The I-Raum: A new shaped hohlraum for improved inner beam propagation in indirectly-driven ICF implosions on the National Ignition Facility

Inertial confinement fusion (ICF) implosion experiments are being conducted at the National Ignition Facility (NIF)¹ with a goal of compressing a spherically layered cryogenic shell of deuterium tritium (DT) fuel² to a sufficient areal density (ρR) to inertially confine the hot fuel for a sufficient duration to sustain a self-propagating burn wave. Most experiments on the NIF employ the indirect-drive technique,³ where the energy of a precisely tailored sequence of laser pulses is converted into a thermal x-ray bath inside a high-Z (typically Au or depleted uranium, DU) enclosure called a hohlraum. This x-ray radiation ablates the outer surface of a low-Z [typically polystyrene (CH),⁴ high-density carbon,^5,6 or Be⁷] spherical shell, which surrounds the cryogenic layer of DT fuel, compressing the fuel to create the high temperature plasma conditions required to initiate DT fusion reactions in the central hot spot core.

A number of factors are critical for the success of these implosions, but in the present work, we will focus on the ability to control and maintain implosion symmetry for as long as possible. The NIF laser is composed of 192 laser beams grouped in individually controllable units of 4 beams called a “quad.” The 48 quads are in turn divided into four cones of beams, which enter the hohlraum at angles of 23°, 30°, 44°, and 50° to the hohlraum axis of symmetry (Z). The 23° and 30° beam cones are collectively referred to as the “inner” cones, and the 44° and 50° cones are the “outers,” as they hit the interior hohlraum wall closer to or further from, respectively, the hohlraum waist or equator. Maintaining implosion symmetry in indirectly-driven ICF relies heavily on the ability to control the laser energy reaching various portions of the hohlraum wall at all times.

A number of experiments have been conducted in recent years on the NIF^8,9 demonstrating that the outer cones, which hit the hohlraum wall at a steeper angle, have smaller spot sizes, and therefore have a higher intensity, generate intense ablation of the wall material that expands into the hohlraum as a relatively low density, but high-Z “bubble.” In this paper, we will generically refer to this as the “Au bubble” (the most widely used wall material), though the same phenomenon occurs in a DU hohlraum wall. The radial bubble penetration toward the hohlraum axis has been measured to be nearly linear in time⁸ with a velocity of approximately 250 μm/ns. For a typical 6.2 mm diameter hohlraum, the bubble will penetrate approximately 1/3 the distance to the axis in ∼4 ns. This bubble increasingly absorbs the inner cone energy, which is intended to reach the hohlraum waist to maintain implosion symmetry. Depending on the hohlraum and implosion details, the inner cone energy can become completely blocked, and the resulting lack of drive at the equator generates a non-recoverably oblate (or pancaked) implosion core. This impaired inner-beam propagation appears to be a reproducible phenomenon across a wide range of low to intermediate gas-filled hohlraums as documented in Ref. 9 with fill densities ranging from 0.3 to 0.6 mg/cc, capsule ablator materials varying from CH to Be to high-density carbon (HDC), and hohlraum sizes ranging from 5.75 to 6.72 mm diameter.

A number of mitigation techniques are being investigated to try to suppress the growth of this Au bubble. These include the well-used technique of increasing the hohlraum gas fill density to effectively tamp the bubble expansion. This has been used extensively in earlier NIF implosions including the early National Ignition Campaign (NIC) experiments (ρ_gas∼1 mg/cc)¹⁰ and the later High-Foot Campaign,^11–15 which used 1.6 mg/cc gas fill. The down-side of this approach is the significant increase in laser backscatter,¹⁶ the onset of cross-beam energy transfer (CBET),¹⁷ and the increased possibility of detrimental hot electron production,¹⁸ which can preheat the deuterium-tritium fuel, and reduce performance. In this study, we will focus solely on low-density hohlraum gas-fills (0.3 mg/cc) that have demonstrated a significant reduction in all of these potential degradation mechanisms.^19,20 It is very important, however, to distinguish the impaired inner beam propagation that occurs in low gas-filled hohlraums (0.3–0.6 mg/cc) with the opposite phenomenon, which was observed in Near-Vacuum Hohlraums (NVH, ρ_gas ∼0.03 mg/cc) where, as pointed out in Ref. 21, “inner laser beam propagation is better than predicted by nominal simulations.” The reason for this very different behavior in NVHs is threefold: (1) the Au bubble density is lower, (2) the temperature correspondingly higher, and (3) the pulse length is shorter, all of which keep the Au bubble transparent to the laser beam over the full duration of the implosion.

