Demonstration of indirectly driven implosion experiments with cryogenic pure deuterium layered capsules on the Shenguang Laser Facility

To achieve ignition in a laboratory via inertial confinement fusion, a spherical capsule containing a frozen layer of deuterium and tritium (DT) fuel will be imploded on an MJ-class laser facility. However, if pure deuterium fuel can be used in place of DT fuel for tuning shots, we may speed up the process of ignition experiments while maintaining the surrogacy by significantly reducing the level of radioactivity. Unfortunately, it has long been assumed that neither the approach of symmetrical infrared irradiation used in the Omega direct-drive experiments nor the method of beta-layering used in the NIF experiments can be used to smooth the D layered capsule in cylindrical hohlraums. The difficulty in smoothing the D ice layer prevents us from taking advantage of cryogenic D-layered capsules in indirect-drive experiments. In this work, we established a procedure to form a uniform D-ice layer for capsules held in cylindrical hohlraums and carried out indirect-drive cryogenic D-layered implosion experiments using a squared laser pulse on the Shenguang Laser Facility in China. The quality of the D ice layer is characterized by phase-contrast imaging. The root-mean-square of the power spectrum in modes 2–100 is about 2.2 μm. The implosion performance of the D-layered capsules is close to the prediction of one-dimensional simulations. The measured neutron yield and areal fuel density are 1.2 × 1011 and 80 mg cm−2, respectively.

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Introduction
For the ignition design of indirect-drive inertial confinement fusion, cryogenic deuterium (D) and tritium (T) fuel is necessary to reduce the laser energy required for ignition. The fuel mass scales as ρ −2 as the areal fuel density is set by ignition physics, So high compressed fuel density, which would become possible by cryogenic fuel and quasi-isotropic implosion, means small fuel mass that is needed in ignition temperature. However, the deuterium and tritium (DT) fuel can cause radioactive contamination, complicating capsule fabrication, diagnostic operation, and laser facility maintenance. Moreover, when the capsules with DT layers are imploded, high neutron yield can create highly harsh and challenging environments. This results in significant impacts and severely limits diagnostics options and experimental schedules. In a high-yield environment, for example, shielding strategies against neutron irradiation damage may lose efficacy, and critical diagnostic information is unavailable. Cryogenic deuterium (D) layered capsules can be used as an alternative to solve this problem. The cross-section of the DD reaction is approximately 100 times smaller than that of the DT reaction. At the same time, the neutron energy of the DD reaction is a few times smaller than that of the DT reaction. As a result, the radioactive contamination and harsh environments are mitigated when DT fuel is replaced with pure D fuel. Meanwhile, the surrogacy errors are minimal since the D hotspot is assembled nearly the same way as the DT hotspot. An additional advantage of using D fuel is that the energy balance of the D hotspot decouples from alpha-heating and burn propagation. This feature can be utilized for isolating ignition failure modes.
To the author's knowledge, no successful indirect-drive cryogenic layered D target implosions have been reported before. In the US, direct-drive cryogenic layered D target implosions were carried out on the Omega laser facility in 2000-2006 [1][2][3][4][5]. These targets were driven by squared or shaped pluses. When driven by the squared pulse with total laser energy ∼23 kJ, the neutron yield is between 1 × 10 10 and 1 × 10 11 . The highest DD neutron yield (∼1.8 × 10 11 ) among those experiments was obtained by imploding the D 2 wetted foam target. The indirect-drive cryogenic layered target implosions were not carried out until the completion of the NIF laser facility in 2009 [6][7][8][9]. Only DT and THD targets were used. The implosion performance was improved through extensive design optimizations and engineering efforts [10][11][12][13][14][15]. The ignition was finally achieved on 5 December 2022 with laser energy gain equal to 1.5. The DT-wetted foam targets were also used on the NIF to study the effects of convergence ratio on the implosion behavior [16]. In Japan, the direct-drive implosion experiments with D 2 wetted foam targets were carried out on the Gekko XII laser facility in 90s [17]. The laser energy was 3.8 kJ in a 2.5 ns stacked Gaussian pulse. The neutron yield was about 7 × 10 6 . In France, recently, it has been reported that the indirect-drive cryogenic layered DT target assembly is in development, and future implosion experiments are in planning [18].
