer was used in the experiments reported here to reduce the background Cu Kα emission, thereby facilitating the detection of fast electron transport.

According to the radiative hydrodynamic simulations, the peak areal density in this solid sphere target is ~0.06 g cm−2, higher than that in a mass-equivalent shell target (~0.04 g cm−2); while the core temperature in the former is ≲200 eV, colder than that in the later (~380 eV). With the temperature dependence of detection efficiency of the Cu Kα imager taken into account, this solid sphere target is more suitable for detecting the fast electron transport than the conventional shell target.

Lasers

Twelve GEKKO lasers were applied to compress the target, with each laser operating at a wavelength of 526 nm (2ω) with an energy of ~200 J. All of the lasers were focused with an F/3 lens, resulting in a focal spot of ~170 μm in full width at half maximum (FWHM) at the target surface. The pulse shape was Gaussian with a FWHM of 1.6 ns, leading to a peak intensity of ~4.8 × 1014 W cm−2. The pulse shape, as shown in Fig. 1b, was measured by an oscilloscope in each shot. In joint shots, the short pulse LFEX laser was injected into the target in the equatorial plane to produce a fast electron beam. Its wavelength and pulse duration were, respectively, 1053 nm (1ω) and 1.5 ps in FWHM. It was focused 230 μm ahead of the target center [see Fig. 1a] with a focal spot of 80 μm in FWHM. With energy ranging from ~190 J to ~420 J, a peak on-target intensity of ~3.7 × 1018 W cm−2 could be achieved, as shown in Table 1. The relative timing between the GEKKO and LFEX lasers was measured offline in two successive shots by, respectively, irradiating the GEKKO and LFEX lasers at very low energy onto a diffuser placed at the target chamber center. The scattered light was detected by a high-speed photodiode coupled with an oscilloscope. In both shots, the oscilloscope was triggered by the GEKKO laser; consequently, the on-target delay of LFEX relative to the peak of GEKKO was obtained by comparing the recorded signals in these two shots. The delay measured in this way had an uncertainty of ±150 ps due to the intrinsic jitter of the LFEX timing.

Diagnostics

The Cu Kα imager used a spherically bent quartz (2131) crystal to image the emission within a spectral bandwidth of 5 eV (FWHM) centered at 8.048 keV (Cu Kα1) from the target onto an image plate. The magnification and spatial resolution were, respectively, 17.5 and 13 μm (FWHM). A 10 μm Cu filter was placed in front of the image plate to reduce the background. This imager was installed perpendicularly to the LFEX axis.

A planar highly oriented pyrolytic graphite (HOPG) crystal spectrometer, also perpendicular to the LFEX axis, was applied to measure the x-ray spectrum in the range of 7.7–9.2 keV. It was absolutely calibrated for the Cu Kα line emission in a separate experiment by comparing with the results measured by a calibrated single-photon counting camera, resulting in a calibration factor with an accuracy of ±30%. Because of its large detectable energy range, the HOPG spectrometer would not be affected by the shifting and broadening of the Cu Kα line due to temperature enhancement.

Simulations

The compression of the target was simulated by the FLASH code32 in 2D-cylindrical geometry coupled with a hot-electron-preheat module38. FLASH is a radiative hydrodynamic code using 3D-in-2D ray trace algorithm for the laser energy deposition. Therefore, the twelve GXII lasers could be set up exactly the same as the experimental conditions, including the beam energy, pulse shape, incident direction, F-number and spot size. The radiation transport was solved by a multigroup (6 groups) radiation diffusion model with tabulated opacity. A flux-limited model with the Larsen square-root flux limiter was applied to the calculation of thermal conduction. The hot-electron-preheat module was coupled to take into account the effect on the target compression caused by the energy deposition of GXII-produced suprathermal electrons. The necessity of considering this preheat effect was demonstrated by our previous experiments under similar configurations38. This simulation code was benchmarked by comparing the simulated temporal and spatial evolutions of the target self-emission (i.e., the XSC result) with the experimental data, as shown in Fig. 2. Details of this simulations was also introduced in ref. 38.

