Implosion shape control of high-velocity, large case-to-capsule ratio beryllium ablators at the National Ignition Facility

Improving low-mode symmetry is at present a priority for experiments at the 192 beam National Ignition Facility (NIF).^1–3 Inertial Confinement Fusion (ICF) experiments at the NIF seek to push beyond the alpha-particle heating regime of compressed deuterium-tritium (DT) plasma⁴ into the state of runaway thermonuclear burn. To accomplish this, a high temperature radiation environment is created by laser absorption and x-ray emission inside of Au (or depleted U) hohlraums, which ablatively drives low atomic number capsules containing the DT fuel. By imploding the capsule and interior layer of cryogenic DT ice using a series of increasing pressure shock waves, the adiabat of the capsule and fuel can be kept low allowing for maximum compression.⁵ At sufficient compression (∼1 g/cm² areal density), the dense DT layer will stop the alpha particles emitted from the hot (∼4 keV) central region of the implosion bootstrap heating a large fraction of the dense fuel.

At such extreme central pressures, the DT plasma will find any shell areal density non-uniformities as a means of escape. Furthermore, non-radial motion during the implosion or asynchronous stagnation can reduce the achievable compression and disrupt hot spot formation.¹ For these reasons, designs are sought that keep the radiation flux from the hohlraum as symmetric around the capsule as possible through all stages of the laser pulse.

The recent transition to low-fill pressure hohlraums and shorter laser pulses^6–8 improves the likelihood of reaching the required drive symmetry for ignition since backscatter from laser-plasma instabilities is significantly reduced in this design space.⁶ Predictability of these implosions is still lacking in many respects, but the general trend is found that laser pulses reaching peak power prior to significant hohlraum wall motion match better the predicted capsule and hot spot shapes.⁹ This condition is often difficult to achieve, however, since pulse duration scales with capsule thickness, which must be of sufficient dimension to withstand the growth of Rayleigh-Taylor (RT) instabilities.

A recent work⁹ also suggests that arbitrarily increasing the laser power in the early time picket to speed up the first shock also increases the speed of the outer cone Au hohlraum “bubble” that eventually moves into the path of the inner cone beams. Earlier Be implosion designs¹⁰ that used large 1.06 mm radius capsules inside 6.72 mm diameter hohlraums consistently produced oblate implosions likely due to this effect. As a means of overcoming these hohlraum plasma issues to achieve better symmetry control and predictability, we have conducted experiments at the NIF using large case-to-capsule ratio (CCR) hohlraums and Be ablators. Increasing the CCR leads to a physically greater initial separation between the capsule surface and the hohlraum, creating more room for laser propagation. In this article, we present the first shock timing and symmetry data through various stages of the implosion to verify the assumption that this enhanced beam clearance improves symmetry control.

Capsules made from Be are used as one ablator type for indirect-drive targets in NIF experiments primarily due to its excellent hydrodynamic stability properties^11–15 stemming from the high mass ablation rate.¹⁶ From this same property, we find that high ablation pressures can be achieved for lower peak radiation temperatures permitting the use of large radius hohlraums without substantial degradation in ablation pressure or implosion velocity. On the other hand, it is possible that the increased mass ablation rate could eject more Be plasma toward the hohlraum wall again leading to disruption of inner cone propagation. Taking these considerations into account, a potential optimal design space for Be includes larger hohlraums and thinner shells (relative to other ablators such as CH) requiring shorter duration laser pulses. The shorter pulses then lead to better time-dependent symmetry control since the laser power is delivered before significant hohlraum wall motion occurs. We note that high-density carbon (HDC) ablators also make use of short laser pulses; however, they require significantly higher laser power during the early part of the pulse to shock melt the HDC crystal structure, which may lead to greater wall motion inside their smaller diameter hohlraums.¹⁷ 

Experiments at the NIF tested these hypotheses by using 6.72 mm diameter, 11.24 mm long Au hohlraums, and 1.6 mm diameter Be capsules (CCR = 4.2). Figure 1 shows a diagram of the capsule, which is 100 μm thick and consists of pure Be on the inner and outer most layers and Cu-doped Be (1.1 at. %, 2.7 at. %, and 1.1 at. %) in three interior layers near the inner surface. (There is also about 0.5 at. % Ar in the shells due to the atmosphere used in the coating process.) The Cu-doped layers prevent excessive Au M-band x-ray preheat from reaching the fuel and are positioned to minimize the in-flight Atwood number.^12,13 For a review of Be capsule development and fabrication challenges, we direct the reader to Refs. 18–20.

