Deuterium–deuterium (DD) is nonradioactive and easy to obtain compared with other, tritium-containing, hydrogen isotope compositions. It is therefore widely used in inertial confinement fusion (ICF) experiments to help understand implosion physics.1–4 The layering of DD in a cryogenic capsule is very different from that of deuterium–tritium (DT). With the latter, the ice thickness tends to be uniform under the radial thermal gradient produced by beta heating from natural radioactive decay of tritium.5,6 The same principle can be applied to DD layering by the artificial introduction of uniform infrared irradiation that is absorbed by the DD ice.1,7 However, the complexity and asymmetry of indirect-drive cylindrical targets8 makes this very difficult to achieve in practice. Fortunately, DD fuel can still be formed into a spherical ice shell because of the good infiltration between liquid DD and polymer capsules.7 However, owing to the lack of a natural radial thermal gradient, the spherical solid DD layer is thermally unstable. It will degenerate and ultimately stack around the coldest position of the capsule. The rate of degeneration is proportional to the thermal nonuniformity of the capsule.9 Preparing and maintaining a spherically symmetrical DD ice shell until the laser shot is a prerequisite for successful ICF experiments. It requires that the temperature difference be kept to less than 50 µK on a millimeter capsule to prevent a 1 µm deviation of the ice thickness, presuming a 30 min readiness time between the formation of the symmetrical ice shell and the laser shot.9 Obtaining DD ice layers with quality approaching that of DT layers is the main focus of DD cryogenic target fabrication.

Thermal uniformity and stability are very important in the cryogenic target layering process. Many simulations have been performed to investigate and optimize the thermal performance of indirect-drive cryogenic targets. London et al.10 and Moll et al.11 have studied thermal perturbations of the capsule caused by removing the target shrouds before the laser shot. Huang et al.12 and Sun et al.13 have investigated the improvements in thermal performance obtained by separating the cylindrical hohlraum into several regions. Li et al.14,15 have simulated the influences of tamping gas composition and pressure on capsule temperature and have considered the impact of thermal resistance at some important interfaces. Zhao et al.16 have shown that the uniformity of capsule temperature can be improved by dynamic heating modulation.

Up to now, all of the simulations have focused on the macroscopic variables in target design. They have provided great support for the design of indirect-drive cryogenic targets, as well as two main engineering approaches to improve the uniformity of capsule temperature. In one of these approaches, the effect of the relatively cold equator of the capsule is mitigated by having two heater rings assembled symmetrically on the top and bottom of the cylindrical jacket. This method has been tested, but has been found to have only a weak effect for our small target, which is just half the size of the NIF ignition target.8 To preserve adequate material stiffness in part machining and target assembly, the jacket and diagnosis band (DB) of our target could not be as slim as the those of the NIF ignition target, and it was therefore difficult to create the required thermal gradient along the hohlraum axial direction. The other approach is to reduce the transmissivity of the laser entrance hole (LEH) films by coating them with aluminum. This has been tested and has been found to lead to good improvements in the thermal uniformity and stability of the capsule, provided that the aluminum thickness is at least ∼35 nm. Increasing the aluminum thickness much above this value, however, appears to lead to a plateau in the improvement, and indeed an aluminum thickness of ∼35 nm provides an ice quality that is within the acceptable range for implosion experiments. Owing to the long time for which the ice quality has to be maintained before the laser shot, this method has been adopted a the main design principle for current indirect-drive cryogenic targets filled with DD fuel. Once the LEH films have been coated with sufficiently thick aluminum, heater rings around the target waist are no longer essential, which simplifies the target structure.

