Design of the first fusion experiment to achieve target energy gain $G>1$

In this work we present the design of the first controlled fusion laboratory experiment to reach target gain $G>1$ N221204 (5 December 2022) [Phys. Rev. Lett. 132, 065102 (2024)], performed at the National Ignition Facility, where the fusion energy produced (3.15 MJ) exceeded the amount of laser energy required to drive the target (2.05 MJ). Following the demonstration of ignition according to the Lawson criterion N210808, experiments were impacted by nonideal experimental fielding conditions, such as increased (known) target defects that seeded hydrodynamic instabilities or unintentional low-mode asymmetries from nonuniformities in the target or laser delivery, which led to reduced fusion yields less than 1 MJ. This Letter details design changes, including using an extended higher-energy laser pulse to drive a thicker high-density carbon (also known as diamond) capsule, that led to increased fusion energy output compared to N210808 as well as improved robustness for achieving high fusion energies (greater than 1 MJ) in the presence of significant low-mode asymmetries. For this design, the burnup fraction of the deuterium and tritium (DT) fuel was increased (approximately $4\%$ fuel burnup and a target gain of approximately 1.5 compared to approximately $2\%$ fuel burnup and target gain approximately 0.7 for N210808) as a result of increased total (DT plus capsule) areal density at maximum compression compared to N210808. Radiation-hydrodynamic simulations of this design predicted achieving target gain greater than 1 and also the magnitude of increase in fusion energy produced compared to N210808. The plasma conditions and hotspot power balance (fusion power produced vs input power and power losses) using these simulations are presented. Since the drafting of this manuscript, the results of this paper have been replicated and exceeded (N230729) in this design, together with a higher-quality diamond capsule, setting a new record of approximately $3.88\mathrm{MJ}$ of fusion energy and fusion energy target gain of approximately 1.9.

Figure 1

(a) Schematic of the target configuration showing the hohlraum and spherical diamond capsule that contains DT fuel. Radiation hydrodynamics simulations of the integrated hohlraum and capsule (top) show the material positions and plasma filling into the hohlraum at time equal to 6 ns for N221204 (right) compared to N210808 (left). Also shown are simulated laser ray powers and an expanded view of the density and temperature at stagnation for N221204 vs N210808 from $\alpha$-off simulations (simulations where $\alpha$-particle deposition is turned off). (b) The radiation drive symmetry was controlled by transferring energy between laser beams through wavelength detuning $\mathrm{\Delta }\lambda$ and by precisely defining the balance of laser powers between the inner (${23}^{\circ }$ and ${30}^{\circ }$) and outer (${44}^{\circ }$ and ${50}^{\circ }$) beams throughout the duration of the laser pulse. The peak of the laser power was extended by about 300 ps to drive the thicker diamond capsule and the trough was lengthened to preserve the shock timing. (c) The simulated hohlraum internal radiation temperature $T_{\text{rad}}$ as a function of time shows the extended and higher radiation temperature for N221204 compared to N210808. The near vertical rise of $T_{\text{rad}}$ at the end of the drive for both cases is due to reheating [17] of the hohlraum from the capsule fusion output. (d) Calculated change in inner cone power (e.g., on the ${23}^{\circ }$ cone) post energy transfer. This amount of transfer was increased for N221204 (red lines) compared to N210808 (black lines) via increasing $\mathrm{\Delta }\lambda$ from $1.8\AA$ to $2.75\AA$ to maintain symmetry with the longer laser pulse and thicker ablator. (e) Ratio of the full inner cone power to total laser power for the incident laser pulse (solid lines) and post-transfer pulse (dashed lines).

Figure 2

(a) Increase in ignition metric $E{P}^2$: inferred hotspot pressure $P$ and internal energy $E$ for previous DT layered experiments at NIF in relation to the ignition boundary (black dashed lines denote approximately $E{P}^2$). The gray points under the ignition boundary are from simulations. The increase in ignition metric $E{P}^2$ for the N221204 design compared to N210808 is shown in the red shaded region, calculated using a range of assumed perturbations (1D and 3D effects). (b) Tradeoffs in implosion metrics with increased capsule thickness: ratio of simulated 1D implosion metrics compared to N210808 as a function of increased HDC ablator thickness. The calculated hotspot $E$, hotspot $E{P}^2$, and total areal density $\rho R$ are taken at peak compression or bang time (peak neutron production) from simulations with $\alpha$ off. The calculated peak implosion velocities and fusion neutron yields are also shown. (c) Increase in areal density for this work compared to N210808: neutron yield as a function of DSR, ratio of downscattered neutrons to primary neutrons. Black and red circles are data and the shaded curves are simulations showing the expected increase in DSR at a given yield for this new design from 1D simulations and considering potential 3D degradations (see the text for details).

