Current indirect drive implosion experiments on the National Ignition Facility (NIF) [Moses et al., Phys. Plasmas 16, 041006 (2009)] are believed to be strongly impacted by long wavelength perturbations driven by asymmetries in the hohlraum x-ray flux. To address this perturbation source, active efforts are underway to develop modified hohlraum designs with reduced asymmetry imprint. An alternative strategy, however, is to modify the capsule design to be more resilient to a given amount of hohlraum asymmetry. In particular, the capsule may be deliberately misshaped, or “shimmed,” so as to counteract the expected asymmetries from the hohlraum. Here, the efficacy of capsule shimming to correct the asymmetries in two recent NIF implosion experiments is assessed using two-dimensional radiation hydrodynamics simulations. Despite the highly time-dependent character of the asymmetries and the high convergence ratios of these implosions, simulations suggest that shims could be highly effective at counteracting current asymmetries and result in factors of a few enhancements in neutron yields. For higher compression designs, the yield improvement could be even greater.

Indirect drive Inertial Confinement Fusion (ICF) implosions1,2 on the National Ignition Facility (NIF)3 have so far been limited to neutron yields below 1016. These yields are significantly less than the goal of fusion ignition and the yields of 1018 neutrons projected in early design studies.4 Post-shot modeling and analysis of the experimental data from a number of implosion experiments suggest that two main factors are responsible for the current ceiling in neutron yield:5,6 a very large perturbation seeded by the capsule support tent7,8—subsequently amplified by ablation front Rayleigh-Taylor growth—and large, long-wavelength perturbations driven by asymmetries in the radiation field of the hohlraum.9,10 Additional effects, such as surface roughness, the capsule fill tube, and hot electron pre-heat, likely also contribute, but these appear to be secondary effects according to current understanding.

Based on this assessment, intensive efforts are now underway to mitigate these two largest degradation sources. To reduce the impact of the tent, various alternative capsule support mechanisms are being explored both in simulation and experimentally. As for the low-mode perturbations driven by the hohlraum asymmetries, extensive efforts are underway to produce a more symmetric and controllable hohlraum irradiation environment. Efforts to control and ultimately “tune” the low-mode asymmetry have been underway since the beginning of implosion experiments on NIF11,12—and before13–15—but to-date have proven challenging. Establishing good low-mode symmetry control has been especially challenging give the poor predictability of hohlraum performance in simulations and that these simulations generally require large ad hoc “multipliers” on laser powers, laser cone fractions, or even laser frequency to match experimental data.16 In this sense, hohlraum modeling and design has proven to be a largely empirical exercise of trial, error, and iteration. Some progress has recently been made in demonstrating control and predictability for short pulse length, low convergence implosions,17,18 but these are far from the longer pulse length, higher convergence implosions necessary to achieve ignition at the NIF energy scale.

In considering the problem of symmetry control in NIF implosions, it is important to recognize that this is not exclusively a problem of hohlraum design. Clearly, modifications to the capsule design can also be made to lessen the symmetry requirements from the hohlraum radiation environment—or exacerbate them. Said another way, options exist for changing the capsule design so as to make the implosion more or less robust to a given hohlraum asymmetry environment. Reducing the capsule convergence ratio or increasing the hohlraum case-to-capsule ratio to increase the geometric smoothing of the radiation impinging on the capsule19 are obvious examples of this and have already been exploited in recent experiments.20 These modifications reduce the performance or robustness of the implosion in other ways, however, and more subtle design modifications that can gain resilience to asymmetries without sacrificing convergence need to be found. An encouraging example of such a design modification, albeit in a somewhat different context, is the recent demonstration of improved stability in NIF implosions using higher picket drives that do not sacrifice compression.21–26 This simple design modification was shown experimentally to reach the same high compression as low foot implosion experiments from the National Ignition Campaign (NIC)27 but with stability properties, and hence neutron yields, similar to those of the more recent high foot campaign.28 While this improvement was gained by stabilizing short wavelength instability growth, these results beg the question of whether similar modifications to the pulse shape, capsule dimensions, or other capsule design parameters could also confer robustness to long wavelength asymmetries. While these types of implosion design modifications are currently under study, another more obvious possibility is simply to misshape the capsule deliberately so as to counteract the expected asymmetries of the hohlraum. This technique, generally referred to as “shimming,” is the subject of this study.

Shimming as a means of controlling the low-mode asymmetry of ICF implosions has been discussed for several decades. As examples, experiments at the Z Facility29 demonstrated the control of Legendre modes P2 and P4 at a convergence of ∼1.5 using a shimmed gold overcoat on a plastic capsule.30 Z-pinch-driven implosion designs were also described at that time using an azimuthally varying dopant concentration to shim out intrinsic radiation asymmetries.31 Shimming was subsequently proposed for symmetrizing implosions in the polar direct drive configuration on NIF.32 More recently, experiments using gas-filled plastic capsules at the OMEGA Laser Facility33 have shown both the efficacy of shimming to modify the imploded core shape34 and to improve substantially the implosion neutron yield compared to un-shimmed implosions.35 While these results are encouraging, the effectiveness of shimming in ignition relevant implosions for NIF has been questioned on the grounds of the very high convergence of NIF ignition implosions, as well as the highly dynamic, time-dependent flux asymmetries that are expected in NIF hohlraums driven by long, multi-step laser pulses. The fabrication difficulties associated with manufacturing precisely shimmed capsules and then aligning them correctly within a hohlraum are additional, oft-cited challenges.