A 2D cylindrically symmetric code, eTrans, has been developed to simulate the transport of an electron beam in a specific plasma. In eTrans, the electrons propagate straightly along their initial velocity directions and their transport is governed by the collisional stopping power with scattering effect considered43; namely, fields are neglected. With this stopping power, the energy deposited in the plasma is calculated. With the Cu Kα emission cross-section44 and the spatial distribution of the Cu atoms, eTrans is also able to calculate the Cu Kα emission along the path of fast electrons. By taking into account the 3D projection along the line of sight of the Kα imager, the target opacity, and the detection efficiency of the Kα imager due to temperature enhancement, a 2D Cu Kα image is obtained. eTrans also provides the total (spatially integrated) Cu Kα photon number (with the opacity considered but the detection efficiency neglected), so that the result can be compared with the experimental data given by a temperature-independent detector, such as the HOPG spectrometer.

In our eTrans simulations, the plasma conditions were given by the FLASH output, while the fast electron beam consisted of two components, with each characterized by an exponential distribution for the energy spectrum and by a Gaussian distribution for the angular divergence:

$$f\left( {E,\theta } \right) = \frac{{N_1}}{{T_1}}{\mathrm{exp}}\left( { - \frac{E}{{T_1}}} \right)\exp \left( { - 4{\mathrm{ln}}2\frac{{\theta ^2}}{{\theta _1^2}}} \right) + \frac{{N_2}}{{T_2}}{\mathrm{exp}}\left( { - \frac{E}{{T_2}}} \right)\exp \left( { - 4{\mathrm{ln}}2\frac{{\theta ^2}}{{\theta _2^2}}} \right),$$
(1)

where T1 < T2. The T2-component was completely determined by the experimental data from ESMs (see Supplementary Fig. 3). For the T1-component, because of its low energy, it suffers strong deposition and deflection when passing through the target; as a result, it could hardly be measured by the ESMs. Therefore, the slope temperature (T1) and the divergence angle in FWHM (θ1) were chosen to be free parameters, while the population (N1) was always constrained to match the calculated total Cu Kα photons with the experimental data measured by the HOPG spectrometer. All these fast electrons were injected into the target at the critical density surface (nc = 1021 cm−3).

The 2D particle-in-cell (PIC) code, FISCOF (ref. 45), was used to simulate the propagation of the short pulse LFEX laser in the coronal plasmas and the production of fast electrons. The parameters characterizing the LFEX laser were obtained from the experiments. Namely, both spatial and temporal profiles were Gaussian functions with FWHMs of 80 μm and 1.5 ps, respectively. For the injection time at 2.6 ns (4.6 ns), the experimentally measured LFEX energy was ~420 J (~190 J), resulting in a peak intensity of ~3.7 × 1018 W cm−2 (~1.7 × 1018 W cm−2). The density profile of the fully ionized CH plasma was taken from the FLASH-simulated results at the corresponding time, as shown in Supplementary Fig. 1a, ranging from 0.1nc to 1.5nc (3.9nc) for tLFEX = 2.6 ns (tLFEX = 4.6 ns). The maximum density was chosen to avoid penetrating of the LFEX laser through the plasma. As a result, the simulation box was 240 × 280 μm2 (140 × 400 μm2) for tLFEX = 2.6 ns (tLFEX = 4.6 ns) with a spatial resolution of ~0.1 μm and 10 particles per cell. The temporal resolution, determined by the plasma frequency of the maximum density, was 0.046 fs (0.028 fs) for tLFEX = 2.6 ns (tLFEX = 4.6 ns). Reflection boundary condition was applied to the fields. Particles escaping from the simulation box were re-injected from the opposite boundary with a thermal velocity. Fast electrons were observed at 1 μm beneath the rear surface of the plasma, which corresponded to ~140 μm from the target center for both simulation cases. To collect all the fast electrons, the simulation was run for 6 ps (5 ps) for tLFEX = 2.6 ns (tLFEX = 4.6 ns).

To eliminate the influence of the difference in laser intensities on the simulated results, another simulation was performed for the tLFEX = 4.6 ns case by using the same laser intensity as that for the tLFEX = 2.6 ns case (~3.7 × 1018 W cm−2).