However, two important issues arise. First, the capsule thermal uniformity appears to be very sensitive to the details of target fabrication. The DD ice shapes and lifetimes obtained differ greatly, even among the same batch of targets (Fig. 1). This makes comparison difficult for implosion experiments. This article will investigate the effects of various details of the target fabrication procedure, such as adhesive penetration during assembly, the fill tube diameter and thermal conductivity, the optical properties of the hohlraum and film surfaces, the jacket–hohlraum connection, deviations in the capsule location, and asymmetrical contact at the arm–jacket interface. Second, in the absence of direct heat input to the capsule, it is not possible for the fill tube to always be cooler than the capsule. This results in catastrophic disruption of the seed crystal preparation protocol and unstable growth of the monocrystal deuterium. To prepare a stable and smooth DD ice shell,17 it is essential to ensure that the fill tube is always cooler than the capsule. This also a requirement for control of fuel quantity.

The indirect-drive cryogenic target is designed with a thin hohlraum surrounded by a thick jacket and DB components, together with thin films to seal the helium gas inside. The capsule is made from a glow discharge polymer (GDP). It is supported at the center of the hohlraum by just by a tapered tube with tip diameter ∼20 µm, which also acts as the deuterium fill tube. In cryogenic experiments, the target is supported and cooled by two silicon arms (i.e., cooling arms) connected to each half of the jacket. The silicon arms are mounted on a robust rod made from oxygen-free copper. Sensors and heaters are installed on the silicon arms and integrated with a circuit to tune an appropriate thermal gradient across the capsule during the DD layering. The main features of the target structure are shown in Fig. 2.

In the following analyses, a basic numerical model is constructed by incorporating all of the components and fabrication details, including possible adhesive penetration during assembly, the fill tube shell, optical behavior on the hohlraum and film surfaces, silicon claws, and the torus between the jacket and hohlraum. The end of the copper rod is connected to a fixed cold source to make the capsule temperature slightly lower than the DD triple point of 18.7 K.18 The thermal shield at 120 K outside the target is simplified by considering a uniform ambient temperature. The hohlraum is filled with helium gas at 1 kPa, which acts as the heat exchange medium between the capsule, hohlraum, and films. In the helium gas region, the thermal nonuniformity and gravity-induced natural convection will be taken into account when solving the conservation equations for mass, momentum, and energy. In the other regions, only the conservation equation for energy (i.e., the heat transfer equation) is solved. The temperatures are automatically coupled at the boundaries between the helium gas and other regions. Thermal radiation is an important load on the cryogenic target. The irradiation energy on the capsule’s outer surface includes components from the ambient radiation passing through the semitransparent films and from the reflection and emission from the surrounding hohlraum and film surfaces. The discrete ordinates (DO) radiation model19–21 is introduced to take account of all of the radiation transfer paths, especially for the semitransparent films. It calculates all of the optical phenomena, including absorption, reflection, emission, and transmission, in the helium gas medium and on its boundaries (i.e., the inner surfaces of the hohlraum and the films, and the outer surface of the capsule). The ambient radiation is introduced by treating the LEH films as semitransparent exterior walls as depicted in Fig. 3. Assuming that the ambient temperature outside the film is T_rad and that the outer surface of the aluminum layer has emissivity ε, the radiation incident on the surface is σTrad4 and the radiation reflected from it is 1−εσTrad4, where σ = 5.67 × 10⁻⁸ W/(m²K⁴) is the Stefan–Boltzmann constant. The other component εσTrad4 will experience a total absorption of E_α in the thickness direction of the coated film. The component passing through the whole film can be defined as τσTrad4, where the parameter τ represents the percentage transmission of the total incident energy (i.e., the film’s transmissivity). This component will be transported through the helium gas and be multiply reflected between the boundaries of the gas, which will result in nonuniform irradiation of the capsule’s outer surface. If absorptions by the aluminum layer and the polyimide film are neglected, then the transmissivity will be equal to the emissivity of the outer surface. This assumption is reasonable for a conservative analysis and provides a convenient definition of transmissivity in the numerical models.