The laser beams enter through upper and lower laser entrance holes (LEH) that are 3.9 mm diameter in four different angle cones (inner cones—23.5° and 30°; outer cones—44.5° and 50°) relative to the hohlraum axis and grouped into four beam “quads.” The inner cones nominally irradiate the midplane of the hohlraum, as shown in Fig. 1, while the outer cones reach the hohlraum about 3.5 mm up the wall towards each pole. We employed outer cone split pointing where the 44.5° cone points inward of the 50° cone by 230 μm, and two beams from each outer quad are separated azimuthally by 500 μm. Simulations suggest that splitting the outer beams in this way reduces the overlapped intensity on the hohlraum wall, which should then lower the Stimulated Brillouin Backscatter (SBS) and may also produce a more axisymmetric intensity pattern on the hohlraum wall.¹⁰ 

The nominal inner and outer cone laser pulse shapes are shown in Fig. 2 for the designed energy of 1.2 MJ and the peak radiation temperature of 275 eV. The first 0.6 ns of the pulse uses very low power to burn through the LEH windows to prevent hot electron production later in time.²¹ The remainder of the pulse is characterized by three steps of increasing power that launch three shocks designed to merge just inside the DT ice/gas interface. (In the experiments we present here, the DT ice layer is replaced with 5 μm of additional Be.) The first shock is just strong enough to melt the Be microstructure and along with the final two shocks set the fuel on a designed adiabat of 2.0 in an actual cryogenic implosion using DT ice.

Radiation flux symmetry is controlled by changing the inner cone-to-total laser power fraction (cone fraction) while maintaining a constant total power.^7,22 Two-dimensional integrated simulations using the code HYDRA²³ predicted spherically symmetric implosions of this design at 23.7% cone fraction at peak power (final 3 ns of laser pulse). This cone fraction is lower than the NIF optimal efficiency value of 33% (all 192 beams reach the same peak power level) largely due to the thin shell, and thus low foot energy, for this small radius capsule. We anticipate that increasing radius capsules hydro-scaled to maintain a constant peak radiation temperature and velocity will require thicker shells, higher foot energies, and higher cone fractions to tune round. A long term goal is to find the capsule scale that uses this optimum cone fraction.

Figure 2 shows the predicted trends of the self-emitting hot spot shape (Legendre modes P2/P0 and P4/P0) for peak power cone fractions (inner cone relative to total laser power) above and below the symmetric value. The predicted trends for the DT ice-layered target exhibit increased sensitivity in both modes to cone fraction largely because of its greater convergence.

Our primary goals in the experiments we present here were to test the predicted shape and our ability to tune the implosion round. Given two shots to measure the in-flight and stagnation shape tunability, we chose to intentionally induce oblate and prolate implosions with the assumption that round could be achieved by cone fraction interpolation at peak power. For best implosion symmetry control, however, it is also imperative to control the early time shock symmetry. If the radiation flux and thus ablation pressure at the pole and equator are asymmetric during the shock transit stage, those regions of the capsule could reach different adiabats changing the pole vs. equator compressibility (and peak velocity). A possible consequence of combined asymmetry sources is an implosion that may achieve a P2/P0 ≈ 0 at a desired time but has $|dP2/dt|≥0$ (it undergoes a symmetry “swing”); thus, its ability to do useful work on the fuel is reduced. We next discuss the measurements and tuning of shock symmetry for these large CCR Be targets.

To examine the timing accuracy of the three-shock system and their symmetry between the pole and equator, we use the 2-axis version of the NIF Keyhole platform.²⁴ Here, an Au cone is inserted into the side of the hohlraum and through a hole punched in the capsule as illustrated in Fig. 3. A line-imaging velocity interferometry (VISAR) probe laser enters through the cone; half of the VISAR line views the inside surface of the shell at the equator, and the other half reflects off a mirror at the capsule center and views the shell's north pole. From a computational design perspective, the Keyhole experiment allows us to correct for early time drive uncertainties by setting ad-hoc power multipliers (on laser power remaining in the hohlraum after removing the measured backscatter power)²⁵ to match the VISAR data. The drive uncertainties differ depending on the hohlraum and laser conditions, so VISAR data are needed whenever these conditions are changed in the experiment.

The pulse shape for the Keyhole experiment was modified from that shown in Fig. 2 to that shown in Fig. 4 by reducing the total peak power to 200 TW and delaying the start of the rise to peak power by 1 ns. These modifications had the two-fold effect of reducing M-band preheat that may otherwise have led to ionization blanking of the VISAR probe laser inside the liquid deuterium fill and delaying the merger of the 3rd shock with shocks 1 and 2. The requested and measured keyhole pulses are both shown in Fig. 4 for comparison.

