Radiation driven Hohlraum using 2ω for ICF implosions at the NIF

One of the most challenging tasks in laser inertial confinement fusion (ICF) experiments¹ is achieving adequate time-dependent symmetry of spherically compressed deuterium and tritium (DT) fuel up to the high convergence ratios required for ignition. In these experiments, spherical targets containing DT fuel are accelerated to ∼400 km/s using a Hohlraum radiation drive that is created via laser irradiation of a high Z cylinder. Laser beam propagation through the harsh plasma-filled Hohlraum environment over the duration of the laser pulse can result in significant low mode radiation flux asymmetries^2–5 that are difficult to control and model.⁶ If radiation drive symmetry was the only consideration, one could readily make the Hohlraum large enough compared to the capsule to mitigate these asymmetries.^7,8 However, in addition to radiation drive symmetry, simultaneously achieving an adequately high radiation drive is required. Reaching high implosion velocities at large capsule scales with the current National Ignition Facility (NIF) capability, both of which are important for achieving high performance,⁹ requires controlling symmetry at small case-to-capsule ratios (CCR) where doing so is exceptionally difficult. In addition, in the nominal ICF experimental configuration, the capsule has a direct view to the laser-irradiated wall and unfavorable non-Planckian M-band (>2 keV) portion of the radiation drive spectrum. This M-band radiation and hot electrons produced via laser–plasma interactions (LPI)¹⁰ can preheat the capsule and also degrade the implosion performance.¹¹ 

In this work, we aim to reduce the difficulty in controlling the dynamic laser–plasma environment for achieving capsule symmetry by using the laser beams to irradiate cavities outside of the capsule-containing Hohlraum. In this configuration, the capsule would not have a direct view to the laser-irradiated wall and could be shielded from the x-ray M-band. To enable reaching high enough temperatures in this configuration, we consider the use of frequency doubled laser light (2ω), which has increased conversion efficiency compared to frequency tripled laser light (3ω). In addition, since the drive symmetry in this geometry would not be reliant on uniform laser irradiation at the wall, the use of phase plates producing smaller focal spot sizes could also be considered which would enable smaller laser entrance holes (LEH) and reduced shielding inside the Hohlraum. However, LPI could become an issue for 2ω designs using phase plates producing smaller focal spot sizes, and a more in-depth LPI investigation would be required.

In this design, the radiation flux asymmetry would be more reliant on radiation transport and geometry, vs laser propagation through a plasma, and could be mitigated by applying a thickness variation to the ablator,¹² or shim, which has been recently successfully demonstrated.¹³ Radiation driven Hohlraums are also being investigated for experiments at NIF using 3ω laser light, which are designed to reach high radiation temperatures using smaller outer cavities¹⁴ and control symmetry via shaping of shields within the Hohlraum.^14–18 Frequency tripled designs are advantageous as they can be tested in the current NIF configuration, but may be challenging for laser backscatter and plasma filling of the outer cavities. The designs presented in this paper are calculated to enable reaching sufficiently high radiation temperatures to drive current ICF implosions (270–300 eV) in large (6.4 mm diameter) Hohlraums.

To construct a conceptual design and assess the feasibility of reaching adequate radiation temperatures in this configuration, an initial design space survey was completed using VISRAD¹⁹ calculations that have been benchmarked against radiation hydrodynamics simulations using HYDRA.²⁰ VISRAD is a 3-D thermal radiation code that enables scoping of complex geometries with little computational cost compared to a 3-D radiation hydrodynamics simulation of this geometry. Additional calculations should also be done following this study using HYDRA. We also start from a design point that has been benchmarked against recent integrated experiments at the NIF, which have driven 1100 μm inner radius high density carbon (HDC) capsules to peak implosion velocities of ∼380 km/s and controlled symmetry using cross-beam energy transfer (CBET).²¹ Sections II–IV present the initial starting point for the design and benchmark of VISRAD calculations, a scoping of potential geometries with estimates of the radiation temperature and example radiation flux asymmetries as seen by the capsule and mitigation strategies.