There is a significant technical challenge in fabricating indirect-drive cryogenic layered D targets. Because no process, like the tritium beta decay, can act as an internal heating source to smooth the D-ice layer, an external heating source with spherical symmetry must be provided to redistribute Dice on the inner surface of the capsule. In the direct-drive configuration, infrared radiation (IR) is applied inside a layering sphere to smooth the D-ice layer [19]. However, in the indirectdrive configuration, it is not easy to apply IR illumination with spherical symmetry inside cylindrical hohlraums with two Laser Entrance Holes (LEHs) [20]. Therefore, instead of IR layering, our work established a repeatable procedure in which a uniform D-ice layer would exist for a few minutes. By synchronizing the shot time and the time window of uniform D-ice layer survival, we carried out cryogenic layered D target implosion experiments.

Experimental setup
The indirect-drive D layered capsule implosion experiments use cryogenic gas-filled gold hohlraums. The hohlraums are 4680 µm long with a diameter of 2600 µm and filled with helium gas at densities of 0.1 mg cc −1 . The hohlraums are heated with up to 48 laser beams at a wavelength of 351 nm through two LEHs of 1400 µm in diameter on either end. The beams are arranged in two cones entering through each LEH: the inner cone at angles of 28.5 • and 35 • and the outer cone at 49.5 • and 55 • to the vertical axis. The thermal shrouds protect the hohlraums from environmental IR. There are two thermal shrouds. One is at room temperature. The other is at a temperature of ∼130 K. The thermal shroud is removed about 5 s before the shot time.
The capsules are located at the center of the hohlraums and are supported by the fill tubes with a diameter of 15 µm. As shown in figure 1, these capsules have an outer radius of 960 µm and an outer ablator shell that consists of layers of silicon-doped glow discharge polymer (GDP) materials. GDP is primarily comprised of hydrocarbon (CH) with small amounts of oxygen. The capsules are firstly cooled to 20 K to liquefy the deuterium gas. Liquid deuterium is condensed at the bottom of the capsules with a crescent shape. The capsules are further cooled below the deuterium solidification temperature when the amounts of the liquid fuel inside the capsules meet the design requirements. Following specific procedures of temperature control [21,22], it is found that a uniform D-ice layer can survive for a few minutes inside the capsule. We repeated the procedures of D-ice layering fourteen times for a single target, and by characterizing the ice layer quality with phase contrast imaging (figure 2), we found that there was a 72% chance that the amplitude of mode 1 was less than 2.8 µm, and the RMS of the power spectrum in modes 2-100 was 2.2 µm in average.
The hohlraum energetics was characterized by the same diagnostics as in [23]. The hotspot shape of self-emission was measured by a time-integrated x-ray camera which viewed from the equatorial plane with 10× magnification  through a 300 µm diagnostic hole covered with a 50 µm thick CH patch. The x-ray imaging system can tolerate the neutron damage with current neutron yield of pure D fuel. No radiation harden design was needed so far which should be regarded as the advantage of pure D fuel. The Nuclear Temporal Detector (NTD) [24] was not used in the cryogenic D-layered implosion experiments, since the standoff distance of the NTD was increased for not interfering with the thermal shroud. The increasement of standoff distance reduced the neutron counts, and the signal-to-noise ratio. This problem is more serious for pure D fuel. Alternatively, we measured the neutron bangtime with a scintillator-PMT based system [25]. The areal fuel density was characterized by the energy spectrum of secondary protons, which was measured by a wedged range filter [26]. This method is suitable when the areal fuel density is smaller than a few hundred mg cm −2 , but would fail in the ignition relevant condition. Down scattered neutron ratio can be used to measure the areal density of pure D fuel as well. However, our preliminary design analysis showed that neutron yield is not high enough to produce acceptable signal-to-noise ratio on our current laser facilities. The neutron yield was measured by a scintillator detector and Indium activation diagnostic [27,28]. The ion temperature was measured by a nToF detector with an accuracy of 15% [29].

