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Short-wavelength and three-dimensional instability evolution in National Ignition Facility ignition capsule designs
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10.1063/1.3609834
/content/aip/journal/pop/18/8/10.1063/1.3609834
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/8/10.1063/1.3609834
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

“Pie diagram” of the current Rev. 5 ignition capsule design. The dopant concentrations and layer thicknesses shown in the figure result from the re-optimization described in Sec. II.

Image of FIG. 2.
FIG. 2.

Hohlraum hard x-ray fraction (fraction of x-ray radiation at an energy greater than 1.8 keV) versus radiation temperature. The diamonds correspond to NIF measurements, the squares to integrated hohlraum simulations of those experiments run with HYDRA, and the circles to integrated simulations run with Lasnex. The solid curve plots the hard x-ray fraction from an x-ray source spectrum used to drive high-resolution capsule simulations extracted from a Lasnex hohlraum simulation. The dashed curve is the analogous hard x-ray fraction from a HYDRA-derived x-ray source, and the dashed-dotted curve shows the result of multiplying the hard x-ray fraction of that source by a factor of 1.2. The latter curve reasonably reproduces the hard x-ray fractions from the experimental data base and was used for the high-resolution capsule simulations used in re-optimizing the capsule design.

Image of FIG. 3.
FIG. 3.

Comparison of density profiles during the acceleration phase for the current Rev. 5 design (solid) and the previous Rev. 4 design (dashed) driven by the updated x-ray source. The notch in each profile corresponds to the interface between the dense DT fuel to the left and the lower density plastic ablator to the right. With the updated x-ray source, the previous Rev. 4 design has an unacceptably large Atwood number at this interface leading to substantial mixing of ablator material into the fuel.

Image of FIG. 4.
FIG. 4.

Roughness power spectra versus Legendre mode number as used in high-resolution capsule simulations. The spectra represent fits to measured shell roughnesses as well as constraints found necessary on the roughness based on simulations.

Image of FIG. 5.
FIG. 5.

(Color online) High-resolution 2-D simulation of the current Rev. 5 capsule design shown at peak implosion velocity. The material region is shown on the left half of the panel and the density on the right half. This simulation was run on a 15° wedge at the capsule waist with 1217 × 1024 zones in the radial and angular directions, respectively. The resolution is sufficient to capture Legendre mode numbers of ℓ = 12–1200. The fuel-ablator interface separates the dark blue from the light blue regions. Mixing at this interface results in a fuel clean mass fraction of 0.77 at peak velocity.

Image of FIG. 6.
FIG. 6.

(Color online) High-resolution 2-D simulation of the previous Rev. 4 capsule design using an updated x-ray source. The simulation parameters and resolution are similar to those of Fig. 5. The higher fuel-ablator Atwood number for this implosion as compared to Rev. 5 (see Fig. 3) results in the unacceptable degree of mix between the fuel and ablator. As a result of this mixing, the fuel clean fraction has been reduced to 0.21 at peak velocity.

Image of FIG. 7.
FIG. 7.

Summary of high-resolution capsule simulations plotted in the plane of fuel clean fraction at peak velocity versus peak ablator dopant concentration. The open circles correspond to capsule designs at the 1.55 MJ scale (Rev. 4) and the filled symbols to designs at the 1.3 MJ scale (Rev. 5). By successively increasing the ablator dopant concentration and increasing the fuel and ablator thicknesses, the fuel clean fraction can be raised from 0.21 (Rev. 4) to the 0.77 of the current Rev. 5 design. The effects of the uncertainties in the measured hard x-ray fraction and in the ablator dopant concentration as fabricated are represented by the error bars. Note that the clean fraction reaches a local maximum at 1.0 at. % Ge and decreases when the concentration is increased further to 1.2 at. %.

Image of FIG. 8.
FIG. 8.

(Color online) Results at peak velocity of seeding roughness on selected interfaces only in the current Rev. 5 design: (a) seeding roughness at the inner ice surface only, (b) seeding the fuel-ablator interface only, (c) seeding the internal dopant layers only, and (d) seeding the outer ablator surface only. Seeding at the outer ablator surface results in instability growth predominantly in the relatively long wavelength range of ℓ ≅ 30, but is the largest contributor to the mix fraction of ablator material into the fuel.

Image of FIG. 9.
FIG. 9.