Recent inertial confinement fusion (ICF) experiments at the NIF in the HybridE platform have driven 1100 μm inner radius diamond ablators to velocities of ∼380 km/s in 6.4 mm diameter gold-lined depleted uranium (DU) Hohlraums (11.24 mm in length) using near maximum capability of NIF (1.9 MJ and 480 TW) and 4 mm diameter LEHs.²¹ The symmetry in these experiments was controlled using energy transfer from the outer to inner laser beams in low (0.3 mg/cc) He gas-filled Hohlraums.^22,23 Future experiments plan to increase implosion velocity and reduce coast time in this platform via reducing the size of the LEH to 3.64 mm, also using the full power and energy of NIF and 3ω laser light. Eventually, this platform will reach a maximum achievable radiation drive as the LEH size will be limited by clipping of the laser beams, and the Hohlraum size will be limited by symmetry, or case to capsule ratio (CCR). However, more available laser energy would be useful in driving thicker ablators at the 1100 μm capsule scale or thicker ice layers and reducing coast time.²⁵ 

Operating at a laser wavelength of 2ω, green, laser light, would enable increasing the power and energy per beam up to 3.5 TW and 18.5 kJ, more than 670 TW and 3.5 MJ of total laser power and energy. For a peak power of 3.5 TW the peak pulse duration could be extended by ∼1.3 ns compared to the current NIF capability of 2.5 TW peak power and 10 kJ per beam, which has a peak duration of ∼3.8 ns.

Current indirect drive ICF experiments at NIF use 3ω laser light, as it was found in the 1980s that shorter laser wavelengths can help suppress hot electron generation and result in a higher absorption efficiency.^26,27 However, more recent studies and experiments show that laser–plasma-interactions for 2ω laser light are not intrinsically different than 3ω and can be controlled in high energy density Hohlraums by smoothing the laser beams and decreasing the laser intensity.^28–31 In addition, recent experiments in low He gas fill density Hohlraums have shown a significant reduction in hot electron generation^32–34 compared to high gas filled Hohlraums even in the presence of using CBET to control symmetry^21,23 which also showed negligible amounts of Stimulated Raman Scattering (SRS). While 2ω designs have been explored using the conventional laser cone pointing geometry with the inner beams pointed near the waist of the Hohlraum,²⁸ here we use the extra drive margin to shield the implosion hard x-rays generated in the laser–wall interaction. In addition to providing direct shielding of x-rays, the new geometry does not rely on CBET or high He Hohlraum gas fill density for controlling radiation drive symmetry, both of which can increase deleterious effects caused by LPI. We therefore propose to use no intentional CBET and a near vacuum Hohlraum gas fill density of 0.03 mg/cm³ He that has been shown experimentally to give low hot electron production and low laser backscatter.^32–34 

To benchmark VISRAD calculations of the radiation temperature we first compare to HYDRA simulations of a close design platform to the HybridE configuration, but using a Hohlraum gas fill density of 0.03 mg/cm³ He and 2ω laser light, see Fig. 1. These HYDRA simulations modeled the Hohlraum radiation drive and capsule together in cylindrical geometry using two dimensions with an axis of symmetry along the Hohlraum axis. The radiation drive was calculated using a “high-flux model”³⁵ with detailed configuration accounting (DCA), non-local thermodynamic equilibrium (NLTE) atomic physics, and Spitzer–Härm electron thermal conduction with a flux-limiter of $0.15neTevTe$⁠. Here, n_e is the electron density, T_e is the electron temperature, and v_Te is the electron thermal velocity. The emissivities and opacities were calculated inline using DCA for T_e > 300 eV and using local thermodynamic equilibrium (LTE) tables elsewhere. Multipliers on the laser power during the foot of the pulse were determined from separate shock timing experiments.^36,37 Laser power multipliers applied during the rise and peak of the drive of 83% were used to match the time of peak x-ray production³⁹ in tuning experiments. While high levels of laser coupling were observed, the Hohlraum model requires this multiplier on the radiation drive to match experimental data.