The simulation shown in the inset of Fig. 3 illustrates the predicted shock timing. The first shock arrives at the Be/D2 interface (dashed line) near 5.5 ns where it becomes the reflecting surface²⁶ for the VISAR. The 2nd shock catches up to it near 8 ns, and finally the 3rd shock overtakes the combined 1–2 shocks at 9 ns. These features are clearly seen in the actual data shown as the streak record in Fig. 3.

Figure 5 shows the analyzed shock velocity and position data inside the liquid deuterium combined with postshot simulations. Postshot calculations used the reported as-shot pulse and the measured backscatter (only 1.7% mostly from outer cone SBS). After accounting for these measured parameters, we found that the picket and trough required the use of 1.2 and 0.7 power multipliers, respectively, to match the equator data. Under these conditions, the pole's 1st shock was then calculated to arrive simultaneously with the equator's 1st shock, contrary to the observed 110 ps before the equator shock. Pre-shot design calculations did not predict any variation in the 1st shock's pole-equator breakout time difference with the picket power multiplier, suggesting that this discrepancy is not caused simply by the amount of deposited laser power.

There are various potential sources of uncertainty that could lead to this timing discrepancy. During the “picket” portion of the laser pulse (first 1.5 ns), the inner cones remain at a constant but a very low power level of 2.7 TW in order to burn-through the LEH window. The outer cone picket then turns on at 0.65 ns rising quickly to 30 TW. At this early, low power stage simulations may not accurately predict the time-dependent LEH density decrease or the initial heating of the hohlraum wall. Furthermore, we do predict a small but finite amount of Cross Beam Energy Transfer (CBET) transferring power between inner and outer cones^27–29 starting from the picket and lasting throughout the laser pulse since our inner and outer cones use the same wavelength. The accuracy of the CBET level is uncertain at these low Hohlraum gas fills (0.3 mg/cc He). Also during this early stage where the hohlraum albedo is still low, quad-to-quad power variations may play a larger role in producing drive asymmetries azimuthally around the hohlraum axis, which our 2D simulations do not account for. Some discrepancies between measured and simulated 3rd shock merger times were also apparent, which could potentially be caused by asymmetry in the amount of hard x-ray preheat seen by the capsule.

In the left hand image of Fig. 5, we show the measured and simulated shock trajectories obtained by integrating the shock front velocity histories. Closely matching the various shock merger depths gives us more confidence that experimental adiabats are approaching those in the calculations at these times. The measured velocity asymmetries lead to a 3rd shock merger depth difference between the pole and equator that are within the 3.5 μm error bars and that occur 60 ps apart.

Three experiments at 1 MJ (or above) measured the implosion shape and capsule trajectory in addition to the keyhole experiment N160720-002. These capsules were filled with 30:70 mixtures of D³He at 6.7 mg/cc (2996 Torr at 24 K) to induce D + D and D + ³He fusion reactions as signatures of the stagnation conditions. Specifically, the 2.45 MeV neutron produced from D + D was used to measure the fuel ion temperature via neutron time of flight spreading.^30,31 Table I lists the delivered laser energy, backscattered laser energy from the hohlraum, and primary nuclear observables from these implosions. Yield-over-2D clean simulations were better than 65%, although ion temperatures from the simulated width of the DDn spectrum were somewhat lower than measured. This type of disagreement has been observed in the past and hypothesized to come from bulk fluid motion or residual kinetic energy in the reacting products that is unaccounted for in simulations.^32,33

Experiments N160717-003 and N160728-001 were used to test the shape predictability of the in-flight shell and hot spot while N160814-002 was a higher energy test of the peak implosion velocity. The remainder of this paper focuses on the shape experiments.

Measurements of the shape of both the in-flight shell and the forming hot spot via self-emission as viewed from an equatorial line-of-sight³⁴ provide valuable information to validate simulations. For these measurements, we used the Convergent Ablator (conA) platform on NIF as described by Rygg et al.³⁵ In our experiments, a 10 μm Cu backlighter foil was placed 12 mm from the capsule in the equatorial plane of the target chamber. The 8.4 keV He-alpha line was used to radiograph the Cu-doped Be shell starting 1 ns prior to peak self-emission (bang time) onto a 4-strip gated x-ray detector (GXD) filtered with 12.5 μm of Cu and 250 μm of kapton (polyimide). The last strip of the GXD was timed to capture the self-emission during stagnation. From the GXD data, we extract the first few Legendre modes using the analysis techniques described in Refs. 34–36. In the remainder of this paper, we focus on the P2 results because higher order modes (up to mode 8) were all less than 4% at any time.