Experimental results
There are concerns that the target positioning accuracy could be affected by the engineering features of the cryogenic target assembly, according to earlier works [30,31]. To confirm the locations and orientations of the cryogenic hohlraums at shot time, we examined the images of the upper and lower LEHs acquired by the PHCs. The ideal locations of the LEH centers in the PHC images were calibrated using spatial reference targets, namely gold-coated spheres placed at the same positions as the LEHs in a calibration shot. These targets would not cause additional degradation of positioning accuracy besides the laser pointing accuracy. As shown in figure 3, if the centers of the upper and lower LEHs deviate in the same direction, the hohlraums are translated. If the centers of the upper and lower LEHs deviate in the opposite direction, the hohlraums are rotated. Considering the uncertainty in this method, it is concluded that for most shots, the angles of the hohlraum axis to the vertical line are less than one degree, and the distances between the LEH centers and the centers of the spatial reference targets are less than 50 µm.
To confirm that the cryogenic condensations on the sealing films or the hohlraum inner walls have been eliminated, and that the engineering features of cryogenic target assembly do not affect the measurement of radiation flux leaking from the LEHs, we carried out comparative experiments using three types of targets with same nominal parameters except that they are held by different target positioners and shot at different temperatures. The warm targets held by the warm target positioner are shot at room temperature. The cryogenic targets held by the cryogenic target positioner are shot at room cryogenic temperature. The measured radiation temperatures for the three types of targets are the identical, as shown in figure 4. It is concluded that the condensations and the engineering features of cryogenic targets do not have an observed influence on the measured radiation temperatures [32]. This conclusion  could also be supported by comparing bangtime and scaling of radiation temperature with laser energy among different types of targets.
We use a squared laser pulse of 2.5 ns long with a total energy of 120 kJ for the implosion experiments. The gas-filled capsules are imploded to confirm the drive symmetry. The shapes of hotspot self-emission images characterize the drive symmetry [33]. In current cryogenic layered implosion experiments, we do not control time-dependent drive symmetry via time-varying cone fraction (CF). However, the implosion performance degradation by symmetry swing can be estimated by 2D simulations, which will be addressed in the next section.
The hotspot shape of the gas-filled capsule with CF = 0.3 is shown in figure 5(a). The 20% contour of peak intensity has a P 2 component of ∼8%. We do not further optimize the CF to achieve better hotspot symmetry considering the uncertainty of measurements, the accuracy of laser power control, and the sensitivity of implosion performance to the drive symmetry for these high adiabat, low convergence ratio implosions. The neutron yield of the gas-filled capsule is 7.8 × 10 10 , which reaches 78% of the 1D calculation.
The cryogenic layered implosion experiments have identical conditions as the gas-filled implosion experiments. The D-ice layer has a thickness of 35 µm. The neutron yield is 1.2 × 10 11 . The hotspot shape of the cryogenic D-layered capsule is shown in figure 5(b). The pancake-like distortion and the lack of left-right symmetry is largely attributed to D ice non-uniformity. The thickness of the D-ice layer is found thicker at the equatorial plane, and thinner at the polar area. This non-uniformity pattern of ice thickness is related to the temperature field that is higher in the polar area and lower in the equatorial area. The effects of D ice non-uniformity on implosion performance will be addressed in the next section.

Simulation studies
We perform post-shot simulations for the gas-filled and cryogenic layered capsules using the one-dimensional hydrodynamic code RDMG [34]. The radiation source used in the 1D simulations is derived from 2D hohlraum simulations with as-measured laser powers. The calculated neutron yields, bangtime, ion temperature, convergent ratio, and hotspot pressure are compared with experimental measured or inferred values in table 1. The implosion performance of the gas-filled capsule is close to the 1D prediction. However, the implosion performance of the cryogenic layered capsule falls short of the 1D prediction. The surface roughness, support tents and fill tubes are not the primary cause of implosion performance degradation for the cryogenic layered capsules since the capsules are driven with the squared pulse, and the gas-filled capsule implosions show quasi-1D implosion performance. The contributions to the implosion degradation from the drive asymmetry and ice thickness non-uniformity are discussed in the following.
