High-density carbon ablator ignition path with low-density gas-filled rugby hohlraum

Efforts to demonstrate thermonuclear energy breakeven with indirect drive on the National Ignition Facility (NIF) continue in earnest.¹ Indirect drive uses a laser-heated hohlraum (or high-Z enclosure) for generating soft x rays that irradiate and implode a centrally located capsule filled with deuterium (D) and tritium (T) fuel. The first ignition attempts used a 4-shock low-adiabat drive in cylinder hohlraums at moderate gas-fill density (ρ = 0.96 mg/cc) and large outer-to-inner laser cone wavelength separation to control time-integrated x-ray drive symmetry, leading to good compression² but lower neutron yield than expected.³ Significant fuel self-heating has been recently demonstrated for a higher adiabat 3-shock “high-foot” laser power drive history in cylinder hohlraums at higher gas-fill density (ρ = 1.6 mg/cc) and still large outer-to-inner laser cone wavelength separation Δλ > 5 Å.⁴ The high gas fill is used to constrain the inward motion of the ablating Au or U hohlraum wall plasma, which can otherwise lead to large x-ray drive symmetry swings in time. These symmetry variations result in residual (non-radial) kinetic energy at peak compression⁵ and degraded implosion yield. A large wavelength separation (∼8 Å) is required to compensate for inhibited inner-cone laser propagation at late time and to achieve time-integrated 2nd Legendre mode (P2) drive symmetry. The combination of high gas-fill density and large cross-beam energy transfer (CBET)⁶ from the imposed large Δλ provides for a computationally challenging hohlraum environment, involving 3-D effects and significant plasma-induced laser backscatter (∼40%–50%) on the inner cones. An additional feature is the prevalence of 20%–25% unaccounted drive energy according to “high-flux model”⁷ comparisons with the database that collectively encompasses (1) shock-tuning experiments,⁸ (2) 1-D streaked radiography experiments for direct measurement of the capsule implosion trajectory,⁹ and (3) observed x-ray and neutron peak emission “bang times.”¹⁰ The origin of this missing energy is not known, possibly involving mixing of the high-Z hohlraum material with the low-Z gas fill¹¹ and the role of numerical mesh management¹² in mainline radiation-hydrodynamic (RH) simulations.¹³ 

At the other end of hohlraum gas-fill studies is the near-vacuum hohlraum (NVH) platform (ρ = 0.032 mg/cc of ⁴He) that was successfully used to drive “exploding pusher” or thin plastic (CH) ablators.¹⁴ Due to the short laser pulse length used (∼4 ns), good agreement with RH simulations was achieved without the need for phenomenological drive multipliers,^10,15 i.e., no missing energy was inferred. These results have served as the impetus for recent 2- and 3-shock high-density carbon (HDC) ablator studies on the NIF.^16,17 The strategy is to combine the intrinsically short laser power histories of HDC with the NVH platform for acceptable drive symmetry control without depending on large CBET at high Δλ. A HDC capsule requires an early-time high “foot” in laser drive to ensure melting of the ablator after first shock passage, thereby avoiding the crystalline diamond phase that can seed hydrodynamic instability growth.¹⁶ To date, HDC implosion experiments in NVHs have shown a strong bias towards “equator high” implosion drive asymmetry, in contrast to RH simulation results.¹⁸ The origin of this difference is not firmly established, but may involve ion diffusive effects from interpenetrating low-Z HDC ablator and high-Z hohlraum ions that are not captured in mainline fluid-based modeling tools. According to RH simulations of these NVHs, the stopping length for a fully ionized ablated carbon ion (∼350 μm/ns) into the expanding gold wall (∼−250 μm/ns) is on the order of 500 μm, based on a Au mass density of ∼1 mg/cc and temperature of ∼3 keV just before collision onset. Such long mean free paths challenge the use of RH simulations in a physical regime where kinetic effects are important.¹⁹ For example, ion mixing from kinetic processes may modify the high-Z density and temperature distribution above the capsule compared with RH simulations, and allow for more efficient inner-cone laser propagation after the stagnation time of C/Au because of reduced inverse bremsstrahlung absorption or enhanced inner-beam refraction. A successful HDC ignition campaign based on the NVHs will require a predictive capability for informing studies of high-convergence implosion symmetry.

Low gas-fill densities are attracting interest for potentially simplified hohlraum dynamics: high laser-hohlraum coupling efficiency through minimal backscatter and unaccounted energy, reduced need for CBET, and calculable implosion symmetry. In this Letter, recent experimental results²⁰ with a 0.6 mg/cc ⁴He gas fill that achieved close to optimal cylinder hohlraum performance in driving a 2-shock HDC capsule form the basis for a novel ignition path. The associated design uses a 4-shock drive profile with a comparatively low fuel adiabat (for high ignition margin) and applies the technique of “adiabat shaping”^21,22 for ablation front instability control. The capsule is driven by an oversized rugby-shaped gold hohlraum²³ for high drive efficiency and robust symmetry control that is filled with the same 0.6 mg/cc ⁴He gas. The 4-shock HDC ablator design has high 1-D simulated ignition margin (for achieving >1 MJ yield) and good tolerance to ablator and ice surface roughness, according to capsule-only high-resolution 2-D RH simulations. Hohlraum simulations that integrate laser propagation, x-ray transport and capsule/hohlraum hydrodynamics give a 2-D yield of nearly 15 MJ for only ∼1.5 MJ absorbed laser energy. Based on demonstrated efficient hohlraum performance at low gas-fill densities and RH simulations that suggest strong 1- and 2-D 4-shock HDC implosion performance, an ignition design leveraging this unexplored parameter space is described and proposed as an alternate path for demonstrating ignition on the NIF.