Our earlier experiments that used Be capsules and CCR = 2.7 (Ref. 37) or 3.1 (low-gas fill 6.72 mm diameter hohlraums¹⁰) proved difficult in achieving predictable, symmetric implosions, likely a result of hohlraum wall plasma impeding (or backscattering) inner cone propagation. For the CCR = 4.2 experiments, we wanted to demonstrate that positive P2 could be achieved since the smaller CCR implosions are typically oblate. Paired with a CCR = 4.2 experiment that produced a negative P2, we could assume that P2 = 0 was possible by simple means of CF interpolation based on the preshot design calculations shown in Fig. 2.

A clear change in the shape close to expected preshot values was observed in the data in terms of the observed P2 value as a function of the capsule radius (P0). In Fig. 6, we present GXD data from two NIF shots: one from an 18.7% peak power CF (N160728-001) and the other from a 28.7% peak power CF (N160717-003). Both of these shots truncated the 1.2 MJ design down to 1.0 MJ by removing the final 500 ps of peak power from the pulse. This was done primarily due to uncertainty in backscatter risk prior to the experiments. Data points at P0 greater than 100 μm from Fig. 6 represent the minimum limb x-ray transmission contour shape of the backlit in-flight shell. Points below P0 of 100 μm represent the shape of the self-emission 17% intensity contour near bang time. The approximate time covered by the backlit P0 points can be found via the measured shell velocities, which at P0 = 200 μm were 336 ± 16 μm/ns and 306 ± 12 μm/ns for the 28.7% and 18.7% cone fractions, respectively.

The solid curves in Fig. 6 show the post-shot simulation results that used as-shot laser powers and the picket and trough power multipliers from the VISAR measurement as discussed earlier. A power multiplier of 90% was applied at peak power to match the measured shell velocities and bang time (10.5 ns). The simulations were post-processed in a consistent fashion with the experiments in order to produce the synthetic backlit radiography and x-ray self-emission images from which the Legendre P2 mode was extracted as shown in Fig. 6. We observe very close agreement to the experiments at all times except in the self-emission of shot N160717-003. Due to brighter than expected x-ray emission and high camera sensitivity, we likely saturated the microchannel plate on this shot, which resulted in a larger (by 20 μm) P0 at bang time than in shot N160728-001. This size difference can be seen in the far right images of Fig. 6. The saturation likely increased the P2 by a proportional amount as well leading to the disagreement between the time-integrated (captured by image plate) and time-resolved self-emission data. The fact that P2/P0 ∼ 21% for both time-integrated and time-resolved data supports this idea.

This then leaves the remaining question of why simulations overpredicted the time-integrated P2 by 8 μm for shot N160717-003? Optical profilometry measurements of the capsule showed mode 2 amplitudes (pole-to-equator variation in the outer radius) were less than 150 nm, which at the bang time convergence ratio of 14 could only grow up to about 2 μm of P2. A pre-shot simulation study of possible CBET impact was performed and showed that with no wavelength difference between inner and outer cones, CBET could produce about 2% increase in effective cone fraction at various times, mostly during the second pulse rise and toward the end of peak power (at specified CF of 23.7%). Increasing CF from CBET near peak velocity would tend to increase P2, which is in the opposite direction of the discrepancy that we observe in N160717-003 simulations vs. data. However, it is conceivable that CBET could affect self-emission P2 in the negative direction if it altered the shock timing and merger depths for each shot. Divol et al.³ have used $P2=(2/3)[ΔtVs−Δ]$ to quantify shock symmetry, where Δt is the difference in pole-equator merger time, V_s is the average shock speed prior to the merger, and Δ is the difference in the merger depth. Based on this definition, we find our 3rd shock merger P2_shock = –3.7 μm (pole leading shock), which is approximately the contribution to the in-flight shell made by the shock asymmetry. If CBET (or some other mechanism) changes this value for different cone fractions, then it would likely manifest itself as changes in the bang time shape, possibly with inverted P2. From Michel et al.³⁸ and Pak et al.,³⁹ in the linear gain regime with no pump depletion, CBET power transfer scales as $ΔPinner∝CF(1−CF)Ptot2F(γ)$⁠, where CF is the laser cone fraction, $Ptot$ is the total laser power, and F(γ) is a function describing the plasma conditions and laser cone wavelength difference.³⁸ If the plasma conditions are held constant and only CF changes then from this scaling, we would expect more CBET power transfer to occur for higher cone fractions (up to 50% CF). Based on these arguments, N160717-003 would have had about 34% more power transferred to the inner cones by CBET compared to N160728-001 at peak power, which based on our pre-shot predictions is roughly equivalent to 0.5% greater increase in effective CF due to CBET for N160717-003. This additional CF would have led to a more symmetric value of P2_shock and possibly lowered the self-emission P2 relative to the simulation.