The plot on the left of Fig. 1 shows radiation temperature as a function of time calculated using HYDRA, with a schematic of the configuration (inset). The plot in the middle shows the HYDRA simulated radiation temperature distribution in the Hohlraum at the time of peak radiation temperature (∼8.1 ns). Here, one quarter of the Hohlraum is shown, where x = 0 is oriented along the Hohlraum axis and z = 0 is the direction along the equator. Simulations of this platform are similar in radiation temperature to calculations of the hybridE experimental platform using 0.3 mg/cm³ He and using 3ω laser light, which predicted radiation temperatures of 270–290 eV around the capsule. The plot on the right hand side shows the radiation temperature at the Hohlraum wall–gas interface at 8.1 ns calculated using HYDRA (grey points) compared to VISRAD calculations that were tuned to match the radiation temperature of the HYDRA simulations at the equator (red points). The calculated temperature using VISRAD at the position of the outer beams is lower than HYDRA simulations as VISRAD does not model the expanding wall bubble that becomes under-dense and is heated more by the laser beams. We, therefore, tune to the radiation temperature at the equator and as calculated near the capsule–gas interface.

We calibrate the VISRAD radiation temperature during the peak of the radiation drive to HYDRA, which includes plasma filling and reduced coupling efficiency, by adjusting the albedo in the VISRAD calculations. For this Hohlraum scale the benchmark experiments showed high laser coupling of >98%.²¹ Here, we do not change the diameter of the Hohlraum but increase the plasma temperature at the ends of the Hohlraum. While higher temperatures could result in enhanced plasma filling, increasing the plasma temperature could result in better laser beam propagation and less LPI³⁸ than the benchmark hybridE experiments. Based on this comparison, the calculations using VISRAD in Secs. III and IV should provide a conservative estimate for T_r in the outer cavities. Finally, while the platform aims to reduce LPI, this could be a limiting factor for these designs that use 2ω laser light. A full LPI assessment of the proposed designs is beyond the scope of this work. However, future calculations using, e.g., pF3D,²⁴ and experiments to measure hot electrons and backscattered laser light should be completed to test design feasibility and limitations.

Starting from the configuration described in Sec. II, the HybridE platform with lower gas fill density and 2ω laser light, we make incremental design changes and calculate the radiation temperature using VISRAD, see Fig. 2 for T_r at the wall–gas interface along the equator. The initial radiation temperature from Sec. II was ∼286 eV, shown in Fig. 2 (green point). Repointing of the inner and outer beams closer to the LEH did not significantly change the radiation temperature for this configuration. The Hohlraum was also shortened slightly for the examples in this paper from 1.1124 cm to 1 cm which also had little effect on the radiation temperature. Repointing of the beams to a position of best focus at X = 0 and Y = 0, and near the LEHs in Z, enabled reducing the size of the LEH from 4.0 mm to 3.45 mm. This reduction in LEH size increased the radiation temperature by >10 eV, See Fig. 2 (red point at a peak laser power of 2.5 TW per beam). Then, increasing the peak laser power from 2.5 TW per beam (480 TW total) to 3.5 TW per beam (670 TW total), enabled by using 2ω laser light, increased the radiation temperature by >20 eV with the following relationship $Tr∝(P)0.25$⁠. This scaling is shown as the black curve in Fig. 2 whereas VISRAD calculations are denoted by the red points. The shaded red region depicts the range of calculated Hohlraum temperatures at the wall–gas interface along the equator using VISRAD for the new designs described in this section.

Here, the drive margin enabled by repointing of the laser beams, using a smaller LEH, and going to 2ω laser light was used to add shielding from direct line of sight of the capsule to the laser–wall interaction. The extra shielding increases the temperature in the outer cavities and reduces the temperature at the center of the Hohlraum. However, the calculations suggest feasibility of achieving similar radiation temperatures to current integrated platforms (HybridE) even with the extra shielding.

An example of one of these new designs is shown in Fig. 3, with a schematic of the target including all laser beams and component dimensions (top left) and with representative laser beam for each cone (top right). Here, the laser beams illuminate cavities at the ends of the Hohlraum, and an additional shield is used to block the low angle inner beams. In this configuration, there is no direct line of sight of the laser–wall interaction to the capsule. For a given Hohlraum and LEH size, the shallow angles of the inner beams (23° and 30° cones) set the maximum pointing distance along the Hohlraum axis away from the equator and the size of the inner shields that catch the inner beams. The size of these inner shields can be smaller if the opening between the outer cavities and the central Hohlraum is smaller. However, doing this resulted in lower radiation temperature at the equator. Therefore, in this example, the size of the outer cavity opening to the inner Hohlraum was set by the laser spot sizes of the outer beams. The outer beam pointing along the Z axis away from the equator was also dictated by the size of the LEH and the cone angle. In this example, the best focus of the 23° cone is pointed to $Z ± 6.3 mm$⁠, the 30° cone is pointed to $Z ±5.5 mm$⁠, 44° cone is pointed to $Z ± 5.5 mm$⁠, and 50° cone is pointed to $Z ± 5.0 mm$⁠. The position of the beam foci was pointed to X = 0 and Y = 0 for simplicity but could further be optimized, e.g., splitting of the beams within a laser quad, to help mitigate backscatter by reducing intensity on the wall and to enable further reducing the size of the inner opening and shields.

