2 Experimental setup

The SGII-U laser facility, which can operate eight beams with 1500 J each at a wavelength of 351 nm, was employed to perform the experiment. The energy balance of the laser beams is less than 10%. Figure 1 represents the schematic experimental setup. The profile of each laser beam was temporally shaped into a two-ramp pulse, as shown in Figure 1. The first ramp pulse started with a step and had a rise time of 2.5 ns, intended to generate a fluid phase behind the shock in the CH shell and subsequently compress the shell along the isentropic path. The second ramp pulse, with a rise time of 2 ns and a maximum intensity 140 times greater than that of the first pulse, was used to further compress and accelerate the target. The laser beams were focused to a spot with a 2 mm diameter flat top profile using a continuous phase plate (CPP). For comparison, some shots with a rectangle pulse were also conducted.

Figure 1 Sketch of the experimental setup with the two-ramp pulse profile and the targets. Four laser beams irradiate the CHCl shell targets. A probe laser penetrates the hole of the Au cone and is reflected back by the shock into the VISAR diagnostics. The target self-emissions are measured by SOP.

As the initial step for the DCI scheme, the plasma jets at the cone tips should be carefully characterized before collisions; hence only one cone with a shell target was used. Cl-doped polystyrene (CH) was chosen as the shell to improve the direct-drive implosion performance^[ Reference Zheng, Tao, Jia, Yan and Zheng ^{14 ]}; meanwhile, chlorine was used as a trace element for other diagnostics. Helium-like triplets from Cl were measured by an X-ray spectrometer and used to determine the plasma densities and temperatures^[ Reference Liu, Yang, Zhang, Fang, Zhang, Yuan, li and Zhang ^{15 ]}. The shell was shaped into a spherical cap with a cap angle of 50° and a sphere inner radius of 250 μm, which was glued to the wall of the gold cone. The shell was irradiated by four laser beams with intensities up to $4.6\times {10}^{15}\;\mathrm{W}/{\mathrm{cm}}^2$ . The thickness of the shell was 50 μm. The experimental setup is presented in Figure 1, where the cone was glued to a thin glass pole (Target A) or supported by an Al plate with a hole (Target B). To avoid blocking the instruments to diagnose the jet, type-A targets were used, otherwise type-B targets were used as type-A targets were prone to damage. The shocks generated in the shell strengthen with increased laser intensity. Consequently, the latter shocks propagate faster than the former ones and coalescence at the rear surface of the CHCl shell with the first shock. The CHCl plasma is propelled forward and out of the gold cone through the hole at the tip of the cone. As the CHCl plasma moves forward, it undergoes further compression by the wall of the gold cone.

The shock velocity propagated in the CHCl shell was measured through the hole of the gold cone by the velocity interferometry system for any reflector (VISAR)^[ Reference Yuan, Wang, Wei, Gu, Dai, Zhong, Li, Zhao and Zhang ^{16 ]}, which utilizes a 50 ns pulse-width probe laser^[ Reference Xiao, Pan, Guo, Wang, Wang, Jiang, Li, Lu, Wang, Zhou and Li ^{17 ]}. A 15 mm etalon was used, corresponding to a velocity sensitivity of 4.288 km/s per fringe. An optical fiducial was added to the streak camera to provide absolute timing. The CHCl target has a low reflection for the VISAR probe at 660 nm, and no signal is detected from the CHCl shell through the cone hole before the main laser ablation. The reflector in this experiment is the shock front in the CHCl shell, which can be considered as the beginning of the laser pulse since the shocks are formed rapidly when the laser ablates the CHCl shell. A streaked optical pyrometer (SOP) was employed as a complementary diagnostic to measure the emission of shocks in the CHCl shell.

