(Color) Schematic of NIF ignition target. The hohlraum is made of uranium with a thin passivating layer of gold ∼0.5 μm thick on the inside surface. It is filled with He gas at a density ∼0.96 mg/cc, which controls wall motion for drive symmetry control. The dimensions have been selected based on recent NIF experiments to obtain symmetric implosions. (For a more complete description see Ref. 6).
(Color) Schematic of NIF CH ignition capsule. The capsule ablator has five layers, three of which are doped with Ge to control hydrodynamic instability at the ablator-ice interface. Heating of the inner clean CH layer by x-rays >1.8 keV, which pass through the ice drives a Rayleigh-Taylor unstable configuration at the interface. The amount of Ge is set to control the Atwood number such that instability growth is acceptable. The details of the design attempt to optimize the overall efficiency while controlling instability. (For a more complete description see Ref. 6).
Laser power (solid) simulated x-ray drive temperature in the hohlraum (dot) and pressure in the ice layer (dash) as a function of time. The laser power is stepped in time to gradually increase the x-ray drive on the capsule such that the pressure in the ice is increased in four shocks from ∼1 Mbar to a value in excess of 100 Mbar during the implosion phase. The steps are timed such that the shocks coalesce just inside the ice layer which minimizes the entropy generation in the layer. The first shock enters the ice close to ∼14 ns after it has traversed the ablator.
(a) (Color) Predicted trajectory of equivalent THD and DT (red) implosions in the hot spot ρR, T plane. The implosions are essentially identical until the average temperature in the hot spot reaches ∼3 keV at which time self heating due to α-particle deposition in the DT target begins to become energetically important. The segment of the THD trajectory representing the period of FWHM of x-ray and neutron emission is also shown. (b). (Color) Time sequence (21.19, 21.25, 21.28, 21.32) ns of simulated density fields from 2D simulations, producing the data in 4(a) roughly 40 ps apart. Prior to significant α-heating the THD (lower sequence) and DT (upper sequence) targets look very similar. Once α-heating becomes significant in the DT fuel, the spikes of ice at the hot/cold fuel interface seen in the THD implosion are ablated and the back pressure is enough to halt the implosion by ignition time. In contrast, the hot spot in the THD target continues to shrink as the cooler ice fingers continue to fall towards the center. (c). (Color) Time sequence from a simulated THD implosion of x-ray images filtered for >10 keV, which are very close to the actual hot spot size and low mode shape. As the implosion progresses, the hot spot shrinks as Rayleigh-Taylor instability continues to cause fingers of cold fuel to penetrate ever further into the hot core. The images used 10 μm and 30 ps temporal and spatial resolution, respectively.
(a) X-ray power (solid) emitted from the THD implosion simulation shown in Fig. 4 vs. time. The peak x-ray emission occurs very close to the peak thermonuclear energy production rate, shown by the dashed line normalized to the x-ray production rate. (b) Energy production rates in simulations of THD (dashed line) and the equivalent igniting DT target (solid line). The energy production rate indicated is for the DT ignition target. The peak energy production rate for the THD target has been normalized to that for the DT target to make it easier to compare the shape and timing of the burn history in the two targets. In this particular case, peak energy production rate in the DT occurs slightly later (∼80 ps) than that in the dudded target. This is largely due to the additional time it takes for the hot spot formation process to advance in the run up to ignition.
Simulated 1D clean yield and burn averaged temperature as a function of %D in hydro-equivalent THD targets. The temperature increases with the fraction of deuterium because of a small amount of α-particle heating. As a result the yield increases slightly faster than linear in deuterium fraction. The central gas composition has been assumed to be the same as that of the ice rather than the more hydrogen rich composition that would be expected in order to provide an upper limit. The effect of the depletion of D and T in the initial central gas region, for the case of only 2% D fraction which consequently has a large hydrogen level in the central gas, is calculated to decrease these yields by ∼40%.
(Color) Schematic showing how the four input implosion parameters for ITF (mix, velocity, adiabat, shape) relate to the outputs ρR and T.
