Diagram of the experiment configuration and diagnostic lines of sight. The opacity sample is not shown to scale. Time-gated pinhole camera images from and lines of sight are shown above the diagram. The size scale for the images is different than for the diagrams and the radiance scale for the images at each time is also different. The times given are with respect to peak power emerging from the end of the dynamic Hohlraum. The diagram and images within the left and right dashed boxes correspond to the heating and backlighting phases of the opacity experiment, respectively.
Diagnostic configuration of the time-integrated space-resolved convex KAP crystal spectrometers used to measure the opacity sample transmission. Typical data from the range is shown from the two spectrally resolved slit images.
Calibration spectra used to determine the spectral resolution. Low principal quantum number satellites are partially resolved, but unresolved higher quantum number satellites broaden the main characteristic lines.
Spectral resolution as a function of wavelength. The circles correspond to crystal resolution measurements, the green line indicates the small contribution from source broadening, the red line is a theoretical calculation of the crystal resolution from Ref. 16, and the dashed red line represents the theoretical crystal resolution reduced by a factor of 2.3 to approximately match the data. The black solid line is a convolution of the source contribution and the crystal contribution.
Backlighter radiance averaged over the central diameter spot as a function of time. The zero of the time axis corresponds to peak power emerging from the end of the dynamic Hohlraum. The uncertainties correspond to the influence of timing uncertainty on the normalization of gated pinhole images with XRD signals.
Spectral radiance of the backlighter (red) compared to the sample self-emission (blue) and a Planckian at the sample temperature (green). The sample self-emission was computed with the PRISMSPECT code at the indicated plasma conditions. The self-emission in the and ranges corresponds to the thin-Fe and thick-Fe samples (see Ref. 5).
Backlighter spectrum (black and blue lines, (a)) inferred from an experiment without the Fe and Mg samples (CH tamper only) compared to a subsequent experiment [red and magenta lines (a)] that used a CH tamped Fe and Mg samples. The Fe areal density was , corresponding to the “thin-Fe” sample(Ref. 5) The complete spectrum is stitched together using two separate spectrometers that overlap in the range. The transmission is inferred by dividing the absorption spectrum from the Fe and Mg samples by the equivalent spectrum obtained with the CH tamper only. The spectrum shown in (b) corresponds to an average over 12 separate reproducible transmission measurements using a thick Fe sample with Fe areal density (see Ref. 5).
Calculated optical depth (blue) and transmission (red) for the Mg XI , , and lines used to infer the plasma electron density. The optical depth profiles correspond to an electron density of and a Mg areal density of . The optical depth and transmission profiles are different for lines with substantial depth (such as ) and they are almost the same for lines with small depth . The transmission profile including instrument broadening is shown in black.
Mg XI absorption lines expressed in effective counts. The uncertainty in each wavelength channel is the square root of the number of counts. The background fit (green) used a polynomial representation. Fits were performed using both detailed line profiles (red) and simple Voigt profiles (blue). The large absorption for the and lines leads to high accuracy and it is possible to distinguish between the fits. The and lines are weak and the fit quality is equally good with both profiles.
Calculated Mg XI absorption linewidths as a function of electron density. The widths include the instrument resolution contribution and account for the sample areal densities obtained in Ref. 5.
Mg charge state fractions at (red), 155 eV (black) and 160 eV (blue), expressed relative to their values at 155 eV. The calculations were performed using the PRISMSPECT code at a electron density. The relative population of H-like Mg changes by approximately 40% for a 5 eV temperature change, while the He-like population barely changes at all.
Calculated Mg absorption spectra for three different temperatures, at and the areal densities given in Ref. 5. The change in the absorption while the remains almost unchanged reflects the population variations illustrated in Fig. 11.
Mg XII/XI line ratios as a function of electron temperature. The dotted-dashed, solid, and dashed lines represent electron densities of 8.6, 6.9, and , respectively. These densities correspond to the , nominal, and density values determined from the line broadening analysis. The mean and ratios measured in the experiment are shown as horizontal lines.
Electron temperature and density inferred from the Mg spectra in seven Z experiments. The dots represent the individual experiment results, the red line is the mean, and the green lines are the uncertainties corresponding to in density and in temperature. The individual uncertainties include contributions from measurement errors and the influence of density variations on temperature.
Comparison of measured transmission (blue points with error bars) with three different models (solid red lines) in the spectral range encompassing the Mg absorption lines. The experiment uncertainties are the relative uncertainty as a function of wavelength. The total transmission uncertainty is obtained by convolving with an additional uncertainty (see Ref. 5). The model calculations were performed at the same plasma conditions: , . The normalized is approximately unity for all three models, demonstrating that all three reproduce the data at a single temperature and density value.
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