The purpose of this paper is to counter these criticisms with simulation results specific to the NIF regime. Here, two specific implosion experiments recently shot on NIF are considered, and the efficacy of capsule shimming to improve their performance is assessed. This is an entirely simulation-based study, but it is grounded as much as possible in the best post-shot models for specific NIF experiments, models that reproduce fairly well the experimental observables from these specific shots. In this sense, the predicted impact of capsule shimming is the best projection that can currently be made short of an experimental test. Despite the challenges mentioned above, it will be shown that—in simulations—shims are remarkably effective at mitigating the hohlraum asymmetries that are believed to be impacting current NIF implosions. These results argue strongly for the beginning of an experimental campaign to test their effectiveness on NIF.

In the broader context of controlling low-mode asymmetries in NIF implosions, it is important to bear in mind that shimming is only one tool among many. Cross-beam energy transfer;36 changes to the hohlraum length, diameter, and laser entrance hole size; changes to the hohlraum gas fill;17 and increasing the case-to-capsule ratio20 are all techniques that have been tried. Shims are simply another addition to this list and should not be looked to as the solution to the problem of hohlraum asymmetries, merely part of a larger solution. In combination with the other techniques, however, shims offer the prospect of significantly expanding the hohlraum design space so as to reach a more optimal implosion within the energy constrains of NIF. For example, as shown below, shims are highly effective at controlling P4 asymmetries. If a shim can be relied on to compensate for P4, then a shorter hohlraum can be used to allow easier passage of the laser beams deep into the hohlraum to give better control of P2 asymmetries. A shorter hohlraum would also be overall more energetically efficient and a more optimal target design would result. It should also be noted that the current lack of predictability of the hohlraum performance particularly argues for exploiting the capsule-based remedy of shimming, as opposed to the less predictable approaches of changing the hohlraum size, laser cone fractions, etc.

The principal results of this paper are the following. For two recent NIF experiments, N140520, a representative high foot implosion,37 and N141123, a low foot implosion but with increased picket energy to have ablation front stability characteristics closer to the high foot,24 P2 and P4 shims are found to be highly effective at mitigating hohlraum asymmetries. In both cases, P4 shims can almost totally compensate for the expected time-dependent asymmetries and nearly regain the simulated symmetric yield. The P2 asymmetries are projected to be a smaller effect for both of these implosions, but they can also be compensated by using the appropriate shims. Even when the other sources of yield degradation, namely, the capsule support tent and surface roughness, are included in the simulations, shims are still found to have a noticeable effect on the performance and can increase the yield by factors of a few. If the perturbation from the tent can also be mitigated by developing some other, less perturbing support mechanism, then the simulations suggest that order of magnitude improvements in yields are possible when shims are used. This large increase in yield, of course, reflects the rapidly bootstrapping effect of α-particle self-heating and represents a considerable extrapolation beyond the current experimental database. These latter results are hence highly uncertain; however, they are also highly encouraging for the prospect of improved performance with shims and therefore motivate an experimental campaign to test this method for asymmetry control on NIF.

This paper is organized as follows. Sec. II discusses some of the various types of shims that might be considered for current NIF capsules. Sec. III then describes simulation results for shimming the high foot implosion N140520, and Sec. IV describes a similar simulation study for shimming the higher convergence implosion N141123. Sec. V then concludes and discusses possible experimental plans for testing the effect of shims on NIF.

At least three types of shimming can be imagined for the ICF capsules currently shot on NIF. These are illustrated in Fig. 1 and reflect the fact that the capsule radial build consists broadly of three layers: an inner deuterium-tritium (DT) ice layer (shown in light blue), inner plastic (CH) ablator layers doped with silicon (shown in green and yellow), and an outer un-doped ablator layer (shown in beige). The three types of shims shown in the three panels in Fig. 1 are a modulation at the outer surface of the ablator (left), a modulation in the silicon dopant layer thickness (middle), and a modulation in the ice-ablator interface (right). In the case shown, a P2 shim is applied, although the same can be imagined for any sufficiently low mode number. As suggested by the figure, combining these three different shim types can be imagined to offer some amount of time-dependent symmetry control. That is, as the various shocks, rarefactions, and the ablation front propagate through the capsule, they encounter each shimmed layer at different times. By properly setting the phasing and amplitude of each shim, a discrete approximation of the antidote for a dynamic asymmetry might be possible. In the cases examined below, it will be found that a single shim type for a single mode number appears to be adequate; however, for other asymmetry cases, it can be imagined that combining these sequenced shims could be helpful.

FIG. 1.

Three possible shim types compatible with current CH NIF target designs. In each panel, the capsule radial build is “rolled out” and plotted in radius versus polar angle. The left most panel shows an example of an outer P2 shim, the middle panel shows an example of a shim in the silicon dopant layers, and the right panel shows an example of an inner shim at the DT ice-ablator boundary.

FIG. 1.

Three possible shim types compatible with current CH NIF target designs. In each panel, the capsule radial build is “rolled out” and plotted in radius versus polar angle. The left most panel shows an example of an outer P2 shim, the middle panel shows an example of a shim in the silicon dopant layers, and the right panel shows an example of an inner shim at the DT ice-ablator boundary.