3 Experimental results and simulations

Figure 2 shows the measured VISAR images for a typical rectangle pulse shot (Figure 2(b)) together with the results for a two-ramp pulse shot (Figure 2(c)). The horizontal direction of these images corresponds to the spatial direction transverse to the shock velocity, while time increases from top to bottom. Figure 2(a) shows the reference image for Target A without the main laser pulses, where only the bright fringes of the VISAR laser beam reflected by the wall surface at the tip of the gold cone can be detected. The fringes corresponding to the stationary CHCl shell were too weak to be detected since most of the VISAR laser passes through the CHCl shell. The laser energy for rectangle pulse was 5.6 kJ with a pulse duration of 2 ns. Simulations showed that a pulse of 2 ns is a preferable choice, which can drive the jet to eject from the tip of the cone near the end of the laser pulse. This can efficiently convert the laser energy to jet kinetic energy for a rectangle pulse. Due to the malfunction of the laser cooling system during the experiments, a relatively stronger pre-pulse was observed before the main pulse. This pre-pulse irradiated the front surface of the transparent CHCl shell and caused an increased refection efficiency of the VISAR laser beam. Consequently, relatively dark fringes can be observed from the CHCl shell before the arrival of the main pulse, t = 0 ns, in Figure 2(b). When the main pulse arrived, the shock in the CHCl shell became a reflector, and the signal of fringes increased abruptly. After the main pulse, at t = 0.51 ns, the VISAR signal disappeared as the shock broke out at the rear surface and released into the vacuum. This indicates a shock velocity of 98 km/s.

Figure 2 VISAR images for a rectangle pulse and two-ramp pulse shots. (a) The reference image of Target A without the laser shot. (b) The VISAR image for the rectangle pulse shot with Target A. (c) The VISAR image for the two-ramp pulse shot with Target B. The red line represents the temporal intensities of VISAR fringes extracted from the dashed rectangle box.

For comparison, Figure 2(c) shows the VISAR result for the two-ramp pulse shot, along with the temporal intensities of the VISAR fringes. Before t = 0 ns, the relatively bright fringes represent reflections of the VISAR probe laser from the wall at the cone tip and the supporting Al plate (see Target B in Figure 1). Similar to the rectangle pulse case, the weak fringes at the cone hole can be observed by the reflection of the coarse surface of the CHCl shell due to the pre-pulse before the two-ramp pulse. From t = 0 ns, the main pulse irradiates the CHCl shell and forms shocks within it, and the fringes reflected from these shocks can be clearly observed. Unlike the rectangle pulse case, the fringes in this two-ramp shot last for 3.1 ns before disappearing. This is because the first ramp pulse is much weaker than the rectangle pulse, resulting in weaker shocks that propagate slower. This ramp compresses the shell close to an isentropic compression. When the first ramp pulse arrives at t = 0 ns, the increase in the fringe intensity indicates the formation of a shock reflector. The weak fringe signals caused by the beginning of the first ramp pulse suggest that the initial shocks may still be nearly transparent for the probe laser beam. From 0 to 3.1 ns, the temporal rise in signal intensity suggests that the shocks are getting stronger with time, and thus the reflectivity for the probe laser beam becomes larger^[ Reference Barrios, Hicks, Boehly, Fratanduono, Eggert, Celliers, Collins and Meyerhofer ^{18 ]}. The VISAR blanking observed at around 1.0 ns may be due to either the photoionization of the target material ahead of the shock by the X-rays from the ablation corona^[ Reference Laffite, Baton, Combis, Clerouin, Koenig, Recoules, Rousseaux and Videau ^{19 ]} or the CHCl material being compressed to a state that turns optically opaque to the probing laser^[ Reference Hartley, Zhang, Duan, Huang, Jiang, Li, Yang, Pelka, Wang, Yang and Kraus ^{20 ]}. At 2.5 ns, the second ramp pulse irradiates the target and causes a short discontinuity in the fringes. At 3.1 ns, the sudden increase in fringe signals indicates that the shocks generated by the second ramp pulse overtake the former shocks generated by the first ramp pulse and break out at the rear surface of the CHCl shell, which then causes the fringes to disappear. This agrees with the simulation well (see below) and suggests that the CHCl shell undergoes a quasi-isentropic compression before being accelerated as a whole by the later ramp.