In this article, we present the first timing and symmetry data of indirectly driven, large case-to-capsule ratio Be targets. These targets were designed to have reduced adiabats relative to earlier Be implosions^10,15 and high implosion velocity. By increasing the CCR, we demonstrated improved predictability and symmetry control using 2-axis (pole/equator) shock velocity measurements and x-ray imaging of the in-flight shell and stagnating hot spot. The observed symmetry control stems from a combination of added beam clearance (relative to previous high-foot NIF implosions) between the capsule and the hohlraum wall and a shorter laser pulse made possible by the decreased Be shell thickness. These design choices limit the amount of hohlraum and capsule plasma that the inner and outer cones must propagate through, which is often the source of hohlraum modeling uncertainties.

Measured shock symmetry (arrival time difference of each shock at the pole and equator) at a peak power cone fraction of 23.7% showed only a 110 ps early polar shock while the 2nd and 3rd shocks were within 60 ps. Conversely, simulations using the as-shot reported laser pulse tuned using ad-hoc power multipliers of 1.2 (picket) and 0.7 (trough) chosen to fit the measured equator breakout time and shock velocity calculated that the polar 1st shock should arrive simultaneously with it.

Radiography of the in-flight shell near peak velocity and x-ray emission imaging of the hot spot revealed that the implosion P2 shape could be tuned from negative (oblate) to positive (prolate) values by changing the inner and outer cone power fraction at peak drive. These experiments measured an average shell velocity of 315 μm/ns about 500 ps before bang time at 1 MJ of total energy. After accounting for the measured 2.5% average laser backscatter, we found that simulations could match these velocities with an ad-hoc peak power multiplier of 0.9. As with almost all indirect-drive implosions on NIF, this observed drive deficit was present in our large CCR experiments. At only 10% reduction, it is smaller than previous Be high-foot, small CCR implosions, which had 15%–25% (Refs. 10 and 15) deficits, suggesting that at least a portion of the lost drive energy occurs during laser propagation through underdense hohlraum or ablator plasma. These earlier Be implosions used thicker shells, and thus longer pulses, which likely contributed to the missing drive energy even at low hohlraum gas fills of ≤0.6 mg/cc. Indeed, the recent work with HDC ablators¹⁷ using shorter duration laser pulses observed better agreement with as-shot laser power similar to the current Be implosions discussed in this article.

Very close agreement between the measured in-flight symmetry and simulations using the tuned laser parameters were found for both cone fractions. It appears that the 110 ps difference in the measured 1st shock arrival time was not large enough to make an observable difference in in-flight symmetry from the radiography experiments, since simulations matched in-flight symmetry assuming symmetric 1st shock arrival. We do speculate, however, that if a mechanism such as CBET were active and changed for the two different cone fraction pulse shapes, this could change the shock symmetry and subsequently change the bang time shape from what was calculated. This is our current best hypothesis for the discrepancy between measured and simulated self-emission P2 shapes at bang time for shot N160717-003, which had a higher specified CF and thus likely had more power transfer by CBET compared to N160728-001. Additionally, the laser power multipliers on the picket (1.2×) and trough (0.7×) essentially offset each other causing no more hohlraum wall expansion than would be expected from the 1.0× total foot multiplier; thus, our late time flux symmetry was mostly unaffected by these particular values of early time multipliers.

While uncertainties remain, mostly in laser and hohlraum modeling, we demonstrated a large step in implosion shape control at high-velocity using large CCR targets with moderate adiabats of 2.0. It is likely that the physics producing these modeling uncertainties are still present in our experiments, and we have simply reduced sensitivity to them with the target design described in this paper. We anticipate that large CCR targets can be used as a stable and predictable implosion platform for continuing to unravel hohlraum modeling uncertainties and for studying the physics of hot spot formation.

This work was performed under the auspices of the National Nuclear Security Administration Inertial Confinement Fusion Program (Steve Batha, LANL ICF Program Manager). The authors would like to thank the National Ignition Facility, General Atomics for target fabrication efforts, including John Bae for beryllium capsule coating, LANL MST-7 target fabrication, and LLNL target fabrication. We would also like to thank David Strozzi for helpful discussions on backscatter issues and the NIF Backscatter Working Group for helping to evaluate our pulse shape designs.