Figure 3

Simulated performance for the N221204 design (red curve and circles) compared to the N210808 design (black curve and circles) for a range of values of various perturbations including instabilities from (a) ablator and ice roughness (open circles vary ablator roughness with fixed $1\times$ roughness on the ice and closed circles vary the ice and ablator roughness), (b) ablator mixing into the hotspot, and (c) low-mode asymmetries from the radiation drive (see the text for details).

Figure 4

(a) Simulated yield as a function of roughness of the diamond ablator interfaces and ice layer for future designs that increase the diamond ablator thickness compared to N221204 (red curve) by an additional $4\mu \mathrm{m}$ (blue circles), $6\mu \mathrm{m}$ (orange circles), $8\mu \mathrm{m}$ (magenta circles), and $10\mu \mathrm{m}$ (green circles) using the same 2.05 MJ laser energy and hohlraum geometry with adjusted shock timing. (b) Simulated performance as a function of roughness of the diamond and ice layers and (c) increased low-mode asymmetries from the radiation drive for designs that increase the diamond ablator thickness compared to N221204 (red curve) by an additional $4\mu \mathrm{m}$ (blue circles) and $10\mu \mathrm{m}$ (green circles) using 2.2 MJ of laser energy and hohlraum geometry with adjusted shock timing. The black circles and curves are simulations of the N210808 design.

Figure 5

Simulated sensitivity of $\alpha$-on fusion energy yield to hotspot oblateness (P2) from $\alpha$-off simulations, using a total degradation model of the N221204 design (red circles), where the flux asymmetry was adjusted in the simulations to vary hotspot P2. The hotspot P2 was approximately $-12\mu \mathrm{m}$ for N220919 and approximately $0\mu \mathrm{m}$ for N221204. We predicted that a performance increase of greater than 2× vs N220919 could be achieved by improving the hotspot P2 to within a few microns of round and a higher increase in performance if the hotspot was closer to round ($\mathrm{P}2=0$). The range of yields at a given level of hotspot P2 results from different assumptions about the magnitude of the time-varying P2 of the hotspot and DT shell, which will be benchmarked against data in coming experiments.

Figure 6

(a) Temporal histories of the simulated hotspot power (in watts) balance for N221204 (dashed curves) compared to N210808 (solid curves), normalized to the respective bang times (peak neutron production) showing significantly higher $\alpha$ heating for N221204. (b) Simulated hotspot areal density vs ion temperature for N221204 (red curve) vs N210808 (black curve) showing higher initial areal densities for N221204 and a substantial increase in areal density and ion temperature over the burn duration. Here a bang time of $\pm 50$ ps is denoted by the green dashed curves.

Figure 7

Calculated neutron yield as a function of areal density (taken at time of peak neutron production) of the HDC diamond ablator (squares), DT fuel (triangles), and total (circles) for the N221204 design (red) compared to N210808 (black) from 1D hydra simulations. Here the yield range is sampled by artificially varying the reaction cross sections on these designs. The difference in areal density between the two designs is largest at low yields, with $\alpha$-particle deposition off, and the areal density for both designs is reduced at higher yields as the burn occurs upon expansion when the hotspot and surrounding dense DT shell are larger.

Figure 8

Calculated Atwood number at the interface between the DT fuel and diamond ablator for N221204 (red curve) compared to N210808 (black curve) as a function of fuel-ablator radius (see the text for details). For an imploding capsule a lower or more negative Atwood number is more stable to Rayleigh-Taylor mixing.

Figure 9

Changes made to the input laser pulse to reach target gain $G>1$ following the first new design attempt N220919 (1.22 MJ) and N221204 (3.15 MJ). (a) The amount of transfer was increased for N221204 (red) compared to N220919 (black) via increasing $\mathrm{\Delta }\lambda$ from $2.5\AA$ to $2.75\AA$. The input laser powers (solid lines) and calculated laser powers (dashed lines) are shown for all cones post energy transfer for N221204 (red) vs N220919 (black). (bottom) The requested input cone fractions (solid lines) were also adjusted, i.e., the ratio of the inner cone power to total laser power, to optimize the time-dependent symmetry based on the updated hohlraum model (see Sec. 1 of the Appendix). The post-transfer cone fractions (dashed lines) are shown for N221204 (red) vs N220919 (black).

Figure 10

Mode 2 of the simulated Legendre decomposition of the radiation flux asymmetry (P2/P0) for N210808 (black) N220910 (red) and N221204 (blue) plotted together with the scaled requested laser power as a function of time (black solid lines), and cone fraction (ratio of inner laser cones to total power) as a function of time (dashed lines). The P2 decomposition is within the specification during the foot, until the rise to peak power, but is allowed to swing during the peak of the pulse (see the text for details). Values of P2/P0 $<0$ have higher radiation temperature at the waist of the hohlraum.