Close modal

Note that it may also be possible to shim the DT ice layer. Differential heating around the hohlraum is currently used to control the symmetry of the DT-ice gas interface prior to shot time on NIF. It should be feasible therefore to apply a P2 or P4 shim to the ice layer using this same set of heating coils. However, given the significant density difference between the DT ice and the CH ablator, a given radial amplitude shim in the CH is roughly four times as effective as an equivalent amplitude in the DT ice. Hence, quite large amplitudes will likely be required for deliberate “ice shimming” and will complicate the cryogenic layering process and layer characterization. For this reason, ice shims are not considered further here.

Regarding target fabrication challenges, each of these shim types should be practical to fabricate either by machining the capsule outer surface (for the case of an outer shim), machining the dopant layer midway through capsule layering and then continuing the layering and perhaps machining smooth the outer surface (for a dopant shim), or layering the capsule on a pre-machined mandrel (for an inner shim). Of course, for all shim types, alignment of the capsule in the hohlraum is crucial, and this may be particularly challenging for the inner and dopant shim cases. Radiography of the capsule and perhaps adding fiducial markers to the capsule surface are conceivable ways to address these alignment challenges. The question of whether short wavelength roughness will be enhanced by any machining of the capsule is also an important consideration, but this can only be addressed by manufacturing actual prototypes and characterizing any degradation of the surface quality. Whether a shim in the ablator will also imprint an asymmetry into the ice layer is another consideration (particularly for an inner ablator shim), but given the differential heating capability already mentioned for NIF hohlraums, it seems likely that this effect can be controlled. Clearly, some target fabrication development is required, but fabrication should be within feasible limits. The success of recent OMEGA experiments using shims34,35 is clear proof of this.

Additionally, it should be noted that shimming techniques are not exclusive to the CH ablator targets discussed here. While shimming high density carbon ablators38 seems challenging due to the necessity of laser cutting, shimming beryllium ablators should be straightforward by conventional machining. Indeed, beryllium ablator designs,39 with their better ablation front stability characteristics compared to CH,40 may be better candidates for shimming, given that any high frequency surface roughness introduced by machining the surface will be less prone to grow in a beryllium implosion than in a CH implosion.

The starting point for this study was the two-dimensional (2D) post-shot capsule-only simulation of the high foot implosion N140520. This implosion used a 1.8 MJ/390 TW laser pulse in a gold-lined depleted uranium hohlraum filled with 1.6 mg/cm3 of helium gas. The post-shot simulation for this implosion was run using HYDRA41 and followed a similar methodology to the simulations described in Ref. 5, except that in this case a 2D simulation was used instead of a 3D simulation. With current computer resources, it is impossible to run the multiple 3D simulations that would be necessary for the parameter scans presented below. For this reason, the significant simplification of 2D axi-symmetry must be assumed and some loss of fidelity accepted. Given the axisymmetric shims considered here, however, the essential trends and basic results can be expected to be similar in 2D simulations as in more complete 3D simulations.

Table I gives a comparison of several simulated observables from the 2D simulation against the measured values. With the exception of the burn-weighted ion temperature, the simulated observables match the data to within 10%–20%, even for such nonlinear quantities as the neutron yield. As shown in Ref. 5, 3D simulations generally give an even closer match to the data than 2D; however, in this case, the 2D results are sufficiently close to the observed values to have confidence that the results below are a reasonable representation of the experiment.

TABLE I.

Simulated and measured performance for NIF shot N140520. Here, the x-ray self-emission shape is characterized in terms of the customary Legendre moments Pn of the 17% emission contour.42 The primary neutron image (PNI)43 size is similarly given in terms of the Legendre moment P0. Tion refers to the burn-weighted temperature inferred from the width of the primary emitted neutron spectrum, and the down-scattered ratio (DSR) is the ratio of the 10–12 MeV to 13–15 MeV components of the emitted neutron spectrum.44 Y13–15 MeV refers to the primary neutron yield in the energy range of 13–15 MeV.

2D simulationExperiment
Bang time (ns) 15.88 15.96 ± 0.03 
Burn width (ps) 120 145 ± 30 
X-ray P0 (μm) 30.7 27.1 ± 1.1 
X-ray P2/P0 −0.16 −0.16 ± 0.04 
X-ray P4/P0 − 0.06 0.01 ± 0.04 
X-ray M0 (μm) 40.0 35.7 ± 2.1 
PNI P0 (μm) 31.7 27.6 ± 4.0 
Tion (keV) 4.3 5.5 ± 0.2 
DSR (%) 4.6 4.1 ± 0.2 
Y13–15 MeV 9.8 × 1015 7.6 ± 0.1 × 1015 
2D simulationExperiment
Bang time (ns) 15.88 15.96 ± 0.03 
Burn width (ps) 120 145 ± 30 
X-ray P0 (μm) 30.7 27.1 ± 1.1 
X-ray P2/P0 −0.16 −0.16 ± 0.04 
X-ray P4/P0 − 0.06 0.01 ± 0.04 
X-ray M0 (μm) 40.0 35.7 ± 2.1 
PNI P0 (μm) 31.7 27.6 ± 4.0 
Tion (keV) 4.3 5.5 ± 0.2 
DSR (%) 4.6 4.1 ± 0.2 
Y13–15 MeV 9.8 × 1015 7.6 ± 0.1 × 1015 