The numerical model is constructed using the finite volume method. Convergence of the mesh size has been checked to obtain appropriate mesh sizes for simulating the fabrication details. The adhesive, tube tip, and hohlraum torus are meshed with element sizes of 2–4 µm. The capsule ablator and adjacent helium gas are meshed with element sizes of ∼10 µm. The tube wall and films are simulated by shell and membrane models, in which several layers can be contained in the thickness direction without mesh singularities. Other common regions of the target are meshed with element sizes of 20–40 µm. These discretizations provide sufficient precision when determining heat transfer in the various parts of the structure and in the boundary layer of the helium flow. Finer meshes would incur unnecessarily high computational costs. The main material properties of the basic numerical model are listed in Table I. Unless otherwise specified, these are the default parameters in the following analyses.

Fixing the fill tube and sealing the groove on the DB with adhesive is an important procedure in target assembly. An epoxy adhesive with specified viscosity is applied to fill the gaps. Owing to uncontrollability of the flow of adhesive during manipulation, its final distribution in the gaps will differ between targets. In practice, the inward penetration of adhesive in the gaps cannot be examined nondestructively after target assembly. Therefore, a series of simplified numerical models are employed to analyze the thermal impact of different distributions of the adhesive. Three main types of possible adhesive distribution are considered (Fig. 4). The first (denoted by AD1) assumes that the adhesive merely fills the gap between the jacket, tube, and DB. The second (AD2) assumes that the adhesive has some inward penetration and additionally fills the gap between the two halves of the jacket. The third (AD3) assumes that the adhesive has deeper inward penetration than AD2 and additionally fills the gap between the hohlraum and the jacket. During the assembly procedure, adhesive penetration into the hohlraum can be observed under the microscope. If this happens, the target will be treated as a defective product, and so this case does not need to be considered in the numerical analyses. All the adhesive distribution types are simulated based on the above model by applying different materials (gas or adhesive) to the reserved penetration area. The analyses are performed under a steady scenario in the cryogenic experiments.

The calculated temperature distributions on the outer surfaces of the target and capsule are shown in Fig. 5 for the AD1 case. As can be seen, on the outer surface of the DB, the exposed adhesive surface with greater emissivity than the neighboring area will absorb more ambient radiation and reach a higher temperature. The maximum temperature difference on the capsule’s outer surface is 29 µK. The top and bottom of the capsule are warmer because they are closer to the LEH films and farther from the hohlraum wall. The horizontal characterization holes (HCHs) and the fill tube appear as cold spots at the corresponding locations on the capsule. Detailed comparisons between the different adhesive distribution types AD1, AD2, and AD3 and thermal conductivities k_a are shown in Fig. 6. The first case (black curve) corresponds to the assumption that the DB is intact and without adhesive gaps. In addition, to decouple the influence of the fill tube, a series of similar models without a fill tube are analyzed under the same load conditions (Fig. 7). All of the curves depict temperatures on the circle of intersection of the capsule’s outer surface and the target’s equatorial plane [X–Z in Fig. 5(b)]. They mostly represent the circumferential thermal uniformity of the capsule. According to Fig. 6, the maximum difference in temperature on the capsule’s equatorial boundary is about 10 µK. If the fill tube is absent (Fig. 7), the adhesive gap will make the capsule a bit warmer (∼20 µK) than in the case with an intact DB. From a comparison with the corresponding case in Fig. 6, it can be seen that this warming effect will be counteracted by thermal conduction by the tube. Overall, the perturbations of the thermal uniformity of the capsule by different adhesive distribution types and thermal conductivities are within ∼3 µK. This is relatively small compared with the global temperature differences [Fig. 5(b)] on the capsule.

The above simulations show that the presence of the fill tube leads to a strong breaking of the symmetry of the capsule temperature distribution. The fill tube is designed with a tip diameter of about 20 µm to give it enough strength to support the capsule in the hohlraum center. Optimizing the tube material and fabrication technique to improve its strength is one way to reduce the tip diameter, as required by the ICF implosion experiments. A typical technique for strengthening the tube is to add a coating made from a strong material such as carborundum. If this approach is adopted, then the tube’s thermal conductivity will be changed, depending on the coating material and its thickness. The influence of the fill tube on the thermal uniformity of the capsule is analyzed for different values of tip diameter d_t and thermal conductivity k_t, and the results are compared in Figs. 8 and 9 with those for the idealized case in which the tube is absent.