Other options for mitigating the Au bubble in low gas-filled hohlraums include adding a low-density foam material, again to tamp the bubble expansion, but now in a more localized manner. Such a technique is currently being investigated experimentally on NIF in hohlraums with reduced gas fill density (∼0.3 mg/cc), and may be able to minimize the detrimental impacts of LPI (Laser Plasma Interaction) caused by higher gas fills. These are still in the testing phase, but do raise additional difficulties in target fabrication and increase concerns about debris from the fragile foam structures falling on and perturbing the implosion of the capsule.

An alternative to tamping with either increased gas fill or a low-density foam is to simply recess the Au bubble by adding a small pocket at the location where the bubble originates. That is the approach considered here.

Figure 1 shows the modified hohlraum geometry being considered. It has been named the I-Raum, as it somewhat resembles the shape of a capital letter “I.” It is based on a 6.2 mm diameter hohlraum that is widely used for NIF implosions.²² A small recessed cylindrical pocket is added. The pocket depth d = 260 μm increases the outer diameter to 6.72 mm, which is the largest size hohlraum that can currently be fielded on NIF. [Modifications to the thermal housing that supports and cools the hohlraum, the thermal-mechanical package (TMP), are being made to allow larger diameter hohlraums in the future.] The axial dimensions of the recessed pocket are sized to accommodate the pointing used in a recent shot, N170601,²² which will be the cylindrical basis for all comparisons within this paper.

In that shot, the outer cones were axially repointed as shown in Fig. 1 to minimize the wall intensity. The pocket axial length is initially set to 2.8 mm, and the pocket center location is 2.5 mm from the equator to fit this outer cone pointing. The surface area increases by 7.0% over the 6.2 mm diameter hohlraum, and is 3.4% smaller than a larger, 6.72 mm cylindrical hohlraum that is also frequently used for NIF implosions.²³ These dimensions serve as a starting point for design studies and will later be optimized.

A primary motivation behind the I-Raum is to reduce the impact of the Au bubble with the minimal number of changes to existing hohlraums. With that in mind, the list of parameters that remain unchanged in the I-Raum is extensive: the LEH (Laser Entrance Hole) diameter, the hohlraum corner radius, the beam pointing, and the hohlraum waist radius are all unchanged. Importantly, the hohlraum gas fill is kept the same at 0.3 mg/cc.²⁴ The hohlraum wall material for this study will also be limited to DU²⁵ to obtain the best A/B comparison with N170601, though this may not be essential for future experiments. The only changes to currently used hohlraums are the pocket and the capsule diameter, which will be discussed in Sec. III.

Figure 2 shows the computational mesh used to compare the bubble evolution and resulting implosion performance between a cylinder and an I-Raum. The simulations are performed using the radiation-hydrodynamics code HYDRA.²⁶ The pocket is added as a simple modification of the hohlraum wall contour maintaining the same ablative wall zoning (4 nm minimum mesh radial spacing). The zoning and all physics parameters of the simulation are held constant between the two geometries. In particular, the mesh is logically divided into two computational blocks, one containing the capsule (inside the red contour shown in Fig. 2) and the other containing the hohlraum (outside the red contour). All zoning and physics parameters in the capsule block are held constant.