The recent low gas-fill density target that was fielded on the NIF combined the benefits of high efficiency of NVHs and the inherent symmetry control of gas-filled hohlraums for the purpose of driving a 2-shock HDC design over a ∼7 ns laser pulse length.²⁰ The recognized challenges with the 2-shock ignition design are suitable control of implosion symmetry and the low 1-D ignition margin due to the intrinsically high fuel adiabat. Late time symmetry control is challenging because of significant wall motion and the ensuing laser absorption close to the hohlraum symmetry axis. To reduce the risk of excessive hohlraum filling with high-Z wall material, the low gas-filled cylindrical hohlraum was enlarged to 6.72 mm diameter from the standard 5.75 mm. The larger hohlraum results in greater geometric smoothing of intrinsic hohlraum radiation modes at the capsule ablation front and ensures greater laser clearance at the laser entrance holes (LEHs). The incident laser energy was 1.5 MJ with a peak power of 370 TW, and no wavelength separation (Δλ = 0) was chosen. The demonstrated backscatter was <4%, the effective x-ray drive was inferred to lie much closer to high-flux model predictions for typical gas-filled hohlraums (ρ = 0.96–1.6 mg/cc ⁴He), and improved imploded core symmetry in good agreement with modeling was observed.²⁰ Remarkably, increasing the gas fill for HDC implosions did not incur a drive penalty compared with NVHs.

The early experimental success with a low gas-fill hohlraum platform opens up a promising ignition path for HDC ablators that are now described. The three main design challenges are ensuring (1) high 1-D performance margin, (2) robustness to instability growth at the ablation front and fuel-ablator and DT gas-ice interfaces, and (3) favorable hohlraum energetics with robust symmetry and preheat control.

The demonstrated favorable symmetry control and energetics with a low gas-filled hohlraum density mean that 4-shock capsule designs with their ignition-relevant low 1-D fuel adiabats α (or ratio of pressure to Fermi degenerate pressure) now become viable. Reference 17 compared the relevant 1-D implosion properties between 2- and 4-shock HDC designs, but without the potential benefit of adiabat shaping from laser pickets.^21,22 Both capsule designs have comparable peak implosion speeds υ of ∼380 μm/ns, but with a significantly higher adiabat for the 2-shock design (3.7 vs 1.5 for the 4-shock design). The ignition threshold factor ITF = M + 1 is related to the ignition performance margin M and scales as $α−2.6⋅υ8$⁠,²⁴ giving more than a 10× higher margin for the 4-shock design. The current 2-shock design in a cylinder NVH uses undoped HDC,¹⁸ allowing for larger ablation-front stabilization of Rayleigh-Taylor instability growth but low 1-D margin. Table I lists the key properties of the 4-shock design used in the integrated hohlraum tune [described below]. However, “adiabat shaping” of the drive history may significantly reduce the exposure of the 4-shock target to ablation front instability growth. Adiabat shaping refers to the launch of a decaying first shock with a strong laser picket [see Figs. 1(a) and 2(a)] to potentially raise the adiabat of the outer ablator for ablation front stability control while keeping the fuel on a low adiabat. The shock pressure is designed to remain above 7 Mbars at the ablator-fuel interface, minimizing the risk of instability seeding from multi-phase HDC. The linear growth factor ∼1200 for the 4-shock HDC design with adiabat shaping is 2× lower compared with the 4-shock low-adiabat CH design.¹⁷ Figure 3(b) shows the simulated perturbation growth for the 4-shock design at the time of maximum shell kinetic energy using the (“$1×$”) measured surface roughness spectra on all material interfaces from an as-built (undoped) HDC capsule. Up to ∼2.5× the measured roughness on all surfaces is predicted to still lead to ignition, according to RH simulation parameter scans. The simulated clean fuel fraction—defined as the fraction of DT fuel with less than 5.0 at. % of carbon at the time of maximum shell kinetic energy—is a favorable 80% and lies above the threshold for onset of important 3-D effects.