The state of the imploded DT fuel at the time of peak neutron production (bang time) is shown in Fig. 2. The axis of symmetry is horizontal in this figure with the upper half plane showing the material density distribution and the lower half plane showing the material regions. Here, dark and light blue indicate the DT fuel (broken into what was initially DT gas versus DT ice), and the greens indicate the various doped ablator layers. As is characteristic of implosions on NIF (high foot as well as low foot5,6), a large low-mode asymmetry, driven by asymmetries in the hohlraum radiation field, is evident in the imploded core. Also evident are the aneurisms in the shell at roughly 45° in polar angle due to the defect caused by the capsule support tent.7,8

FIG. 2.

Bang time configuration from the 2D post-shot simulation of N140520. The symmetry axis is horizontal, and the upper half plane shows the material density, while the lower half plane shows the material region. Dark and light blue correspond to the regions that were initially DT gas and DT ice, and the green regions show the various doped ablator layers.

FIG. 2.

Bang time configuration from the 2D post-shot simulation of N140520. The symmetry axis is horizontal, and the upper half plane shows the material density, while the lower half plane shows the material region. Dark and light blue correspond to the regions that were initially DT gas and DT ice, and the green regions show the various doped ablator layers.

Close modal

Obviously, essential ingredients in this simulation are the flux asymmetries imprinted on the capsule from the hohlraum. The two lowest even modes (P2 and P4) used in this simulation are shown as functions of time in Fig. 3 along with the radiation temperature for reference. These asymmetries are extracted as moments of the hohlraum radiation flux in 2D integrated (hohlraum and capsule) simulations as described in Ref. 6. Note that these hohlraum simulations are empirically tuned so that simulated diagnostic signatures match the measured values in terms of the implosion timing, velocity, and low-mode shape. That is, the laser power levels in the simulation and the effective laser cone fractions are adjusted as a function of time to force agreement with the VISAR,45 1D ConA,46 2D ConA,47 and hot spot x-ray self-emission data.42 In this sense, the flux asymmetries shown in Fig. 3 represent the best current understanding of the flux asymmetries for this shot but are not predicted from first principles.

FIG. 3.

Flux asymmetries used in the post-shot simulation of N140520. The black curve shows the P2/P0 flux asymmetry as a function of time and the right curve shows the analogous P4/P0 as a function of time. For reference, the lower black curve shows the symmetric hohlraum radiation temperature versus time with the scale on the right. Note that while the P2 asymmetry is dominantly positive, the P4 asymmetry is dominantly negative, especially in the peak of the x-ray drive.

FIG. 3.

Flux asymmetries used in the post-shot simulation of N140520. The black curve shows the P2/P0 flux asymmetry as a function of time and the right curve shows the analogous P4/P0 as a function of time. For reference, the lower black curve shows the symmetric hohlraum radiation temperature versus time with the scale on the right. Note that while the P2 asymmetry is dominantly positive, the P4 asymmetry is dominantly negative, especially in the peak of the x-ray drive.

Close modal

On the other hand, the presence of the capsule support tent, an effect not included in the low-resolution hohlraum simulations,6 is known to modify the hot spot x-ray self-emission.5 The fingers of cold, dense DT penetrating the hot spot in Fig. 2 are apparent, and in simulations, these result in a synthetic hot spot self-emission image that is ∼10% more oblate than if the tent were not included. Since the hohlraum simulations were empirically tuned to match this self-emission shape in the absence of the tent, they can then be expected to exaggerate the late-time P2 flux asymmetry compared to experiment and in fact do not match the observed hot spot symmetry when the tent is included. For this reason, the P2/P0 asymmetry shown in Fig. 3, and used in the capsule simulations described here, has been reduced in the peak of the laser pulse (∼13.5–15.5 ns) relative to the original hohlraum asymmetry to regain agreement with the measured self-emission when the tent is included. The early-time portion of the asymmetries that are constrained by VISAR and ConA data, and are unaffected by the tent, are left unchanged.

Two points deserve emphasis with respect to Fig. 3. First, as described, the flux asymmetries shown in Fig. 3 are inferred from simulation and cannot be directly measured. While the simulations have been tuned to force agreement with various asymmetry diagnostic signatures, in particular, VISAR and 2D ConA data, and these data are quite constraining, the asymmetries shown in Fig. 3 are not necessarily unique. Given the experimental error bars and the temporal gaps between various diagnostic signatures, there remains considerable uncertainty in the asymmetries shown in Fig. 3. Improving the understanding of these asymmetries and assessing the impact of the remaining uncertainties are in progress, but the incomplete state of current knowledge must be recognized.