As shown by the curve and axis graduations (5 µK in Fig. 8 and 20 µK in Fig. 9), the deviations in values between angles of 0° and 180° represent the maximum thermal nonuniformity introduced by the fill tubes in the different simulated cases. They reveal that reducing the tube tip diameter from 20 to 10 µm gives a 5 µK reduction in thermal nonuniformity. A further reduction in diameter to 5 µm has an insignificant effect on the uniformity. The cold spot is still present owing thermal conduction by the tube. The red and blue curves in Fig. 9 indicate that the thermal uniformity is disrupted considerably as the tube’s conductivity increases, even though it is not very high compared with that of carborundum itself.22 Therefore, care should be taken when modifying the tube material or applying coating layers as an engineering solution.

The above numerical models with transmissivities of 0.005 and 0.001, respectively, on the LEH and HCH films reveal remarkable inhomogeneities in the capsule’s thermal field. It has been conjectured that the thermal radiation-related optical properties of the boundaries of the helium gas region may have important effects on the thermal uniformity of the capsule. Therefore, the influences of the HCH transmissivity τ_HCH and hohlraum inner surface emissivity ε_h,in are analyzed. The fill tube is suppressed in the model to allow investigation of the nonuniformities caused by each factor individually. Figure 10(a) compares the temperature profiles around the capsule’s equator for different combinations of the optical properties. All the curves are modified by offsetting the average temperatures to the same value as the default model (the black curve). The roundness of the curve then provides a visual representation of the thermal uniformity. As can be seen, when the emissivity of the hohlraum’s inner surface is kept constant at 0.02, increasing the HCH transmissivity causes a deterioration in the equatorial thermal uniformity. The best scenario appears at an HCH transmissivity of around 0.006. The uniformity appears to be sensitivity to transmissivity variation of just 0.001. Therefore, fine tuning of the aluminizing process is necessary to mitigate the influence of the HCHs. However, the emissivity of the hohlraum’s inner surface always has a positive effect on the capsule’s equatorial thermal uniformity. Figure 10(b) shows the variation of the global thermal parameters of the capsule when the hohlraum’s inner surface emissivity is changed, with other parameters held constant. It can be seen that a greater emissivity of the inner surface of the hohlraum is associated with a lower temperature and a lower temperature difference. This is reasonable, since a greater emissivity corresponds to less reflection from the hohlraum’s inner surface, and because this surface is cylindrical, such reflection results in asymmetrical irradiation of the capsule. The curve of temperature difference is not very smooth, because of the influence of HCH transmissivity. During target fabrication, the emissivity of the inner surface of the hohlraum is affected by the machining and electrodeposition techniques. According to the calculated results, a range of 8 µK is acceptable for optimum thermal uniformity.

The cryogenic target design requires a full and reliable fit between the two halves of the jacket and the hohlraum tori (Fig. 2) to ensure good and symmetrical thermal conductivity. However, the deformations of the hohlraum and variations in assembly techniques may cause an indeterminate obliqueness of the hohlraum axis. This leads to fractional and unreliable contact between hohlraum and jacket. A series of scenarios are modeled here to assess the thermal impact of this contact asymmetry. The fractional connections between one half of the jacket and the corresponding hohlraum torus are defined as four typical thermal contact points (TCPs), which are right at the centers of the four quadrants in the horizontal section [Fig. 11(a)]. The first scenario assumes that there are only valid connections at the four TCPs. The second scenario assumes that there are only valid connections at TCP2, TCP3, and TCP4. The third scenario assumes that there are only valid connections at TCP3 and TCP4. The fourth scenario assumes that there is only a valid connection at TCP4. The definitions of the scenarios are the same for both halves of the jacket. The capsule’s thermal fields are calculated in the models without a fill tube. The results for the four scenarios are compared in Fig. 11(b) with the basic case in which the hohlraum tori and jacket are fully connected. The deviations between the curves indicate that there is a maximum difference of ∼3 µK between the simulated scenarios. The deviation in the capsule’s X–Y section has also been examine, with the same conclusion. This means that the existence of fractional connections between the jacket and the hohlraum tori has a relatively small impact on the capsule’s thermal field.