The tradeoff between capsule robustness and hohlraum performance is best illustrated by considering the drive duration. Fuel adiabat control benefits from longer pulse lengths,²⁴ but hohlraum symmetry control and coupling efficiency (through reduced laser backscatter and x-ray drive corrections) favor shorter pulses. In order to accommodate the ∼9 ns drive history of the optimized 4-shock capsule tune, added margin is sought by using a rugby-shaped Au hohlraum with a 7 mm diameter, 1.09 cm length, and a comparatively large LEH fraction of ∼60% [see Fig. 4]. The use of a rugby hohlraum over a cylinder allows for a greater volume above the capsule, while preserving the hohlraum drive efficiency through a nearly fixed wall surface area. Added benefits of the rugby hohlraum include potentially benign (gold) M- band x-ray preheat [see Fig. 2(b)] from reduced laser intensity at the curved wall, less hot electron generation, greatly reduced time-dependent drive symmetry variations in time, reduced exposure to specular laser glint and a reduced gold “bubble” feature in the wall blow-off that is typically seen in cylinder hohlraum experiments²⁵ and simulations.¹¹ The peak M-band fraction shown in Fig. 2(b) is predicted to remain below 20%, which compares favorably with the measured and simulated ∼21% level in NVHs. A lower level of M-band preheat translates into smaller dopant concentrations that are needed in the ablator for higher ablation velocities and, in turn, higher performance and stability margins. The gold bubble may lead to impaired inner beam propagation at late time, but the curvature of a rugby-shaped wall distributes the incident laser energy over a larger area for a reduced risk of non-uniform wall ablation. Figure 4 shows the laser propagation at peak laser power, indicating robust inner cone (23° and 30°) propagation past the incipient (small) gold bubble produced by the outer cones (44° and 50°). However, the NIF rugby hohlraum database for 4-shock low-adiabat CH implosions (∼20 ns laser pulse length) has shown some symmetry anomalies compared with RH simulations using the high-flux model—unless the outer laser cones are significantly displaced inward toward the capsule.¹¹ The origin of this anomaly is not established, but may involve hydrodynamic mix or ion diffusion across the gold-helium interface near the LEH. To minimize this risk (beyond the benefit of a ∼2× shorter laser pulse with HDC), a comparatively larger LEH (∼60% vs 50.6% for low-foot rugby hohlraums with 1.2 mg/cc ⁴He fill¹¹) is used in the 4-shock design [See Fig. 4]. Figures 1(a) and 1(b) depict the requested laser power history and cone fraction. Use of an early time high (inner) cone fraction is intended to appreciably ablate the window before onset of the ∼70 TW picket in order to suppress hot electron generation by the two-plasmon decay instability. There is the potential for generating (non-azimuthal) CBET during the picket from the expanding LEH window even for low Δλ. However, use of just the 44° cones to drive the picket pulse can be shown to remove this risk. By removing CBET on the picket, the usual hohlraum modeling uncertainties arising from choice of density saturation parameter are bypassed. There is also some CBET near peak laser power at Δλ = 0, but a nominally small value of Δλ can largely suppress this contribution to hohlraum symmetry. Figure 5(a) shows the associated simulated capsule ablation pressure asymmetry history (P2/P0), indicating very low symmetry swings on the order of ±2% compared with the 2-shock HDC capsule in cylinder NVHs (∼±5%). For low-adiabat implosions in rugby hohlraums, the relatively low level of P2 symmetry swings compared with cylinders has been experimentally confirmed.¹¹ The key figure-of-merit is the degree of symmetry control at the end of the laser pulse. Effective inner-cone laser propagation at late time is predicted because of the large volume between the capsule and rugby equator and the large LEH fraction. Figure 5(b) shows the imploded fuel just before ignition, suggesting keen symmetry control without relying on late time CBET from large Δλ as in higher density gas-filled hohlraums. The energy output is over 15 MJ, corresponding to a gain of ∼10.

The low gas-fill hohlraum design also benefits from remaining in the fluid regime, which facilitates modeling with mainline RH simulation methods. The carbon stopping length in the helium gas fill is on the order of 20 μm, largely preventing the carbon blow off from penetrating the Au plasma. In addition, the low gas-fill density delays deceleration onset of the classical Au/⁴He interface compared with high gas-fill platforms,¹¹ lessening the amount of Rayleigh-Taylor instability growth after (wall/gas) stagnation onset.

The alternate ignition path described herein is the culmination of promising early data with low-density gas-filled (cylindrical) hohlraums,²⁰ recent capsule designs that both exploit adiabat shaping for improved stability control and optimize performance margin,²² and rugby-shaped hohlraum simulations for improved efficiency and symmetry control. However, the path to ignition is justifiably fraught with uncertainty over the fidelity of the mainline simulation tools, thereby requiring a careful and long-term experimental plan to benchmark the calculations and iterate on the design as necessary.

In summary, a low density gas-filled hohlraum regime shows promise towards a novel ignition path that combines the energetics benefits of a NVH and the symmetry control advantages of a gas-filled hohlraum. A 4-shock HDC capsule design uses an oversized rugby-shaped hohlraum filled with the same ⁴He density for greater margin to impaired laser propagation and potential symmetry anomalies. Further energetics margins can be obtained with depleted uranium hohlraums and the associated ∼6% improvement in energy coupling.²⁶ 

Useful input from O. L. Landen and J. Milovich is gratefully acknowledged. The suggestions of L. Berzak-Hopkins, S. Khan, S. Nagel, R. J. Rygg, and D. Turnbull are appreciated. Work performed under the auspices of Lawrence Livermore National Security, LLC (LLNS) under Contract No. DE-AC52-07NA2734.