Temporal emissions from the shock in the CHCl shell, measured with the SOP, are shown in Figure 3(a), together with an illustration of the gold cone indicating the corresponding spatial locations. The horizontal direction corresponds to the time, increasing from left to right. Initially, the emission is observed to be well collimated. As time increases, the spatial size of the emission increases, and the intensity also strengthens. The full widths at half maximum (FWHMs) of the emission source are plotted in Figure 3(b) as a function of time. The FWHM of the source is 100 ± 5 μm from t = 2.95 ns to t = 4.59 ns. This is identical to the diameter of the cone tip hole (100 μm), indicating that the plasma is inside the cone. The starting time (t = 2.95 ns) for this constant FWHM also serves as a cross-check of the VISAR results for the time when the shocks break out at the rear surface of the shell. A sharp increase in the FWHM can be seen from t = 4.59 ns, followed by a quick decrease in less than 1 ns. This is because the SOP records mainly the emissions from the tip cone hole before t = 4.59 ns and from the expanding plasmas passing through the cone’s tip hole after t = 4.59 ns. By combining the expanding spatial distance and the travel time, the expansion speed of the plasmas can be estimated to be 126.8 ± 17.1 km/s. This speed is in agreement with the results from an X-ray pinhole streak camera (XPSC)^[ Reference Zhang, Yuan, Zhang, Liu, Fang, Zhang, Liu, Zhao, Dong, Liu, Dai, Gu, Li, Zheng, Zhong and Zhang ^{21 ]}. A similar jet with a velocity of about 600 km/s was reported^[ Reference Azechi, Sakaiya, Watari, Karasik, Saito, Ohtani, Takeda, Hosoda, Shiraga, Nakai, Shigemori, Fujioka, Murakami, Nagatomo, Johzaki, Gardner, Colombant, Bates, Velikovich, Aglitskiy, Weaver, Obenschain, Eliezer, Kodama, Norimatsu, Fujita, Mima and Kan ^{22 ]} at a laser intensity of 700 TW/cm².

Figure 3 SOP signals of the two-ramp shot. (a) Streaked image of emissions, with an illustration of the gold cone shown to indicate the corresponding locations. (b) Temporal FWHM of the emission source. (c) Lineout along the central axis of the CHCl shell in the SOP image.

Emission signals along the central axis of the CHCl shell are extracted and are shown in Figure 3(c). Starting from 1.45 ns, an emission signal appears in the SOP record, albeit at the same level as the background. The steady increase in emission implies a gradual strengthening of the shock over time. This is consistent with the VISAR results, where increased shocks are also observed. Emission signals from the strong shocks generated by the second ramp become clearly distinguishable from 2.5 ns onward. Although these strong shocks have not overtaken those of the first ramp at that time, their emissions can penetrate through the preceding shocks, which are not fully opaque. Rare signals are detected from the shocks generated by the first ramp, suggesting that the compression is along an isentropic path. This self-emission reaches its maximum value at 4.91 ns.

The experimental results are simulated with the 2D cylindrical hydrodynamic code FLASH^[ Reference Fryxell, Olson, Ricker, Timmes, Zingale, Lamb, MacNeice, Rosner, Truran and Tufo ^{23 ,} Reference Dubey, Antypas, Ganapathy, Reid, Riley, Sheeler, Siegel and Weide ^{24 ]}, which includes radiation transport, electron thermal conduction, laser energy deposition and the three-temperature model. The simulation results are shown in Figure 4. The laser energy is 5 kJ, with a wavelength of 0.351 μm and a spot radius of 250 μm, the same as the experimental design conditions. In the simulations, the laser propagates along the cone wall and focuses at the top of the CH target. The input parameters are the exact experimental design conditions for the laser and target, with the exception that the simulations employ a CH target due to lack of opacity data for CHCl targets. The MPQEOS equations of state^[ Reference Kemp and Meyer-ter-Vehn ^{25 ]} and the SNOP opacity tables^[ Reference Eidmann ^{26 ]} are used for the CH target. The target has an inner radius of 250 μm and a thickness of 50 μm, as shown in Figure 4(a).

Figure 4 Temporal density distributions in the CHCl shell. (a), (b) Simulation of density distribution in the CHCl shell for rectangle pulse shots at t = 0 and t = 0.589 ns. (c)–(f) Simulation of density distribution in the CHCl shell for two-ramp pulse shots from t = 2.550 ns to t = 4.450 ns.