(a) Amplitude of perturbation applied to the outer surface of the ablator in the 2D simulations reported in this article. This is composed of a sum of modes <100 with cosine amplitudes as defined in Sec. IV A. (b) Amplitude of perturbation applied to the inner ice surface in the 2D simulations reported in this article. This is composed of a sum of modes <100 with cosine amplitudes as defined in Sec. IV A.
(a) Simulated maximum implosion velocity of the fuel as a function of peak x-ray drive flux for the THD capsule shown in Fig. 2 (solid). The nominal x-ray drive (x = 1 corresponding to TR = 300 eV) used is shown in Fig. 3. The drive amplitude was varied by multiplying the flux during the 4th (main) pulse by “x.” The equivalent peak radiation temperature is also shown. The dashed curve is a logarithmic fit . (b) Simulated burn averaged hot spot ion temperature as a function of peak x-ray drive flux for the THD capsule shown in Fig. 2. Tion is expected to vary linearly with velocity and therefore is also approximately linear in the drive [see Fig. 9(a)]. The dashed curve is the linear fit . (c) Simulated burn averaged down scattered neutron fraction (dsf) as a function of peak x-ray drive flux for the THD capsule shown in Fig. 2. The dashed curve is the quadratic fit . (d) Simulated neutron yield as a function of peak x-ray drive flux for the THD capsule shown in Fig. 2. Over-plotted (dash) is the 1D scaling relation from Ref. 10, which reproduces the calculated behavior very well over most of the range.
(a) (Color) Simulated down scattered neutron fraction vs. mass averaged fuel entropy (adiabat) at peak velocity from ensemble of 1D and 2D simulations for the capsule show in Fig. 2 in which various shock mis-timings have been introduced. The peak drive was ∼285 eV equivalent to a laser energy ∼1 MJ. The composition was as described in Sec. III (for the solid layer—H:D:T = 24:2:74; for the central gas at t = 0 H:D:T = 0.92:0.0078:0.072). 1D results are red, but show the same quantitative trend as the 2D results. Key: squares, up to ±60% 1st shock level combined with −200 ps 4th shock mis-timing; crosses, ±35% 1st shock level mis-timing only; triangles, 4th shock advance between −100 and −400 ps (dsf reduction increases as shock advance increases); 45° crosses, nominal shock timing with up to ±40% asymmetry in the imploded configuration (has little effect); circles, 4th shock delay by up to 400ps; diamonds, nominal 1D simulations. (b) Simulated x-ray image sizes for the set of simulations described in Fig 10(a). The size increases monotonically as the fuel entropy/adiabat or degree of shock mis-timing increases and compressibility decreases. (c) Simulated burn averaged ion temperatures for the set of simulations described in Fig 10(a). A similar trend to the other observables is seen. (d) Simulated neutron yield for the set of simulations described in Fig 10(a). The theme of performance vs shock timing holds for yield also. However the spread in the values due to other effects such as 1D vs 2D and small velocity changes as the shocks are delayed, for example, are more obvious in this observable.
(a) Simulated neutron yield as a function of ablator roughness for 1 MJ (solid) and 1.3 MJ (dash) implosions of the capsule shown in Fig. 2. The surface was varied by applying a multiplier (x-axis) on the surface form shown in Fig. 8(a). Also shown (dot) is the 1 MJ curve plotted as if the roughness were only 50% of that applied. This curve is close to the 1.3 MJ curve because the predicted ablation front growth factors at 1 MJ are ∼50% of those at 1.3 MJ. (b) As Fig. 11(a) but for inner ice surface roughness. In this case there is no difference between the scaling between 1 MJ (triangles) and 1.3 MJ (squares). We attribute this to two factors. First the ice roughness is the dominant effect reducing hot spot yield in these simulations. Second both 1 and 1.3 MJ implosions undergo similar deceleration growth so that the yield degradation is similar in both cases.
Predicted x-ray spectrum at peak x-ray power for a nominal THD implosion meeting design requirements. The spectral emission peaks at ∼10 keV. The cut off on the low energy side is due to attenuation by the dense fuel shell. The fall off on the high energy side follows the bremsstrahlung relation. The dense shell is effectively optically thin above ∼30 keV. The K-edge due to Ge in the ablator can be seen clearly at about 10 keV.