(Color online) 3-D high-resolution simulation of Rev. 5 shown at peak velocity. This simulation was run on a 2.5° × 2.5° patch at the capsule waist with 1006 × 256 × 256 zones in the radial and angular directions, respectively, and resolves modes ℓ = 72–1200. The resulting peak velocity fuel clean fraction is 0.76, very close to the analogous 2-D result of 0.77. Note, however, that due to the limited angular extent that can be simulated in 3-D (2.5° versus 15°), this simulation cannot resolve the ℓ ≅ 30 growth which is a substantial contributor to the mix fraction. Nevertheless, that the mix layer remains coherent and does not develop turbulence in 3-D suggest that the 2-D simulations should be approximately correct in optimizing the mix.

Image of FIG. 10.
FIG. 10.

(Color online) Fuel-ablator interface from the 3-D high-resolution simulation of Fig. 9: (a) seen from the ablator side, and (b) seen from the fuel side. From the fuel side, mushroom-like structures can be seen around the tips of the bubbles of low density ablator material rising into the higher density fuel. This is uncharacteristic of coupled Rayleigh-Taylor-Kelvin-Helmholtz instabilities where the mushroom-like structures typically appear around the spike tips and not the bubble heads.

Image of FIG. 11.
FIG. 11.

(Color online) Initial outer ablator surface used in a 3-D lower resolution simulation of Rev. 5 (see Fig. 12). The surface is taken from a measurement of a fabricated prototype shell and includes a number of bumps and divots ranging up to 400 nm in height.

Image of FIG. 12.
FIG. 12.

(Color online) 3-D lower resolution simulation of Rev. 5 at peak implosion velocity. The color scale gives the density. This simulation includes 1004 × 512 × 512 zones and resolves modes ℓ = 4–200. In addition to the outer ablator roughness (Fig. 11), power spectrum roughness was initialized on the inner ice surface, the inner ablator surface, and all internal interfaces. Nonlinearly large perturbations have grown up, visible in the dense red-colored region, though they have not broken through the shell.

Image of FIG. 13.
FIG. 13.

(Color online) The fuel-ablator interface at peak velocity from the simulation of Fig. 12 as viewed from the ablator side. The initial ablator defects (Fig. 11) have produced a number of pronounced features at the fuel ablator interface of nonlinear amplitudes.

Image of FIG. 14.
FIG. 14.

(Color online) Comparison of height maps of the fuel ablator interface at peak velocity from (a) the 3-D simulation (cf. Fig. 13) and (b) the prediction of linear growth factors. The color scale gives the radial location of the interface from the implosion center and is the same in both (a) and (b). The agreement is remarkably close between the growth factor prediction and the simulation result, despite the perturbation amplitudes having reached weakly nonlinear amplitudes.

Image of FIG. 15.
FIG. 15.

(Color online) Hot spot shape close to ignition time from the simulation of Fig. 12. The left and right boundaries of the simulation domain show the ion temperature and material density, respectively. The red surface traces the 400 g/cm3 density isosurface which approximately captures the shape of the igniting hot spot. Large upward going bubbles and downward falling spike sheets are evident at the hot spot boundary. Despite these perturbations, the simulation ignited to give a yield of 17.63 MJ.

Image of FIG. 16.
FIG. 16.

(Color online) Comparison of height maps of the hot spot shape from the 3-D simulation (cf. Fig. 15) and hot spot growth factor predictions. The hot spot growth factors can be used as an upper bound on the hot spot surface RMS but do not capture the detailed hot spot shape as they do the peak velocity fuel-ablator interface shape. The effect of nonlinearities are apparently non-negligible for the hot spot.

Image of FIG. 17.
FIG. 17.

(Color online) Comparison of 3-D Miranda and 2-D HYDRA simulations of a fill tube test problem at selected times: (a) in the plane of the 3-D fill hole tilt and (b) out of the plane of tilt. The 3-D Miranda simulation includes a tilt to the fill hole of 1.72°, a taper to the fill hole from 8 μm to 5.2 μm, and fill hole roughness. Despite these perturbations, the 2-D HYDRA simulation quite closely captures the propagation rate and lateral expansion of the jet generated by the fill tube perturbation.

Image of FIG. 18.
FIG. 18.

Comparison of injected ablator and glass fill tube mass from the Miranda (solid) and HYDRA (dashed-dotted) simulations shown in Fig. 17. The cluster of lines to the left give the integrated mass of ablator material in the simulation domains (integrated transversely and as a running integral in the axial direction) as a function of axial distance, and the cluster of lines in the lower right give the integrated mass of glass. Both simulations are in reasonable agreement on the mass included in the fill tube jet (∼20 ng at 10.0 ns) but show a factor of a few discrepancy in the mass of glass injected.

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/content/aip/journal/pop/18/8/10.1063/1.3609834
2011-08-03
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Short-wavelength and three-dimensional instability evolution in National Ignition Facility ignition capsule designs
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/8/10.1063/1.3609834
10.1063/1.3609834
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