For a real target, the capsule cannot be ideally located at the center of the hohlraum, because of assembly errors and asynchronous shrinkage at low temperature. Based on the assembly procedure, the thermal impact of deviations in capsule location is analyzed for several typical scenarios. For the global and local coordinate systems for describing deviations in capsule location, see Fig. 5(b). The global coordinate system is always static, whereas the capsule’s local coordinate system always moves with the capsule. Deviations of capsule location are defined in the global system, whereas capsule temperatures are extracted in the local system. The local X–Z and X–Y sections represent typical equatorial and polar paths, respectively, on the capsule’s outer surface. Figures 12 and 13 show the thermal impact of different scenarios of the capsule location deviation. All of these numerical simulations take the fill tube into account. As can be seen from the results, a capsule location offset of 50 µm decreases the outer average temperature by about 5 µK in general, since the capsule is closer to the hohlraum wall. When the capsule is not at the center of the hohlraum, the temperature on the side of the capsule that is closer to the hohlraum wall is lower, while that on the opposite side is higher. This may change the coldest point on capsule’s outer surface (although the hottest points are always near the poles owing to the cylindrical hohlraum geometry and transmitted radiation from the LEHs). In the scenarios in which the capsule is offset 50 µm along either the −X or +Z direction, the positions near the HCHs become the coldest on the capsule’s outer surface. In other scenarios, the coldest points are still at the fill tube contact positions. The influence on the global temperature difference of a location offset of 50 µm is shown in Table II. It seems that a capsule location offset can even improve thermal uniformity in some scenarios. The maximum temperature difference is reduced by 3.7 µK when the capsule is offset 50 µm along the −X direction (the blue curves in Figs. 12 and 13), which moves it farther from the tube-side hohlraum wall and mitigates the thermal nonuniformity caused by the fill tube. If the influence of the HCHs is ignored, the blue curve in Fig. 12 indicates a remarkable reduction by 7.5 µK of the capsule’s equatorial thermal nonuniformity.

The above analyses have been performed under the assumption that both the top and bottom halves of the jacket and the cooling arms are have uniform thermal connections. However, the real thermal conductances at the arm–jacket interfaces may be not ideally symmetric owing to rounding errors ar the interface and inconsistent adhesion during assembly. The cooling arms are designed with flexible claws to hold the target reliably at low temperature. In general, the silicon claws are fitted over the jacket periphery for good mechanical performance, while the small gaps around the claws are filled with adhesive for good thermal performance. A series of models including details of the cooling arms and claws are used to analyze the thermal impact of different scenarios of asymmetric contact at the arm–jacket interfaces. The models are derived from the same basic model simply by suppressing different parts of the claw–jacket interfaces in the different scenarios. In the basic model, the jacket material is aluminum and all the arm–jacket interfaces are assumed to be connected uniformly. Both the ends of the arms are about 70 mm away from the hohlraum center. The temperatures of the ends of the arms are 17.5 K. The LEH and HCH film transmissivities are set as 0.01 and 0.005, respectively, to reduce interference from thermal nonuniformity around the capsule’s equator. Other loads and parameters have their default values. The basic model gives a maximum temperature difference of 0.068 mK on the capsule for the following comparison.