Second, the asymmetries in Fig. 3 are visibly very dynamic in time, swinging from positive to negative at several points in the implosion. This might appear to suggest that a single, “static” shim (e.g., a given amplitude modulation at the ablator surface at the start of the implosion) would be incapable of counteracting the very dynamic asymmetries that are impacting the capsule. As discussed further below, the simulations suggest that this is not the case and that “simple” shims are remarkably effective, even for the highly variable asymmetries shown in Fig. 3. This effectiveness appears to be due to the fact that the perturbations caused by the flux asymmetries are dominantly radial in nature with a noticeable azimuthal component arising only very late in the implosion. Similar to the methodology described in Ref. 35, each azimuthal sector of the implosion may then be thought of as a separate 1D implosion driven with a slightly different time-dependent x-ray flux and only weakly coupled to its neighboring elements. Counteracting the excess or deficit in flux on a given azimuthal sector of the capsule then merely amounts to adding or subtracting mass from that sector so that the final velocity of that sector is aligned with the average velocity of the shell. In this sense, only the time-averaged amount of asymmetry on a given slice is important and not the details of its variation in time. With this in mind, it might additionally be expected that the uncertainties between the actual asymmetries present in experiment (which cannot currently be measured) and the simulated asymmetries shown in Fig. 3 would result only in a shift in the amplitude or phase of the shim necessary to counteract the real asymmetry. The general efficacy of the shim, however, can be expected to hold, and it is only the particular shim amplitude and phase that must be tuned experimentally.

The individual effects of the P2 and P4 asymmetries from Fig. 3 are shown in Fig. 4. In the left panel, only the P2 hohlraum asymmetry is included, and in the right panel, only the P4 asymmetry is included. The P4 perturbation is visibly much larger than the P2 perturbation in this implosion, and this is reflected in the relative neutron yields in these simulations. While the P2-only simulation has a yield of 2.2 × 1017, within a factor of two of the symmetric yield of 4.5 × 1017, the P4-only simulation has an order of magnitude lower yield of 2.8 × 1016.

FIG. 4.

Effect of P2 and P4 asymmetries in isolation from the post-shot simulation of N140520. The left panel shows the effect of the P2 hohlraum asymmetry, and the right panel the effect of the P4 asymmetry. Both cases are shown at their respective bang times. The reduction in neutron yield is roughly a factor of two compared to symmetric for the P2 asymmetry but nearly a factor of twenty from the P4 asymmetry.

FIG. 4.

Effect of P2 and P4 asymmetries in isolation from the post-shot simulation of N140520. The left panel shows the effect of the P2 hohlraum asymmetry, and the right panel the effect of the P4 asymmetry. Both cases are shown at their respective bang times. The reduction in neutron yield is roughly a factor of two compared to symmetric for the P2 asymmetry but nearly a factor of twenty from the P4 asymmetry.

Close modal

With this disparity in impact between P2 and P4 in mind, Fig. 5 shows the simulated effect of an outer P4 shim for this implosion with the P4 asymmetry from Fig. 3 as the only perturbation source. The horizontal axis corresponds to the shim amplitude in microns, and the vertical axis gives the simulated total neutron yield. As shown by the red symbols, a P4 shim of –2.5 μm amplitude results in a substantial increase in yield (∼15×) and manages to recover ∼80% of the symmetric yield shown by the dashed horizontal line. The two insets in the figure illustrate the substantial symmetrizing effect of the shim at bang time. Note that, although the yields shown in the plot include the effect of α-particle deposition, the shimmed inset shows a simulation with α-particle deposition switched off. This eliminates the artificial smoothing that occurs in such high yield simulations due to α-particle deposition, and hence gives a truer picture of the purely hydrodynamic symmetrization due to the shim.

FIG. 5.

Effect of an outer P4 shim in correcting the P4 asymmetry for N140520. The horizontal axis shows shim amplitude and the vertical axis shows total neutron yield. The insets show the resulting implosion shapes at their respective bang times. Note that, in order to remove the self-smoothing of the hot spot that accompanies α-particle self-heating, the shimmed inset shows a simulation with α-particle deposition switched off even thought the vertical axis gives the deposition-on yield. With a –2.5 μm P4 shim, nearly 80% of the symmetric yield of 4.5 × 1017 can be recovered.

FIG. 5.

Effect of an outer P4 shim in correcting the P4 asymmetry for N140520. The horizontal axis shows shim amplitude and the vertical axis shows total neutron yield. The insets show the resulting implosion shapes at their respective bang times. Note that, in order to remove the self-smoothing of the hot spot that accompanies α-particle self-heating, the shimmed inset shows a simulation with α-particle deposition switched off even thought the vertical axis gives the deposition-on yield. With a –2.5 μm P4 shim, nearly 80% of the symmetric yield of 4.5 × 1017 can be recovered.

Close modal

To address the residual degradation due to the P2 asymmetry, Fig. 6 shows an analogous plot of total yield versus shim amplitude for both an outer P2 shim and a dopant shim. Here, the only perturbation is the P2 flux asymmetry from Fig. 3 that results in roughly a factor of two reduction in neutron yield. As shown by the blue symbols, the outer shim is relatively ineffective for this P2 asymmetry; however, the dopant shim, as shown by the green symbols, is highly effective and recovers greater than 90% of the symmetric yield. The insets again emphasize the symmetrizing effect of the shims. It is interesting that the appropriate shim to correct the P2 asymmetry is different both in its radial location in the capsule as well as its sign when compared to the appropriate P4 shim from Fig. 5. This appears to be due to the different time dependence of the P2 and P4 asymmetries shown in Fig. 3. That is, while the P2 asymmetry is dominantly positive, especially at the peak of the x-ray drive, the P4 asymmetry is dominantly negative and remains negative through the peak. This large positive P2 asymmetry at the peak of the drive apparently requires an offsetting asymmetry in the late-time ablation pressure that can be affected by the positive P2 shim in the dopant layer. The predominantly negative P4 asymmetry on the other hand requires a negative P4 shim.