In this study, the hohlraum, laser pulse, and capsule are all based on shot N170601, which delivered one of the highest primary neutron yields to date.²² The hohlraum was discussed in Sec. II. The capsule of that shot used a high-density carbon (HDC) ablator with a thickness of 70 μm and an outer radius of 980 μm. The capsule pie diagram is shown in Fig. 3(a). A 0.3% W-doped layer of thickness 18 μm was used to shield against high-energy x-ray preheat.²² 

Initial simulations in the I-Raum will use this same HDC capsule, but as will be shown in Sec. IV, the I-Raum geometry provides extended time for inner-beam propagation. This additional time can be used in several ways to improve implosion performance. The first shock strength could be decreased, lowering the fuel adiabat and increasing fuel compression. This would require a longer pulse for the slower velocity 1st shock to transit the ablator. Note, however, that this is not an option for HDC ablators, which require a minimum shock strength of ∼12 Mbar to completely melt and prevent re-solidification of the ablator. Other ablators (CH or Be) could make use of this option. Alternatively, the pulse could simply be lengthened to maintain drive on the capsule longer, reducing “coast time” (the time between the end of the laser pulse and bang-time). The reduced coast time has been shown to improve implosion performance.²⁷ In this study, however, the extended inner cone propagation time will simply be used to drive a larger diameter, thicker capsule. The x-ray energy absorbed by the capsule is a very strong function of the capsule outer diameter, and increasing capsule scale is a strong lever enabling improved performance.

Figure 3(b) shows a 12% scaled-up capsule with inner and outer radii of 1022 and 1100 μm, respectively, and a total ablator thickness of 78 μm. This capsule will be used extensively in this study. As will be shown in Sec. VI, this is probably the largest capsule that can be driven in an I-Raum with the dimensions considered in this study, though larger versions are also under consideration for future experiments.

Figure 4 shows the laser pulse that is used for I-Raum simulations. Figure 4(a) shows the total laser power in TW, Fig. 4(b) is the cone-fraction (CF), which is the ratio of the inner cone power to the total pulse power. Figures 4(c) and 4(d) show the inner and outer cone laser powers/beam, respectively. The current maximum power/beam for the NIF laser is indicated with the dashed magenta line.

For all plots in Fig. 4, the pulse for shot N170601 is shown in black, while modified pulses of increasing duration for the I-Raum are shown in blue, green, and red. The blue pulse is slightly longer than N170601 at 7.6 vs. 7.2 ns. The green and red pulses are used to explore the effect of pulse length by increasing the pulse duration to 8.1 and 8.6 ns, respectively. The total pulse energies are all within the capabilities of the NIF laser²⁸ at 1.6, 1.8, and 2.0 MJ, respectively.

In Fig. 4(a), the first difference seen is that all pulses for the I-Raum are scaled in time by 12% to accommodate the larger capsule of Fig. 3(b). Several other aspects of the pulse, however, remain unchanged. The power in the early part of the pulse (the “foot”) is kept constant to avoid any issues with early-time window burn-through, melt of the HDC ablator during the first shock, etc. This removes uncertainties for future experiments, since the impact of this foot on the hohlraum and ablator has been well-characterized in previous shots.²² The peak laser power is also kept constant at 453 TW. This again minimizes changes from an experimentally tested condition. In order to enable the full use of the NIF laser, however, the cone fraction is clamped at 0.33 for the entire main pulse to keep both inner and outer pulses below the maximum allowable, as is clearly seen in Figs. 4(c) and 4(d). This is in contrast to the pulse of N170601, which had the inner beam power at the NIF limit. This presents a limitation to shot N170601 as will be discussed in Sec. V, where it is shown that the implosion symmetry was ∼20% oblate and thus would require more inner beam power to obtain a round implosion. That power is unavailable in the cylindrical hohlraum.