In the first scenario (Fig. 14), four claws of the top cooling arm are assumed to be out of contact with the top jacket, while the other claw interfaces remain thermally well connected. The results for this scenario show that the jacket region without claw contact is 0.8 mK warmer than the opposite but well-connected region. Correspondingly, the top side of the capsule’s surface near the disconnected claws is 0.06 mK warmer than the bottom. The maximum temperature difference over all of the capsule’s surface is 0.103 mK. In the second scenario (Fig. 15), the bottom cooling arm is added with another four disconnected claws on the same side as the top. The thermal nonuniformity on the jacket appears to be slightly inferior to that in the first scenario. However, the capsule’s global temperature difference is relieved a little, possibly owing to the neutralization effect. The hottest regions on the capsule, pointing to the disconnected claws on both the top and bottom, are as expected. The third scenario (Fig. 16) spreads the disconnected claws twice as far in the clockwise direction compared with the second scenario. This is to simulate a catastrophic failure in target fabrication. All the jacket and capsule thermal uniformities become extremely poor.

An optimization scheme is proposed in which the jacket material is changed from aluminum to oxygen-free copper (C10200), which has a very high thermal conductivity of 777.4 W/(mK) at 18 K.23 This optimization is analyzed and compared with the fourth scenario in Fig. 17, from which it can be seen that the copper jacket significantly smoothens the thermal nonuniformity caused by the asymmetric thermal contact at the arm–jacket interfaces. The calculated maximum temperature difference on the capsule’s outer surface decreases to 0.087 mK, which is only slightly worse than the basic ideal model.

It is evident from the results of the above simulations that asymmetric contact at the arm–jacket interfaces, the optical properties of the hohlraum and films, the presence of the fill tube, and deviations in the capsule location all have remarkable impacts on the thermal uniformity of the capsule. Thus, the spherical symmetry and lifetime of the DD ice layer are determined mainly by these factors. However, not all of them can easily be optimized in target fabrication. The easiest approach is to alter the jacket material to a high-conductivity one such as oxygen-free copper. However, this risks hampering the ability to tune the vertical temperature to counteract the effects of gravity on fuel layering. Therefore, adequate insulation between the two halves of the jacket is essential. Bearing this in mind, it is recommended that the aluminum DB be retained. Optimizing the fill tube, the surfaces of the hohlraum and film, and the capsule location all pose significant challenges to target fabrication techniques. The requirements of implosion physics, such as precision in capsule location and limits on hohlraum roughness, should be considered in the optimization. The physics design may impose restrictions on how far the capsule’s thermal uniformity can be improved by increasing the hohlraum’s inner surface emissivity and offsetting the capsule’s location. However, changes in some of these factors fulfil both physics and engineering requirements, for instance, reducing the tip diameter of the fill tube.

The above analyses also reveal the relatively insignificant impacts of adhesive penetration and jacket–hohlraum connection. This is understandable, because under symmetric thermal loads on the circumference and with little heat outflow from the hohlraum interior (DD does not generate internal heat), the impact of defects in the jacket–hohlraum gap is extremely limited. Furthermore, the helium gas in the gap and the fairly high conductivity of the gold hohlraum also mitigate the influence of asymmetry.

In the past, cryogenic targets were sealed with relatively thin aluminum films. Ambient radiation passing through the LEHs is transformed to heat flow from the inside of the capsule, which is then taken away by the fill tube and hohlraum wall. This is achieved through conduction and convection in the surrounding helium gas. Thus, a stable heat flow path is created on the capsule fill tube assembly (CFTA) and in addition the fill hole becomes the coldest part on the capsule. The tube tip therefore provides a reliable bed for seed crystals at the beginning of DD ice growth. However, this reliability disappears when the film’s transmissivity is reduced considerably by a thick aluminum coating. Preserving a seed crystal at the tube tip becomes fortuitous and difficult for current targets (Fig. 18). If the radiation passing through the LEHs cannot dominate the input energy to the capsule, then the regular thermal gradient along the fill tube may cease to exist because of (a) insufficient thermal conductance at the tube–hohlraum interface and (b) radiation absorption on the outside part of the tube. It is also possible that the fill tube will cease to be the coldest component for other reasons, as shown by the blue and green curves in Fig. 12. Reduction in the transmissivity of the sealing film significantly improves the thermal uniformity and thus extends the lifetime of the DD ice shell. This is however, in conflict with the traditional protocol for single crystal growth.24 Ensuring that the fill tube is the coldest component is also important for controlling the fuel quantity in experiments. After tuning the film’s transmissivity, the tube–hohlraum interfacial thermal conductance, and the outside radiation parameters, it may be possible to obtain the best configuration in which simultaneously the capsule has good thermal uniformity and the tube is the coldest component. However, it is extremely hard to maintain consistency and precision during target fabrication. To deal with this issue, a mechanical component can be incorporated in the target to enable separate control of the tube temperature. A schematic of a preliminary design is shown in Fig. 19. This fill tube thermal controller consists principally of block and wire parts made from copper. An adiabatic support made from epoxy resin is used to hold the connector close to the fill tube. A heater ring and temperature sensor are mounted at appropriate positions to control the connector temperature.