FIG. 6.

Effect of P2 outer and dopant shims in correcting the P2 asymmetry for N140520. Like Fig. 5, the horizontal axis shows the shim amplitude and the vertical axis the total neutron yield. The blue curve shows the effect of an outer P2 shim, and the green curve shows the effect of a dopant shim. Also as in Fig. 5, the insets showing the shimmed cases are from simulations without α-particle self-heating to avoid the self-smoothing of the hot spot with α-particle self-heating included. While the outer shim is relatively ineffective at correcting the asymmetry in this case, a 7.5 μm dopant shim can recover nearly the symmetric yield.

FIG. 6.

Effect of P2 outer and dopant shims in correcting the P2 asymmetry for N140520. Like Fig. 5, the horizontal axis shows the shim amplitude and the vertical axis the total neutron yield. The blue curve shows the effect of an outer P2 shim, and the green curve shows the effect of a dopant shim. Also as in Fig. 5, the insets showing the shimmed cases are from simulations without α-particle self-heating to avoid the self-smoothing of the hot spot with α-particle self-heating included. While the outer shim is relatively ineffective at correcting the asymmetry in this case, a 7.5 μm dopant shim can recover nearly the symmetric yield.

Close modal

Figs. 5 and 6 have shown the substantial effectiveness of shims in correcting the individual P2 and P4 perturbations in the simulation of N140520. As shown in Fig. 2, however, there are other large perturbation sources present in this implosion, notably the capsule support tent and the capsule surface roughness. With regard to the efficacy of shims in experiment, the question then arises of whether the positive effect of the shims shown in Figs. 5 and 6 will still be apparent when all of the other perturbation sources are present.

Fig. 7 shows how these multiple perturbation sources add together. Like Figs. 5 and 6, the horizontal axis in Fig. 7 shows shim amplitude, and the vertical axis shows neutron yield. The blue dots and associated insets show the results of individual simulations with varying shim amplitude. The nominal simulation, as illustrated in Fig. 2, corresponds to the purple dot and inset at a shim amplitude of 0.0 μm and a neutron yield of 9.8 × 1015. As shown by the purple dot at a shim amplitude of –2.5 μm, adding an outer P4 shim to this implosion results in a three-fold improvement in the neutron yield to 3.1 × 1016 even including all perturbations: Evidently, the effect of the shim should still be visible even in the presence of all perturbation sources. For comparison, the lower horizontal dashed line shows the simulated yield when no hohlraum flux asymmetries are included, and the capsule defects (tent, surface roughness, etc.) are the only perturbation sources. That is, given that the simulated yield in this case is 6.0 × 1016, the P4 shim alone has effectively recovered half of the maximum possible yield in the case where there are no hohlraum asymmetries at all.

FIG. 7.

Effect of P2 and P4 shims in the presence of all perturbations for N140520. The horizontal and vertical axes show shim amplitude and neutron yield. The nominal post-shot simulation of N140520 is represented by the purple point and inset at 0.0 μm amplitude and a yield of 9.8 × 1015. Adding a –2.5 μm P4 shim, removing the tent perturbation and then adding a 7.5 μm P2 dopant shim result in successive yield improvements of 3×, 6×, and 1.5×, respectively. With all three improvements, the simulated yield increases to 3.6 × 1017, within 80% of the symmetric yield shown by the dashed horizontal line.

FIG. 7.

Effect of P2 and P4 shims in the presence of all perturbations for N140520. The horizontal and vertical axes show shim amplitude and neutron yield. The nominal post-shot simulation of N140520 is represented by the purple point and inset at 0.0 μm amplitude and a yield of 9.8 × 1015. Adding a –2.5 μm P4 shim, removing the tent perturbation and then adding a 7.5 μm P2 dopant shim result in successive yield improvements of 3×, 6×, and 1.5×, respectively. With all three improvements, the simulated yield increases to 3.6 × 1017, within 80% of the symmetric yield shown by the dashed horizontal line.

Close modal

As evident from the inset for the P4 shimmed case, the tent perturbation is now the leading distortion in this implosion. As noted in Sec. I, active efforts are underway to develop an alternative, less perturbing mounting system for the capsule. While the best mounting alternative remains to be identified, there are several promising options that appear to reduce substantially, if not completely eliminate, the imprint from the tent. As an upper bound on the effect of replacing the tent, the shimmed simulation was rerun without the tent perturbation. The result is shown as the purple dot at –2.5 μm and a yield of 2.3 × 1017. That is, removing the tent perturbation results in a further factor of six improvement in yield over the factor of three improvement already found with the shim alone and amounts to a total yield increase of nearly a factor of twenty. Of course, whatever substitute mounting mechanism is found to replace the tent will not be perfectly non-perturbative, so these results are an upper bound. They are nonetheless encouraging that substantial progress should be possible if these two improvements are combined. Finally, if a 7.5 μm P2 dopant shim is added to the P4 shim, again without the tent, another 1.5× improvement in yield is predicted to 3.6 × 1017. Note that this is again within 80% of the symmetric yield of 4.5 × 1017.