P0 coefficient of the 20% contour vs time from gated x-ray images filtered for >10 keV for a THD implosion simulation (solid). The radius of the hot spot (50% density surface) is also shown (dot). As can be seen the x-ray images are slightly smaller than the hot spot, but the size is otherwise well approximated. The normalized emitted power is plotted for reference (dash).
Simulated neutron spectrum from THD (2%) (lower curve) and equivalent igniting DT target (upper curve) showing how important physics signatures are related to various parts of the spectrum.
(Color) World map of THD fuel ρ-R at stagnation from a 3D hydra simulation deliberately engineered to have a large Y 4,4 asymmetry resulting in ρR variations ∼2:1. The section of the shell probed by neutrons (assuming a central point source) scattered into the 10–12 MeV energy range are shown for three of the neutron spectrum detectors on NIF. The central dark region is the section of each LOS sampling the primary 13–15 MeV neutrons. The ρR inferred along each line of sight from the dsf varies because both “primary” and scattered neutrons vary because of the shell ρR variations.
(Color) Correlation between ρR vs down scatter fraction averaged over 4π from a large 2D simulation data base (green). The down scatter fraction is sensitive to the amount of mixing between the ice and ablator [(red) highest 20% vs (blue) lowest 20%]. In the absence of additional information about mixing this introduces an uncertainty in ρR∼±7%.
(Color) Density maps at peak energy production and time integrated primary neutron images (13–20MeV) for THD (top), 1.6 MJ yield DT (middle), and 12 MJ yield DT (bottom) implosions. These are integrated hohlraum simulations that resolve up to mode l∼8 from drive asymmetry alone. No other sources of perturbation have been included. No density image is shown for the DT target because the explosion is very rapid. The THD is the equivalent of the 1.6 MJ DT implosion. The neutron image is weighted towards the central, hottest portion of the hotspot, which grows as the burn wave propagates further with increasing yield.
(a) and (b) 10 μm/70 ps, spatial/temporal resolution, simulated Compton radiograph of a THD implosion: no noise (left) and with noise expected when using short-pulse NIF UV beams to generate the backlighter.
(Color) Predictions of yield from simulated 2D DT implosions plotted against the observable performance metric, ITFX, (Y × dsf2.3), (red dots) and the measurable Lawson criterion (ρR 2 × T4.5 × YOC) (black dots) from the equivalent THD implosions. The performance metric is normalized such that ITFX = 1 when Y DT = 1 MJ. There are 1000 simulation pairs which include various combinations and degrees of off nominal specification to produce the performance variations seen. Both metrics order the DT data well.
(Color) Trajectories in Tion–ρR space showing the threshold behavior of ignition near ITFX or GLC equal unity. Contours of ITFX (GLC) on all plots range from 10−3 to 10. (a) Trajectory of a THD capsule with GLC = 1.5 during the compression of the fuel starting at the time of peak kinetic energy. Points along the curve mark the time of peak kinetic energy, as well as 10% K.E., peak burn rate, and −10% K.E. (expansion). (b) The companion 50/50 implosion with ITF = 1.5 shows the rapid heating due to alpha particle deposition as the implosion approaches maximum compression. (c) The THD and equivalent DT implosion trajectories for an implosion with GLC = 0.85. Although there is some alpha heating, it is not rapid enough to heat the fuel to ignition conditions. (d) An implosion with a GLC = 1.05 has just enough alpha heating power to continue heating during the initial phases of expansion and reaches ignition conditions.
(Color) Probability of ignition (Y > 1 MJ) (red) constructed from the numerical database shown in Fig. 19. Also shown are the expected DT experiment distribution (black) after the tuning campaign and how this distribution is distorted by measurement error of ±10% in each of Y and dsf (blue). Multiple shots should help narrow the latter towards the true distribution.
Physics properties and observables of THD and DT implosions.
Expected THD implosion observables predicted by a large suite of hydra simulations for experiments meeting point design specifications6 after a successful tuning campaign in which the laser pulse and target parameters have been adjusted to meet the point design specifications.7
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