Since the coefficients of thermal expansion of copper and silicon are very different, the fill tube thermal controller has been designed taking account of different material deformations during cooling. The thermal stress on the tube–controller joint may become destructive when the target is cooled from room temperature of 295 K to the DD fuel layering temperature of about 18 K. With the copper wire welded to the connector and finger, the front and back parts can accommodate the cooling procedure to keep the fill tube mechanically safe. However, these slender wires of about 1 mm in diameter may cause poor thermal conductivity along the controller path. Additionally, the silicon arms have a thermal conductivity of 1377 W/(mK) at 18 K, which is larger than that of copper [777.4 W/(mK) for C10200]. The basic purpose of the controller is to ensure that the connected tube remains the coldest component during the formation of DD seed crystals. After a spherical DD ice shell has been obtained, the controller is expected to become slightly warmer to help counteract the thermal nonuniformity caused by the fill tube.

The thermal performance of this preliminary design of tube controller has been analyzed using an experimental prototype. The cooling base end is applied with a fixed temperature of 17.5 K. For a conservative analysis, emissivity of the outside surfaces of the silicon dioxide tube with a polymer coating and with adhesive in the DB gap is set as 1.0. The emissivity of the controller’s outer surface is set the same as that of the silicon arms. The target is exposed to an ambient temperature of 120 K. The temperature distribution of the target’s vertical section is shown in Fig. 20(a). The tube connection point on the controller is cooler than the vertically aligned positions on the silicon arms. However, the tube segment inside the hohlraum has a thermal gradient from the capsule to the hohlraum wall, which is not expected in DD ice preparation. The temperature difference between the capsule and hohlraum on the tube’s internal segment, ΔT_tube, is calculated as −1.2 mK for this model with the preliminary design of tube controller. The effects of radiation absorption by the tube’s external segment and by adhesive have been considered. After separately suppressing the radiation loads on the tube’s external segment and the adhesive in the DB gap, the calculated ΔT_tube becomes 0.6 and 0.8 mK respectively. The thermal gradient of the tube segment inside the hohlraum is reversed. However, this effect is too weak to realize the design objective of the tube controller. The assumption of zero radiation absorption by the adhesive and the tube’s outside segment is too idealized and can easily be violated by target fabrication conditions. It is difficult for heat to be removed from the fill tube, possibly because of the relatively low thermal conductivity of the tube material [0.29 W/(mK) at 18 K]. Therefore, an optimization is proposed in which a copper sleeve is added around the tube’s external segment. The calculated temperature distribution of this optimized design is shown in Fig. 20(b). With the assistance of conduction by the copper sleeve, tube inside the hohlraum has a sufficient thermal gradient to become the coldest component. The calculated ΔT_tube is 53 mK when the controller finger is not heated. This provides an adequate range of modulation for finding a good balance between thermal uniformity and the requirement that the fill tube be the coldest component.