The results described in Sec. II are encouraging that significant improvements in yield are possible by applying shims to current NIF implosions, and even greater improvements are possible when shims are used in combination with some future, less perturbing capsule mounting technique. The high foot implosion N140520 used as an example, however, is fundamentally limited in that its relatively high fuel adiabat limits the maximum possible yield (in the absence of any perturbations) to ∼1 MJ. While this is at the threshold of ignition, this performance level remains below the multi-megajoule yields that were the goal of early NIF implosion designs.4 This begs the question of whether the effectiveness of shims found for N140520 can be extended to other, more ignition relevant implosion designs.

NIF shot N141123 represents such a design that aimed to combine the high compression of the low foot implosions shot during the NIC with the better ablation front stability of subsequent high foot implosions.21–26 When tested experimentally, this design outperformed all NIC experiments with a yield improvement of 3–10× compared to comparable low foot implosions and an absolute yield in the high foot range. Importantly, this was also accomplished at the same compression as other low foot shots, that is, with an areal density ∼50% higher than that of high foot experiments. Note, however, that this shot was at a lower laser power and energy than N140520 and used only 1.6 MJ/340 TW.

Like the post-shot simulation used as the starting point for the shimmed simulations of N140520, the results of a similar 2D post-shot simulation for N141123 are summarized in Table II. The level of agreement between simulation and experiment is qualitatively similar to that shown in Table I, albeit that the yield is over-predicted by a factor of three in this case. This could be due to the larger distortions present in this higher convergence implosion that require a properly 3D simulation for adequate modeling,5 or due to the larger perturbation from the support tent that could be reduced by an even more stable version of this design.24 Nevertheless, this simulation is the current best 2D model that is available for this implosion and is the anchor point for this study.

TABLE II.

Simulated and measured performance for NIF shot N141123. See Table I caption for an explanation of the quantities listed.

2D simulationExperiment
Bang time (ns) 19.86 19.81 ± 0.02 
Burn width (ps) 100 108 ± 13 
X-ray P0 (μm) 20.0 23.5 ± 1.9 
X-ray P2/P0 −0.03 −0.03 ± 0.05 
X-ray P4/P0 −0.06 0.06 ± 0.03 
X-ray M0 (μm) 21.2 26.1 ± 1.3 
PNI P0 (μm) 26.5 25.7 ± 0.1 
Tion (keV) 4.1 3.4 ± 0.2 
DSR (%) 6.2 5.5 ± 0.2 
Y13–15 MeV 3.3 × 1015 1.1 ± 0.01 × 1015 
2D simulationExperiment
Bang time (ns) 19.86 19.81 ± 0.02 
Burn width (ps) 100 108 ± 13 
X-ray P0 (μm) 20.0 23.5 ± 1.9 
X-ray P2/P0 −0.03 −0.03 ± 0.05 
X-ray P4/P0 −0.06 0.06 ± 0.03 
X-ray M0 (μm) 21.2 26.1 ± 1.3 
PNI P0 (μm) 26.5 25.7 ± 0.1 
Tion (keV) 4.1 3.4 ± 0.2 
DSR (%) 6.2 5.5 ± 0.2 
Y13–15 MeV 3.3 × 1015 1.1 ± 0.01 × 1015 

Analogous to Figs. 5–7, Fig. 8 summarizes the effectiveness of P2 and P4 shims for N141123. As shown by the red points, an appropriate P4 outer shim can recover essentially all of the symmetric yield of 5.0 × 1018 for this implosion when P4 is the only perturbation source. Likewise, the green curve shows that a dopant P2 shim can recover more than half of the symmetric yield in the presence of only the P2 asymmetry. In this case, as shown by the blue curve, a similar effectiveness is also found with an outer P2 shim. Finally, simulation results including all perturbation sources are shown by the purple dots and associated insets. Adding a –3.0 μm P4 outer shim in the presence of all perturbations results in a yield improvement of 4× from 3.3 × 1015 to 1.4 × 1016. Rerunning this simulation with the tent perturbation removed results in a further 3× improvement in yield to 4.0 × 1016. Finally, increasing the laser power and energy in the simulation to 420 TW/1.8 MJ, to be comparable to the power and energy of N140520, boosts the yield by another two orders of magnitude to 4.1 × 1018 and illustrates the rapid bootstrapping effect of α-particle self-heating once the confinement is high enough. Clearly, this sequence of improvements represents a considerable extrapolation from the original experimental result for N141123 and is therefore correspondingly uncertain. That the performance of this implosion could be substantially improved by shimming is nonetheless clear. It is also notable that this sequence of improvements brings the projected performance of this implosion close to the original design goal of the NIF ignition point design.4 

FIG. 8.

Effect of P2 and P4 shims for asymmetry only cases and for all perturbations in simulations of the higher compression shot N141123. The horizontal and vertical axes show shim amplitude and neutron yield. The red curve shows the effect of a P4 outer shim when the P4 asymmetry is the only perturbation, the blue curve shows the effect of a P2 outer shim with a P2 asymmetry only, and the green curve shows the effect of a P2 dopant shim with a P2 asymmetry only. The purple dots represent simulations of N141123 including all perturbation sources and successive improvements: the nominal 2D simulation, adding a –3.0 μm outer P4 shim, removing the tent perturbation, and finally increasing the power and energy to be comparable to the high foot implosion N140520. The horizontal dashed line represents the symmetric yield simulated for the as-shot N141123 pulse shape.

