Simulated x-ray streak image of a NIF capsule (Ref. 14) implosion made by postprocessing a radiation-hydrodynamic simulation. Shown is the region where the capsule achieves maximum velocity. This image, along with blurred and noisy versions of it, is used to test for accuracy and precision of the analysis technique.
For a spherical shell the x-ray transmission profile is determined largely by the first three moments of density. To demonstrate this, transmission profiles are plotted for three different density profiles which have the same , , and . Even though these density profiles have significantly different peak values the differences in transmission are small and confined to the region around the limb minimum ( in this case). Inside the capsule, transmission profiles are nearly identical as required by the Taylor expansion given in Eq. (10) which is independent of higher moments.
Simulated x-ray intensity profile at various times (black) along with the best fit from the regularization analysis (red) and the inferred unattenuated intensity (blue). In this particular analysis a skewed Gaussian was used for and a fourth order polynomial for . No spatial or temporal blurring in the simulation or the analysis was used in this test.
The presence of fine-scale mix will cause the original (Ref. 14) opacity profile, (solid line), to change. In the left figure this original profile is convolved over a mix region (red dashed line). The resulting deviation in the inferred mass is shown in the right figure, where the abscissa corresponds to the remaining mass fraction inside the ablation front. The amount of the deviation depends on the relative opacities of the different layers and the position of the ablation front.
Comparison of simulated density profiles (black) with the density profiles inferred using the analysis assuming a skewed Gaussian (red), a symmetric Gaussian (dashed green), and a skewed Gaussian where the x-ray streak had of spatial and 50 ps of temporal blurring (dotted blue). These density profiles are those for which the best fits were obtained in Fig. 3. Although the inferred profiles, particularly those for the blurred image, appear to deviate from the actual profiles the moments of are still captured accurately (see next figure).
Comparison of the simulated , , , and (black) with those inferred using the analysis assuming a skewed Gaussian (red), a symmetric Gaussian (dashed green), and a skewed Gaussian where the x-ray streak had of spatial and 50 ps of temporal blurring (dotted blue). These illustrate how little instrumental blurring and the different assumed density profiles affect the results. Note that for the blurred case, even though the spatial blurring is a factor of 2 or more greater than the width of the density profile, agreement (for these average quantities) remains good. The velocity aberration at 16.35 ns in the blurred case occurs at the boundary between doped and undoped CH.
Illustrative scaling of the fractional random error in (diamonds, red) and (asterisks, green) vs the number of counts per resolution element . Each point was derived from the analysis of a synthetic static radiograph with counts based on Poisson statistics. Both and scale closely with .
Ablation pressure and mass ablation rate for the simulated implosion shown in Fig. 6. The values obtained by fitting the simple rocket model to the experimental observables and are shown as red diamonds and compare favorably with the values obtained directly from the hydrodynamic simulation (black line). Around the time of peak velocity (16.5–17.0 ns) the contribution of the capsule back pressure (dashed line) reduces the accelerating force on the capsule causing an underestimate of the ablation pressure based on the simple rocket model.
Schematic (not to scale) of the OMEGA experimental setup. The vanadium foil is glued on to the slot on the backlighter side of the Hohlraum. A matching slot on the opposite side of the Hohlraum allows x-rays to propagate through the imaging slit to the x-ray streak camera. The imaging slit is positioned to magnify the image by a factor of 20.5.
Hohlraum radiation temperature measured using the Dante soft x-ray spectrometer (Ref. 25) (solid black line). The total laser power incident on the Hohlraum is shown as a blue dashed line.
A sample x-ray streak image of an imploding capsule from OMEGA showing the entire time history of the implosion from shock compression to shell acceleration to stagnation at 3.3 ns. The uv timing fiducials are visible at early times.
Streaked x-ray intensity profile from Fig. 11 at four times (black) along with the best fit from the regularization analysis (red) and the inferred backlighter intensity (blue). Note how evolves in time due to changes in x-ray emission from the backlighter foil and time-evolving attenuation by the ablator blow-off. Data were binned 10 pixels in time and space to reduce noise.
Average ablator radius, velocity, , and remaining mass fraction vs time for targets with either thick (red) or thick ablators (black). Data are binned in time allowing statistical uncertainties to be determined from errors in the coefficients of a local linear fit. Binned points (shown with errors bars) are connected by smoothing splines (solid lines). Dashed lines show radiation-hydrodynamic (Ref. 27) simulations of the same spatially averaged quantities.
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