(Color online) Data illustrating burn-region analysis of two very different implosions at OMEGA. The left-hand column corresponds to shot 27456 (-thick, glass-shell capsule), while the right-hand column corresponds to shot 35176 (-thick, plastic-shell capsule); each capsule was filled with and irradiated with a , laser pulse. The vertical lines in (a) and (e) represent statistical error bars for ; the locations of all individual proton tracks on the penumbral image detector are measured to a fraction of a micron, but needs to be binned with a finite interval in in order to achieve acceptable statistics. Note that the significance of the square root appearing as a coefficient of in the vertical axis labels is discussed in the Appendix in connection with Eq. (A5); this slowly varying coefficient is very close to 1.0 for the data shown here. The heavy lines in (a) and (e) are best fits to the data using the approach described in Sec. III and in the Appendix. Contour plots showing total as a function of and peakedness are shown in (b) and (f); the contour levels correspond to , . In (c) and (g) the inferred radial distributions of reactions in the burn regions are shown; each heavy line corresponds to a best fit, while the lighter lines show alternate fits resulting in the total being larger than the minimum value by 1 (indicating an approximate error envelope for the best-fit profile). The corresponding surface brightness distributions are shown in (d) and (h). The parameters describing the profiles are and (shot 27456) and and (shot 35176).
(Color) Comparison of the measured local emission profile, the measured x-ray surface-brightness profile, and 1D simulations for shot 35176. A x-ray image taken at peak nuclear burn time (a exposure) is shown in (b), and its radial profile is shown in (a) together with a 1D simulation. The burn profile [from Fig. 1(g)] is also shown in (a), together with a 1D simulation. In all cases the measured profiles are bold and the 1D profiles are fine. The profiles are arbitrarily normalized to have the same value at .
(Color online) (a) Data showing the relationship of burn-region size to laser energy for implosions of capsules with fill and either plastic or glass shells. For the thin-glass-shell, exploding-pusher implosions (open diamonds), increasing the laser energy results in a dramatically larger burn region radius. For the thick-CH-shell, compressive implosions, for laser energy (solid diamonds), but data are not currently available for lower laser energies. The ion temperature was strongly correlated with , as shown in (b) where has been plotted vs the burn-averaged ion temperature obtained with neutron time-of-flight systems. (c) Comparison of measurements with values from 1D simulations (triangles).
(Color online) (a) A significant difference in the burn size is shown for (closed diamonds) and (open diamonds) fill pressures in implosions of -filled capsules with 19- to plastic shells. is plotted as a function of the areal density measured from proton energy downshifts. (b) The averages of data in (a) are displayed with fuel-shell interface estimates for (large X) and (small x) implosions, demonstrating agreement in the trends of both and . (c) When the average data are displayed with 1–D calculated (triangles) the same trend is present, but the simulations predict lower values overall and much larger values of with decreased fill pressure.
(Color online) (a) Consistently smaller burn radii are produced with SG4 DPPs and targets (solid diamonds) than with SG3 (open diamonds). is plotted as a function of the areal density for implosions of capsules with 19- -thick plastic shells and fill. (b) The averages of burn radii burn data in (a) are displayed with fuel-shell interface estimates from SG3 (small x) and SG4 (large X) implosions,44 demonstrating agreement in the trends of and . (c) When the average data are displayed with the 1D values (triangles), the same trend is present, but the simulations predict lower values and a smaller change in with the change in phase plates. The reduction in with the change from SG3 to SG4 seems largely dominated by the reduction in initial capsule radius from .
(Color online) (a) The dependence of on plastic-shell thickness provides information about mix and convergence (Refs. 2–10). (b) The trend is more obvious when the data for similar capsule thicknesses are averaged (diamonds). The fuel-shell interface estimates (, X) for these implosions and others demonstrate virtually the same trend. (c) The areal densities measured for the same implosions were only weakly dependent on shell thickness. (d) Predicted values of from 1D simulations (triangles) show the same trend as the measurements but lower values.
(Color online) (a) from Eq. (A2) for , 1, and 2, normalized so each curve has the same total yield. As discussed in the text, is the median radius (containing half the yield). (b) The corresponding curves for . (c) for the case of no data binning. Note that hollow profiles of can easily be added to this family of functions.
(Color online) Contours of total for fits to two real data sets (see Fig. 1) as a function of the shape parameter and either the radius , , or . In each case, the contour levels correspond to .
(Color online) Results of applying the direct inversion method to data from shots 27456 (a) and 35176 (b). The plotted data points with error bars result from application of Eq. (A5) to the data shown in Figs. 1(a) and 1(e), though the data were binned slightly differently [with radial bins at the detector equivalent to bins in the burn region of for (a) and for (b), the effective ratios of bin width to were 0.37 and 0.41, respectively]. The uneven spacing of the data points reflects the fact that values of were calculated from for both positive and negative , and values at negative values were reflected to positive . The fine lines correspond to the profiles shown in Figs. 1(d) and 1(h), including the error envelope.
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