The simulation results for the rectangle pulse are shown in Figures 4(a) and 4(b). The shock positions are clearly discernible by the steepest gradient density distributions. At t = 0.589 ns, the shock reaches the rear surface of the CH shell, indicating that the VISAR signals will soon disappear. This time (0.589 ns) is in good agreement with our experimental results, where the fringes disappear at 0.51 ns, considering the experimental uncertainties (±100 ps). In the simulations of the two-ramp pulse shot, shown in Figures 4(c)–4(f), the first ramp pulse is relatively weak, causing the shock to propagate more slowly in the CH shell compared to the rectangle shot. The first shock reaches the rear surface of the shell at t = 2.55 ns (Figure 4(c)), and the strong shocks start to form due to ablation by the second ramp. This corresponds with the records from the SOP, where strong signals are detected starting at t = 2.5 ns. These strong shocks break out at the rear surface of the CH shell at 3.05 ns in the simulation (Figure 4(d)), coinciding with experimental measurement by VISAR (3.1 ns). The VISAR record disappears at 3.1 ns, making it impossible to gain information from this optical diagnostic beyond this point. Fortunately, the SOP results continue to provide insights into the evolution of plasma both inside and outside the gold cone. The plasmas begin to emerge from the tip hole of the cone at 4.45 ns and subsequently expand freely, as shown in Figure 4(f). This agrees well with the SOP results, which show a sharp increase in the FWHM of the source size from t = 4.59 ns. As we compared above, the time differences between the simulation results and the measurements obtained by the VISAR and SOP are no more than 150 ps. While this value is slightly larger than the experimental errors (±100 ps), it is noteworthy that the experimental laser power is smaller than the designed pulse power. Consequently, it takes more time for the plasmas to emerge from the tip hole in the experiment than in the simulations in which the designed laser shape is used. Considering this respect, we believe that the agreement between the simulations and the experimental measurements is reasonable.

Figure 5 shows the simulated density distributions along the axis of the CH shell targets at different times. From t = 0 to t = 2.55 ns, the CH shell is compressed by the shocks from the first ramp pulse. As time increases, the CH shell is fully compressed to a density of 3.75 g/cm³ by the end of the first pulse. Essentially, this process is the same as a typical spherical convergence, where the CH shell is compressed by converging shock waves (CSWs). The trajectory of the CSW can be well described by the Chester–Chisnell–Whitham (CCW) method^[ Reference Whitham ^{27 ]}. In the strong shock limit, this method is in a good agreement with the Guderley theory^[ Reference Guderley ^{28 ]}: $\frac{R}{R_0}={\left(1-\frac{t}{t_0}\right)}^n$ , where ${R}_0$ is the shock initial position, ${t}_0$ is the arrival time at the center of the shell and $n$ is the similarity exponent, related to the adiabatic exponent $\gamma$ . The simulations shown in Figure 6 plot the normalized converging shock positions against the normalized time relative to the arrival time at the shell center in a log–log coordinate system. The slope of the linear fit to this line gives the similarity exponent, $n=0.798$ , in the Guderley formula. In spherical shocks, this similarity exponent corresponds to the adiabatic exponent $\gamma =1.10$ for ideal gas^[ Reference Bilbao and Gratton ^{29 ]}. Solids with a Grüneisen parameter ${\Gamma}_0$ behave similar to the gas with the adiabatic exponent $\gamma ={\Gamma}_0+1$ ^[ Reference Zeldovich and Raizer ^{30 ]}. Based on this, the Grüneisen parameter was calculated for the CH shell, yielding a value of ${\Gamma}_0=0.10$ . This value is less than that in the common reference data^[ Reference Meyers ^{31 ]}. However, recent calculations and experimental measurements on CH or glow discharge polymer (GDP)^[ Reference Colin-Lalu, Recoules, Salin, Plisson, Brambrink, Vinci, Bolis and Huser ^{32 ,} Reference McCoy, Hu, Marshall, Polsin, Fratanduono, Ding, Celliers, Boehly and Meyerhofer ^{33 ]} suggest that the Grüneisen parameter is less than 0.2 at low densities, which is in good agreement with our results. The peak density of 3.75 g/cm³ in our spherical compression by the first ramp is also higher than the density (less than 3.5 g/cm³) in planar compression^[ Reference Wang, Yuan, Wei, Wu, Gu, Dai, Zhang, Yuan, Li and Zhang ^{34 ]}, indicating that the shock strengthens in the converging process.