Figures 4(e) and 4(f) show the predicted radiation temperature driving the capsule and the energy absorbed by the capsule ablator. The peak Trad shown in Fig. 4(e) increases slightly from 291 to 296 eV going from N170601 to the 1.6 MJ I-Raum pulse. The reason for the slight increase for these two similar-energy pulses is the change from the “drooping” pulse²⁹ of N170601 to a constant peak power pulse. Further increases in the laser pulse length to 8.1 and 8.6 ns increase the peak Trad to 303 and 309 eV, respectively. Finally, Fig. 4(f) shows the capsule absorbed energy for each of the pulses of Figs. 4(a)–4(d). The absorbed energy increases significantly for all I-Raum pulses due to the increased capsule size. The significant increase in capsule absorbed energy with capsule size is in agreement with the expected theoretical scaling³⁰ of E_abs=10⁻² T_rad⁴ A_cap τ, where A_cap is the surface area of the capsule, and τ is the pulse length. For ratios of capsule radius (1100 μm/980 μm), T_rad [296 eV/291 eV, black to blue curves of Fig. 4(e)], and pulse duration (7.6 ns/7.2 ns), the theory predicts an increase of 1.42× from 166 kJ to 236 kJ, in excellent agreement with the simulated value of 232 kJ. As the pulse length increases further (green and red curves), note the abrupt increase in absorbed energy at late time (9.3 ns). This is due to alpha particle energy deposition, which is consistent with the increase in implosion yield seen in Table II below.

In this section, the effect of the I-Raum geometry on the Au bubble is quantified. Figure 5 shows a temporal sequence of the Au material boundaries in 1 ns intervals. In this figure, the boundaries in red are for the 980 μm outer radius capsule of Fig. 3(a) and the cylindrical hohlraum of N170601. The green contours are for the same sized capsule and same laser pulse, but in an I-Raum. The blue contours are for the 1100 μm outer radius capsule of Fig. 3(b) and the 8.6 ns, constant peak power laser pulse of Fig. 4(a), also in an I-Raum. At early time, the bubble can be seen emerging from the initial wall location in a similar fashion, though it remains at all times more recessed in the I-Raum geometry than in the cylinder. For the first 4 ns, the bubble continues to grow, and any difference between the two different sized capsules in the I-Raum is indistinguishable. Interestingly, at 4 ns, the full inner Au wall contour for the I-Raum is “nearly cylindrical,” with the more rapidly growing bubble portion of the wall at nearly the same radius as the inner-cone illuminated equatorial region of the hohlraum. For t > 4 ns, a small difference begins to be seen between the two different sized capsules in the I-Raum. The Au bubble in the I-Raum, which continues to be smaller at all times than in the cylinder, is seen to be further suppressed with the larger capsule. This is to be expected, as the increased capsule absorbed energy of the 1100 μm capsule generates increased ablation of the capsule material, which fills the hohlraum providing an increased back-pressure to the expanding bubble.

Figure 6 quantifies the differences in the Au bubble development in the different hohlraums by plotting the radius of the tip of the Au bubble, i.e., that point which reaches the smallest radius at any given time. For the same sized capsule and the same laser pulse (red and green), Fig. 6 shows that the Au bubble evolves with the same velocity in the cylinder and the I-Raum, and maintains the initial radial offset of 260 μm throughout the implosion. Over the first 4 ns, the bubble radial trajectory is seen to be nearly linear with a growth velocity of 250 μm/ns. At this velocity, the bubble originating from the recessed I-Raum pocket reaches the original cylinder radius at t ≈ 1 ns. As seen in Fig. 6, the bubble maintains this 1 ns delay for the I-Raum throughout the implosion.