In this example, we reach ICF relevant Hohlraum radiation temperatures while delivering radiation flux asymmetries that are mainly P4 in modal content and can be mitigated by shimming the capsule. The inner shield radius and radius of the inner hole can also be optimized to tune the symmetry and change the relative contributions of P2 vs P4 radiation flux asymmetry as seen by the capsule, see Sec. IV. With a peak laser power of 3.5 TW per beam (670 TW total), the radiation temperature at the wall–gas interface calculated using VISRAD near the equator is 270–290 eV, similar to what is achieved in hybridE experiments. Here, the cavities at the ends of the Hohlraum reach a maximum temperature of ∼368 eV. At this peak power, the pulse can be extended by ∼1.3 ns beyond the peak duration of the hybridE pulse (5.1 ns vs 3.8 ns) which will reduce the coast time of the implosion.²⁵ 

Figure 4 shows an additional benchmark of the predicted radiation temperature using 2D radiation hydrodynamic simulations (HYDRA) to VISRAD for the exact configuration shown in Fig. 3 but without the extra inner shields. This provides a more high fidelity estimate of the achievable Hohlraum radiation temperature at these high laser power and energies with potential plasma filling blocking the beams from propagating to the Hohlraum wall. This figure shows the radiation temperature around the capsule as a function of time plotted together with the input laser pulse. The inset is a contour plot of the radiation temperature at 7.2 ns, midway through peak power. The dashed line is the predicted temperature using VISRAD for this exact configuration (with no inner shields) of ∼324 eV. The HYDRA simulations show reasonable inner beam propagation for this scale of Hohlraum and predict temperatures at the waist of the Hohlraum that are comparable to or higher than the VISRAD estimate, indicating that the design in Fig. 3 with the additional shields can reach relevant ICF Hohlraum radiation temperatures.

Figure 5 shows additional configurations, with the radiation temperatures at the wall–gas interface shown below each configuration. All examples use 3.5 TW per beam and a Hohlraum length of 10 mm. Cases (a)–(c) use a 3.45 mm LEH and cases (a)–(d) use a 6.4 mm diameter Hohlraum. Additional shielding dimensions are listed on the images. The example in (a) uses inner shields to block the 23° and 30° cones as in Fig. 3 but uses cone shaped shields vs flat shields with openings in the center of the cones. This enables higher radiation temperatures at the equator than achieved in Fig. 3 by bringing the laser-illumination region close to the center of the Hohlraum, while providing more room between the inner shields and inner entrance holes. The example in (b) shows the radiation temperature for a configuration with only two cavities at the ends of the Hohlraum and no additional shielding to block the inner cones. For this case, to confine all laser beams to the outer cavities, the openings to the central Hohlraum were limited to 1 mm in diameter. The inner opening size was set by the low angle inner beams, so that they would not spill over onto the wall. This resulted in a radiation temperature that was much lower than configurations that used additional shields to block the inner cones and did not reach ICF relevant temperatures in the central Hohlraum.

The example in Fig. 5(c) uses additional shields closer to the LEHs, 2 mm in diameter, to block the inner beams, enabling a larger inner opening to the central Hohlraum. This configuration also results in high temperatures in the central Hohlraum. The example in (d) is the same as the example in (c) except the inner beams use outer phase plates, which produce smaller focal spot sizes, enabling shrinking of the LEH diameter from 3.45 mm to 3 mm, which increases temperature by ∼10 eV. Finally, the example in (e) further reduces the Hohlraum size from the example in (d) to 5 mm in diameter, which raises the temperature of the inner hohraum and outer cavities by ∼10 eV. While the temperature reached here is higher, initial HYDRA simulations of this size Hohlraum suggest that significant plasma filling of the outer cavities could become a problem. This could also be a concern for outer beam stimulated Brillouin scattering (SBS) that is mainly a result of interaction with the high-Z wall material filling the Hohlraum in current experiments.⁴⁰ The maximum temperature in the outer cavities for all cases was <380 eV. In addition, for all cases it was verified that no laser energy was deposited on the wall of the inner capsule containing Hohlraum or onto the capsule.