FIG. 8.

Effect of P2 and P4 shims for asymmetry only cases and for all perturbations in simulations of the higher compression shot N141123. The horizontal and vertical axes show shim amplitude and neutron yield. The red curve shows the effect of a P4 outer shim when the P4 asymmetry is the only perturbation, the blue curve shows the effect of a P2 outer shim with a P2 asymmetry only, and the green curve shows the effect of a P2 dopant shim with a P2 asymmetry only. The purple dots represent simulations of N141123 including all perturbation sources and successive improvements: the nominal 2D simulation, adding a –3.0 μm outer P4 shim, removing the tent perturbation, and finally increasing the power and energy to be comparable to the high foot implosion N140520. The horizontal dashed line represents the symmetric yield simulated for the as-shot N141123 pulse shape.

Close modal

The simulation results described here, for both a high foot-type implosion and a higher compression, ignition-relevant implosion, suggest that shims can be highly effective at mitigating the impact of hohlraum flux asymmetries in current NIF experiments, particularly for P4 asymmetries. Even in the presence of all perturbation sources, factors of a few improvement in neutron yields are predicted in simulations for both cases when only a P4 shim is included. If the current large perturbation caused by the capsule support tent is also mitigated by some other, less perturbing capsule support mechanism, then yields in the 1017 neutrons or ∼1 MJ range are predicted. Finally, if the higher compression implosion type is driven with comparable power and energy as the high foot example, multi-MJ or 1018 neutron yields are predicted. Possibly in combination with other proposed stabilization techniques,48 these simulations suggest that the design goal of ignition on NIF could finally be reached using an improved version of current CH ablator designs.

Of course, the results presented here are entirely simulation based and therefore somewhat speculative. On the other hand, by beginning this study from detailed post-shot simulations of two NIF implosion experiments that are in fair agreement with the measured performance, these simulation results are as grounded in the measured data as is currently possible. Nevertheless, there remain uncertainties in the magnitude and phase of the hohlraum asymmetries that contribute to the yield degradations seen in the two implosion experiments discussed, and these uncertainties surely impact the efficacy of shimming. For this reason, a fundamentally experimental approach will be required for successful implementation of shimmed implosions on NIF. Such a campaign could begin with a 2D ConA implosion to assess if the impact of a given shim is as predicted compared to a baseline un-shimmed implosion. Preliminary design work suggests that the –2.5 μm P4 shim described above for N140520 should be readily discernable in in-flight radiography. A second 2D ConA with a different shim amplitude or phase could then be used to verify that the trends are as predicted in simulations. Assuming that these experiments are successful, planning could then begin for a DT implosion. Ideally, several DT implosions could be tested with varying shim amplitudes to map out experimentally a curve similar to that shown in Fig. 5 or 8.

Note that, even though the actual asymmetries present in experiment may be different from those used in the simulations described here, the overall effectiveness of shimming will likely be similar to that simulated, and only the optimal amplitude and phase of the shim will be different. This has been verified computationally by experimenting with different asymmetry time histories in the simulations and demonstrating that the appropriate shim can equally effectively offset these different asymmetries. The reason for this appears to be that the hohlraum asymmetries introduce a dominantly radial variation in the implosion velocity, at least until very late in the implosion. Hence, only the time-averaged flux asymmetry applied to the capsule and the radial velocity variation it imprints are important to offset by a shim. The detailed time variation of that asymmetry and any azimuthal flow induced by the asymmetry are of secondary importance. It is this fact that enables simple, “static” shims to be so effective despite the very dynamic time variation of the applied asymmetries. Furthermore, given that the high foot platform has shown reproducible performance when the same shot is repeated—both in neutron yield and apparent hot spot shape49—the flux asymmetries in the high foot hohlraum can be expected to be reproducible from shot to shot. Hence, even if not precisely known, these repeatable hohlraum asymmetries should be amenable to shimming, and it remains an experimental question to determine what shim amplitude is optimal.

Finally, it is important to emphasize that shims should not be viewed as a panacea for hohlraum flux asymmetries; they are merely one tool among many. Indeed, it seems more likely that the best solution for the current problems of low-mode asymmetries in NIF implosions will be a combination of shims with other mitigation strategies that will give an overall optimal balance of energetics and hohlraum flux symmetry. For example, according to the results above, shims are highly effective for mitigating P4 asymmetries. This suggests that a more optimal hohlraum design might be one in which the hohlraum is optimized for P2 symmetry control while the P4 asymmetry is mitigated using a shim—instead of relying entirely on the hohlraum to mitigate both P2 and P4 symmetries.

Significantly, shims also do not rely on the current incomplete understanding of hohlraum performance for their effect but are based on the so far better-predicted performance of the capsule. In this respect, they particularly complement other approaches (such as laser cone fraction or case-to-capsule ratio changes) that do rely on understanding the hohlraum dynamics. In effect, shims separably and controllably alter the low-mode symmetry of the capsule implosion in a manner that is independent of the intrinsic and imperfectly known hohlraum asymmetry. In this light, shims might even be thought of as a diagnostic to probe what the asymmetry environment of a particular hohlraum actually is. Clearly, a diversity of approaches should be pursued to address the current hohlraum challenges, and shims should be among those approaches.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.

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