With the larger capsule, however, as was seen in Fig. 5, the tip of the bubble penetrates slower as quantified in Fig. 6 (blue). The time for the bubble tip to reach r ≈ 1 mm, for example, has now been extended by 1.8 ns over that for the cylinder, effectively buying more time for inner beam propagation, as will be quantified later in this section. This is confirmed by looking at the t = 9 ns material contours in Fig. 5. In this plot, the material boundary is shown for the cylinder (red) and I-Raum with the smaller capsule (green) at t = 8 ns, while the boundary for the I-Raum with the 1100 μm capsule (blue) is shown 1 ns later at t = 9 ns. The inward penetration of the Au bubble of the blue curve even with an additional 1 ns of growth is still less than for the cylinder, in agreement with Fig. 6.

While Figs. 5 and 6 quantify the position of the Au bubble between the two hohlraum configurations, the quantitative impact of this difference on laser delivery remains to be assessed. Figures 7 (visually) and 8 (quantitatively) show where the laser energy is deposited. In Fig. 7, pairs of hohlraum material plots are shown for t = 2–7 ns. On the left of each pair is the cylinder, and on the right is the I-Raum. The Au material is plotted in yellow (or gold), the hohlraum fill gas is shown in blue, and both window and ablator materials are shown in gray, though they are easily distinguished by their spatial locations. Superposed on top of these material plots are the laser rays for a 23° beam colored by the laser intensity with white being 100% of the delivered laser intensity, and black being 10% intensity remaining.

Early in time, the inner cones propagate un-impeded to the hohlraum waist in both the cylinder and the I-Raum. At 4 ns, the bubble in the cylinder just begins to absorb laser energy with 1% of the laser being deposited. By 5 ns, the Au bubble in the cylinder now absorbs ∼10%, whereas the I-Raum bubble is just touching the laser cone and absorbing < 1% of the laser energy. By 6 ns, the percentages of laser energy absorbed by the bubble have increased to 40% in the cylinder and 10% in the I-Raum.

Finally, at 7 ns (close to the end of the laser pulse for the cylinder), the bubble now absorbs 82% of the inner cone energy in the cylinder, and still only 37% in the I-Raum. A new issue now begins to be observed in the I-Raum, however. Along with the improved inner beam propagation to the hohlraum waist, there appears to be increased laser absorption in the ablator plasma. This is quantified in Fig. 8, where the distribution of inner-cone (23° and 30°) laser energy deposition is partitioned between all of the materials as a function of time. In Fig. 8, the results for the cylinder are shown with dashed lines, and the results for the I-Raum are plotted with solid lines. Deposition in the Au wall is further partitioned to distinguish deposition at the hohlraum waist, defined as |Z| < 2 mm (black) vs. deposition in the Au bubble defined as |Z| > 2 mm (red). Laser energy deposition in the ablator plasma is shown in green. One can see that at early time (t < 5 ns), most of the inner-cone laser energy (70%–90%) is going where it was intended in both hohlraums, i.e. to the hohlraum waist. There is a little more laser energy from 0 to 2 ns extending to |Z| > 2 mm. This is not being absorbed by the Au bubble, but rather is simply inner cone energy propagation further into the recessed pocket of the I-Raum.

For t > 5 ns, the laser absorption in the growing Au bubble (red) increases rapidly, exceeding the amount of laser energy reaching the hohlraum waist at just before 6 ns in the cylinder and ∼6.7 ns in the I-Raum. At approximately the time at which the laser deposition at the waist and bubble are equal, one can see an increase in the absorption in the ablator plasma (green) as well. This is significantly increased in the I-Raum, likely resulting from the increased amount of ablated material from the larger capsule. This is due to the same effect that further suppressed the Au bubble, as was seen in Figs. 5 and 6, indicating that there is a down side to improved propagation: getting past the Au bubble means that there is more laser energy available to now interact with the ablator plasma, itself. Table I summarizes the laser deposition per material at 1 ns intervals for both the cylinder and the I-Raum.

The simulation of late-time implosion symmetry is a difficult problem, and the predictions should not be trusted unless they are experimentally verified. The approach taken here will be to use an experimentally-based model that comes close to matching the implosion symmetry for an existing shot, N170601. This same model will then be used for all I-Raum simulations.