Figure 5 The density along the target axis at different times for the two-ramp pulse shot.

Figure 6 Converging shock positions versus the time in simulations. The blue dots are normalized shock positions and the red line is the linear fit.

After the first ramp, shocks generated by the second ramp uniformly compress this pre-compressed CH shell to a density as high as 7.5 g/cm³ at 3.05 ns, indicating that these strong shocks reach the rear surface of the CH. Subsequently, the entire CH shell is accelerated forward and simultaneously compressed by the pressure from both the laser ablation and the squeeze from the wall of the gold cone as it moves toward the tip of the cone. This process is 3D. With the drive laser on, the densities of the CH shell remain almost constant (7.5 g/cm³), while the thickness of the shell increases again since its spherical radius decreases when approaching the tip of the cone, shown in Figure 5 at 4.1 ns. At the end of the drive laser (t = 4.5 ns), the central part of the CH shell continues to move at high speed, while the marginal parts move more slowly due to the expansion of the cone wall into the cone, which prevents direct interaction of the laser pulse with the margin of CH shell, and also due to the drag of the inner wall of the gold cone. Consequently, the CH shell becomes flattened, as shown in Figure 4(f). A high-density plasma jet forms due to inertia of the shell. Upon collision between the marginal parts of the CH shell and the cone wall, a recoil force further compresses the jet as it moves toward the cone tip. The highest density of 14.92 g/cm³ is achieved at t = 5.05 ns, represented by the green line in Figure 5. Since the emission is proportional to the density of the plasma, this is also in agreement with the SOP measurements, which show the strongest emission at t = 4.91 ns. Thus, we have shown that with the gold cone, a high-density jet with high velocity can be produced. The gold cone plays an important role in containing and compressing the plasma jet before the jet ejects from the tip hole.

4 Summary and conclusions

The CHCl shell in the gold cone was irradiated by a specially designed laser shape, namely the two-ramp pulse. The shocks generated by the first ramp fulfilled the quasi-isentropic compression of the target. Subsequent shocks generated by the second ramp further compressed and accelerated the shell to generate a high-density jet with high velocity. The shock velocity profiles in the CH shell were measured by VISAR, while the emissions from the shocks were recorded by the SOP. The steady increase in the intensity of both the VISAR fringes and the SOP signals indicates that the shocks grew stronger as they propagated through the CH shell. The measured arrival times of shocks at the rear surface of the CH shell are in good agreement with the simulation results conducted by the hydrodynamic code FLASH, considering the experimental inaccuracies (±100 ps). The plasma jet was ejected from the tip hole of the gold cone and reached the maximum emission at the predicted times given by the code. In addition, for shots with the rectangle laser pulse, the measured shocks with a velocity of 98 km/s were also well reproduced in the simulation results. This gives us confidence in the simulation results and demonstrates our ability to generate the required jet conditions under current laser conditions. The path through which converging shock transported in the CH shell agrees with Guderley’s theory, showing the increasing shock strength. The CH plasma jet, driven by the ablation of the second ramp pulse in the gold cone, can reach a maximum density of 14.92 g/cm³ according to simulations, with a velocity measured up to 126.8 ± 17.1 km/s. In conclusion, generation of high-density and high-velocity plasma jets with a two-ramp pulse has been demonstrated experimentally in a preliminary shock experiment for DCI campaigns. The benchmarked code will be modified to optimize the experimental design, and new diagnostics are being developed for subsequent experiments with an upgraded laser system. These well-characterized jets will be used for the next steps of DCI campaigns, where the two jets will collide into each other and be trapped by external magnetic fields to prepare the necessary conditions for fast heating by fast electrons.