Low mode radiation drive asymmetries can reduce coupling of kinetic energy to hot spot internal energy in ICF implosions^2–4 and can create thin spots in the compressed dense fuel which can limit confinement.⁴¹ Achieving adequate Hohlraum symmetry is usually a trade-off with implosion velocity as the symmetry is generally controlled by making the Hohlraum larger compared to the capsule which reduces the radiation drive. In this design, we propose to use the capsule shielding dimensions to result in radiation flux asymmetries that are near pure P2 or P4 in modal content. We then propose to mitigate the radiation flux asymmetries by applying a shim to the capsule ablator thickness with the same modal content as has been recently successfully demonstrated.¹³ In addition, one can further optimize the radiation shielding to potentially eliminate all radiation flux asymmetries.^14–18 

Figure 6 shows an example of the Legendre decompositions of the radiation flux asymmetry at the capsule–gas interface, modes P = 2 (red) and P = 4 (black), normalized to the mode P = 0 of the radiation flux. These modes are plotted as a function of the size of the inner opening radius for the shields close to the capsule in the configuration shown in Fig. 3. The relative contributions of the P2 and P4 radiation flux asymmetry can be varied by changing this target dimension. The blue ovals denote inner opening radii that result in near pure P2 or P4 modes of the flux asymmetry, which would be easier to mitigate with a capsule shim than mixed mode flux asymmetries. Radiation temperatures at the capsule–gas interface for these two examples are also shown as insets.

Shimming of the capsule has been demonstrated successfully at NIF in plastic ablator experiments to mitigate a P4 radiation flux asymmetry.¹³ Given the measured sensitivity, we estimate that a ∼1.4 μm P4 diamond shim would be required to mitigate the 7.5% P4 flux asymmetry shown in Fig. 6 (and Fig. 3) with a radius of the inner shield opening of 600 μm. For a plastic Glow Discharge Polymer (GDP) ablator this corresponds to ∼4.5 μm due to the mass density difference of the ablators. For a configuration with mainly P2 radiation flux asymmetry, Fig. 6 radius of inner shield opening of 450 μm, we estimate from Ref. 12 that a ∼5 μm diamond shim would be required to counteract the P2 ∼8% flux asymmetry. This is likely an overestimate as the simulated sensitivity of flux asymmetry mitigation to shim thickness was lower than observed for the case of a applying a P4 shim.

This study presents a conceptual design and assesses the feasibility to create a drive where the implosion symmetry relies mainly on radiation transport, where laser beams irradiate the ends of a capsule containing Hohlraum that is shielded from the view of the capsule. We estimate using VISRAD that radiation temperatures for modern ignition designs (270–300 eV) can be reached in this geometry with the use of frequency doubled laser light that has a higher power and energy threshold for the current capability of NIF, up to 670 TW and ∼3.5 MJ. This estimate starts from a currently fielded Hohlraum geometry (6.4 mm diameter Hohlraum in hybridE) to provide a benchmark for the VISRAD calculations and to provide a low laser–plasma-interactions (LPI) environment. We also estimate that smaller Hohlraums could drive higher temperatures in the capsule containing Hohlraum or potentially enable the use of frequency tripled light, but may be challenging for plasma filling and LPI. The symmetry in this design can be mitigated by shimming the capsule ablator thickness, by ∼1.4–5 μm depending on the ablator material which was demonstrated in recent experiments, and through tailoring the shape of the shielding to the laser spots. Future work should benchmark the VISRAD calculations of radiation temperature using HYDRA for configurations that include the inner shields. In addition, experiments and calculations should be done to estimate the impact of these designs on laser–plasma- interactions.

This work was performed under the auspices of the U.S. Department of Energy under Contract No. DE-AC52–07NA27344 and Contract No. 89233218CNA000001. This work has been supported by Laboratory Directed Research and Development (LDRD) award number 19-FS-061. This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.