Figures 9(a)–9(d) repeat the laser pulse from Fig. 4, but with an important modification. Using the requested laser pulse (black solid curves) in a simulation of N170601 results in a highly prolate (+80%) implosion as shown in Fig. 9(e). The data, by comparison, show an oblate implosion (−19%) as shown in Fig. 9(g). This disagreement is very large and suggests that the simulations may be under-predicting the impairment to the inner beam propagation. The experimental data would suggest that either the bubble is growing faster than predicted, or the absorption of laser energy by the bubble is greater than predicted. In an attempt to provide simulations that better reflect the observed data, the following procedure is used. The laser cone fraction is artificially ramped down to zero over a duration of 1 ns as seen with the black dashed line in Fig. 9(b). Figures 9(c) and 9(d) show the effect of this modification on the inner and outer cone power histories, where the inner-cone power ramps down to zero and the outer cone power increases strongly. This has the physical interpretation of the inner-cone beams being completely absorbed by the bubble and depositing their energy in a location that acts as a source of additional outer-cone energy. The timing of this cone-fraction change is further motivated by an improved agreement with additional experimental data.³¹ The resulting implosion symmetry using the modified laser pulse for N170601 (black dashed line) is shown in Fig. 9(f), where the implosion core is now slightly (-13%) oblate in greatly improved agreement with the experimental data of Fig. 9(g).

Based on this improved agreement with the data, this same model is now adopted to predict the implosion symmetry in the I-Raum, with one important difference. It was consistently observed in Figs. 5–8 that the bubble in the I-Raum simulations remains recessed in radius, or its penetration into the hohlraum is at all times delayed relative to that predicted for a cylindrical hohlraum. The cone-fraction truncation model, which gave improved agreement with the data of N170601, is therefore slightly modified to ramp the inner cone power to zero in the I-Raum 1 ns later than in the cylinder as shown in Figs. 9(b)–9(d). The predicted implosion symmetry based on this model is shown in Figs. 9(h)–9(j) for I-Raum laser pulses of total energy 1.6, 1.8, and 2.0 MJ, respectively. The implosion symmetry goes from slightly oblate [−13% in Fig. 9(f)] to slightly prolate [+19% in Fig. 9(h)] in going from a cylindrical hohlraum to an I-Raum at similar laser pulse length and energy. This seems quite reasonable, as every indication from the simulations is that the inner beam propagation should be improved in the I-Raum. Increasing the laser pulse length in Figs. 9(i) and 9(j) allows additional growth of the Au bubble, again further impeding inner-cone propagation, and resulting in an increasingly more oblate implosion.

Table II gives a summary of a wide range of predicted performance parameters for the implosions considered in this study. The implosions considered are cylindrical hohlraum shot N170601, which provides an experimentally benchmarked baseline, the three I-Raum simulations of increasing pulse length and total pulse energy, which have been extensively discussed, and in the final column an optimized I-Raum design. It is important to point out that the three I-Raum designs previously discussed are essentially untuned, i.e., no effort has gone into retuning the shock timing or symmetry to account for the drive changes resulting from the I-Raum geometry, as these tuning changes will need to be experimentally determined. The results in columns 2–4 give the performance of these untuned simulations. A number of design variations have been assessed such as changing the I-Raum pocket location, changing the inner and/or outer cone pointing, altering the foot pulse power and cone-fraction to improve shock timing, changing the hohlraum wall material from DU to Au, and further increasing the peak power, but none of these are included in the simulations of the I-Raums summarized in Table II. Again, the primary goal of this study is to compare the performance of the I-Raum vs. a cylinder with the minimal number of changes.