Fabrication of indirect-drive cryogenic targets is difficult and complicated, involving dexterous manual work and limitations on measurements due to the millimeter scale and special materials, and with indeterminate tolerances. In addition, not all of the proposed designs can yet be realized in practice. For instance, with only one horizontal characterization, it is not possible to measure deviations in ice thickness in the other two orthotropic directions. Reducing the fill tube diameter will require more advanced technology than is currently available. It is also hard to obtain goal-directed verifications of thermal performance, given the impact of all details of microfabrication. However, statistical data on different batches of targets and different targets in the same batch do reveal some good consistency between the results of experiments and simulations. One such result concerns the optimization of the jacket material from aluminum to oxygen-free copper. As mentioned above, because of the particular properties of DD ice shells in the absence of infrared irradiation, the retention time of ice shells is determined by the thermal uniformity of the capsule.9 Earlier targets were designed with aluminum jackets, and the record retention time, defined as the period from a just prepared DD ice shell to the moment of rupture at the top and bottom poles, was ∼35 min. By contrast, nearly all recent targets in which the jackets have been changed to copper have extended DD ice retention times, with most being longer than 60 min. Figure 21 shows an experimental comparison between two sample targets with aluminum and copper jackets, respectively. The DBs of the targets are still made from aluminum to preserve the good tuning capability of the capsule’s vertical thermal gradient. The configuration of copper jacket and aluminum DB has become the standard design for indirect-drive targets, given this remarkable improvement in DD ice retention time.

Consistency is also found between simulated and experimental results for the relation between the uniformity of the temperature distribution and deviations in capsule location. According to the simulated results in Fig. 12, even when the capsule is located right at the hohlraum center, it is cooler on the side facing the fill tube and warmer on the opposite side. Except for the case when the capsule is offset along the +X direction, the other cases all show improvements in its thermal uniformity, with offsetting along the −X direction giving the greatest improvement. These results have been verified by comparing the data among targets in the same batch. There is always some indeterminacy in fabricated targets and experimental results, but obvious regularities appear when the divergence between the deviations in capsule locations of two targets is greater than ∼20 µm along one axis. Figure 22 shows x-ray phase contrast images of ice shells from experiments on three sample targets.25 All of these images were taken at the moment when the upper and lower ice thicknesses were nearly equal. The difference between the ice thicknesses on the tube side and the opposite side then indicates which side is warmer or cooler. The ice shell in Fig. 22(a) has a 23 µm deviation along the +X direction, and the tube side is much colder than the opposite side. The ice shell in Fig. 22(b) shows a remarkable reduction in the divergence in thickness between the two sides owing to the 8.95 µm offset along the −X direction. There is a reduction in the divergence of the ice thickness in the shell in Fig. 22(c) owing to the 79.4 µm sagging along the vertical (−Y) direction, although the effect is weaker than in Fig. 22(b). All of these simulated and experimental results are well matched.

Additionally, different adhesive materials and penetrations in the DB gap have been tested and have been shown to have no obvious impact on the spherical symmetry of the ice shell. This is also consistent with the model predictions. Thus, at least for the data we have obtained up to now, the numerical model can be trusted.

Owing to the absence of a radial thermal gradient, DD layering in cryogenic targets is thermally unstable. Preparing and maintaining a spherically symmetric DD ice layer until the laser shot thus places stringent demands on the thermal uniformity of the capsule. Precise engineering design of the target can eliminate most drawbacks of theoretical models. However, actual targets often diverge from the engineering design owing to fabrication details. Many of the influencing factors are difficult to predict because of indeterminacies and variations in microfabrication. High thermal sensitivity is a disadvantage of DD cryogenic targets because it increases the difficulty of the layering process and degrades the ice quality compared with DT ice. On the other hand, the sensitivity of DD to thermal influence is also helpful for optimization of cryogenic target design and fabrication, owing to the convenience of experimental verification under various thermal conditions.

Acknowledgment. The work reported in this article is supported by the Science Challenge Project (Grant No. TZ2018006), the National Natural Science Foundation of China (Grant Nos. 11804318 and 61803354), the Key Laboratory Foundation of Ultra-Precision Manufacturing (Grant No. ZD18007), and the Young Talent Foundation (Grant No. RCFCZ3-2019-5). The authors are grateful to all of these.