We employ the two-dimensional hydrodynamic code LARED-JC [36] to assess the degradation of implosion performance induced solely by drive asymmetry. These integrated simulations are performed for the gas-filled capsule using nominal capsule parameters. The simulations do not consider the time-varying behavior of backscattered laser energy since the amount of backscattered laser energy is negligible (∼2%). The CF, namely the ratio of inner quad laser energy to total laser energy, is varied in the simulations while the total laser power remains unchanged. Figure 6 shows the calculated hotspot P 2 asymmetry and normalized neutron yield.
When CF is about 0.28, the predicted P 2 component of the hotspot shape is close to zero, and the neutron yield reaches a maximum. The CF used in the experiments is about 0.3. According to the sensitivity of neutron yield to CF illustrated in figure 6, the neutron yield would be decreased by less than 10% when the CF is increased to 0.30 from its optimal value of 0.28.
We employ the two-dimensional hydrodynamic code LARED-S [37] to carry out capsule-only simulations to assess the degradation of implosion performance caused by ice nonuniformity. In these simulations, the capsules are driven symmetrically, and the ice thickness T is described by T(θ) = ∑ n=0 a n P n (cos) θ where a n is the amplitude of the nth Legendre polynomial P n , and θ is the angle between the hohlraum axis and the radial direction. The coefficient a 0 determines the average ice thickness and is 35 µm in the simulations. We have considered six cases, including only P 1 or P 2 components with amplitudes a 1/2 = −3, −6, −12 µm. The negative sign mimics the ice non-uniformity caused by gravity (P 1 ) or environmental IR (P 2 ) leaking from LEH windows. Figure 7 shows the variations of neutron yield with the amplitudes a n . The neutron yields are decreased as the absolute values of the amplitudes are increased. A portion of the shell with less areal density would implode faster than that with larger areal density. For example, the polar area of the shell has higher implosion velocity and stagnates earlier than other parts of the shell, assuming a negative P 2 component of ice thickness. The early stagnated polar jets fall deep into the hotspot, resulting in unconverted shell kinetic energy [38][39][40][41]. This kind of hotspot shape is more susceptible to 3D perturbations which would further decrease the neutron yield. The typical values of a 1 and a 2 in the implosion experiments is about 3 µm and 5 µm, respectively, as characterized by phase contrast imaging. This level of ice non-uniformity will decrease the neutron yield by about 50% according to the capsule simulations.

Conclusion
The cryogenic D-layered targets with minimal radioactivity and low neutron damage are a good surrogate of the cryogenic layered DT targets for studying implosion dynamics. However, the indirect-drive cryogenic D-layered targets prove to be a significant engineering challenge. In this article, we reported the indirect-drive cryogenic layered D implosion experiments on the SG laser facility in China. We developed the procedures to ensure a uniform D-ice layer at shot time.
We also demonstrated that the coupling efficiency of the cryogenic hohlraum is the same as that of the warm hohlraum, and the positioning accuracy of the cryogenic hohlraum is as good as that of the warm hohlraum. The cryogenic gas-filled targets were imploded to confirm that factors other than the Dice quality would not degrade the implosion performance. The cryogenic D-layered targets were finally imploded, and the neutron yield reached 1.2 × 10 11 . We compared the measured implosion performance with 1D simulations. The YOC of the gas-filled target is 78%, while the YOC of the cryogenic target is 26%. Ice thickness non-uniformity is the dominate mechanism for implosion performance degradation, as suggested by the 2D simulations with typical P 1 and P 2 component amplitudes. In the future, engineering and technology efforts will be devoted to improving D-ice uniformity, and pulse-shaping implosion experiments will be performed.