The values listed in the final column, by contrast, do make use of 2 small changes in an attempt to optimize implosion performance. In this simulation, the capsule inner radius was increased from 1022 μm as shown in Fig. 3(b) to 1050 μm, purely for practical reasons, i.e., this is a “standard” size mandrel that is currently being used to fabricate capsules for NIF implosions. Rather than keep the same ablator thickness, this design makes use of a slightly (4 μm) thinner ablator, 74 μm vs. the previous 78 μm. This has three beneficial effects. First, though not shown here, the shock timing in the I-Raum simulations discussed here is not tuned, with the merger of the first two shocks occurring 10–15 μm into the DT ice layer rather than at the ice-gas boundary. This is clearly a result of the slightly lower early-time drive in the 7% larger area I-Raum. Decreasing the ablator thickness allows the first shock to clear the ablator more quickly (Δt = 4 μm/25 μm/ns = 160 ps) resulting in improved shock timing. The second change is that with the increased outer radius of the capsule, more energy is absorbed, 252 vs. the previous 246 kJ in Fig. 4(f). This, together with the slightly thinner ablator, drives a faster implosion with fuel averaged implosion velocity increasing from 380 to 403 km/s. The result, as will be discussed, is a predicted increase in clean 2D yield from 1.7 × 10¹⁷ to 3.7 × 10¹⁷, which is just slightly over 1.0 MJ of energy.

The input parameters of Table II include the laser pulse total energy, peak power, and pulse length, the hohlraum wall material (all DU), and the capsule outer radius, which increases from 980 to 1100 to 1124 μm. The output parameters of the simulation include the implosion primary neutron yield, which initially decreases from 4.1 × 10¹⁶ (cylinder) to 2.5 × 10¹⁶ in the comparable energy I-Raum due primarily to the lower implosion velocity of 363 vs. 378 μm/ns when driving a more massive capsule. As the pulse energy increases to 1.8 and 2.0 MJ, the implosion velocity recovers to that of the cylinder, and the primary neutron yield increases to 8.4 × 10¹⁶ and 17.2 × 10¹⁶, respectively. As was noted earlier, further increasing the capsule outer radius to 1124 μm and thinning up the ablator by 4 μm increases the predicted yield by an additional factor of two, with no change to the laser drive. The coast time is seen to initially increase in the I-Raum, which has later bang-times, but recovers with the longer pulses to a value nearly half of that for the cylinder. The ablator mass remaining gives an indication of how much more these designs can be pushed. Even the highest energy I-Raum pulse with an 1100 μm outer radius capsule is predicted to have slightly more mass remaining that N170601. Pushing this to a slightly thinner capsule in the final column appears to be getting too thin to tolerate, and probably suggests that a limit is being reached in this regard. The final row of the column is the residual kinetic energy (RKE), which is the percentage of fuel kinetic energy at bang-time relative to that at peak implosion velocity.³² This parameter gives a good overall measure of the degree of tuning of the implosion, and reflects the need to fine tune the I-Raums in this study. Work is ongoing to refine these designs and bring the RKE below 5%.

This report has presented the design of a new shaped hohlraum designed specifically to reduce the impact on the late-time propagation of inner-cone laser beams caused by absorption in the radially inward expanding Au bubble. As compared to other approaches which employ increased gas fill or low-density foams, this alternate approach adds a recessed pocket to the hohlraum at the location where the outer cones hit the hohlraum wall. This recessed pocket displaces the bubble radially outward, reducing the inward penetration at all times throughout the implosion and increasing the time for inner beam propagation by approximately 1 ns. This increased laser propagation time allows one to drive a larger capsule, which absorbs more energy and is predicted to improve implosion performance by as much as a factor of 8 in neutron yield.

It bears restating that the I-Raum designs presented here are intended to be as close to an A/B comparison with an existing NIF shot N170601, and therefore have deliberately not yet been fine-tuned, which would be expected to increase the performance further. Future work is ongoing to design an initial series of tuning experiments to establish the initial shock timing, symmetry, laser backscatter, etc. These experiments will be essential for quantifying the potential benefits of this design.

This work was performed under the auspices of the Lawrence Livermore National Security, LLC (LLNS), under Contract No. DE-AC52-07NA27344.