Schematic of the solar interior. The temperature and density information are from Ref. 4 and the values for the location of the radiation convection boundary are from Ref. 5.
Frequency dependent opacity (Refs. 13 and 14) for a 17 element solar composition (Ref. 6) near the base of the solar convection zone compared to . The electron temperature and density were 193 eV and , respectively.
Characteristics of the solar interior composition. The histogram in a provides the mass fractions (Ref. 16). The histogram in b is the fractional contribution to the Rosseland mean evaluated near the base of the solar convection zone using the OPAS opacity model (Ref. 17).
Physical processes responsible for the contribution to opacity by different elements. The calculated (Refs. 13 and 14) total opacity of the solar mixture at the base of the convection zone is compared with the contribution from hydrogen, oxygen, and iron in (a), (b), and (c), respectively.
The iron charge state distribution as a function of electron temperature and density at different depths within the sun. The and values are from Ref. 4 and the PrismSPECT model (Ref. 18) was used to calculate the charge state distribution. The red curve corresponds to just below the convection zone (, , ), the green curve corresponds to , and the blue curve corresponds to . The black curve with triangles corresponds to the distribution for conditions in Z experiments.
Method for transmission measurements used to test opacity models. A spectrometer views a backlight through an x-ray heated foil. The sample transmission as a function of photon energy is determined using measurements of a low-Z tamper only foil (diagram 1) and measurements of the sample material of interest surrounded by the tamper (diagram 2). The synthetic backlighter spectrum is a 314 eV Planckian that is representative of the backlighter used in iron experiments (Refs. 19 and 20). The absorption spectrum was calculated with PrismSPECT (Ref. 18) at the experiment temperature and density values and the transmission spectrum was obtained by dividing the absorption spectrum by the backlighter spectrum.
Comparison of absorption spectra from two sequential Z experiments. No scaling or other intensity adjustments were applied in this comparison, other than correcting both spectra for the film response.
Diagram of the experiment configuration used in point projection opacity measurements (adapted from Ref. 22).
X-ray heating provides the ability to volumetrically heat opacity samples (a). A significant portion of the heating x rays stream through the sample, providing relatively uniform but inefficient heating. Transmissions through room temperature iron/magnesium foil and iron/magnesium plasma heated to 150 eV are shown in (b), compared to the heating x-ray spectrum provided by a 200 eV Planckian source (c). The areal density and composition of both the room temperature foil and the plasma are the same as in Refs. 19 and 20.
X-ray absorption spectra exhibiting reflectivity defects that may masquerade as spectral lines. The image in (a) is from Z experiments (Refs. 19 and 20) and the image in (b) is adapted from Ref. 23. Vigilance is required in experiments to ensure that such defects do not introduce artifacts into the inferred transmission.
Calculated (Ref. 18) transmission for iron plasma at the experimental conditions in Refs. 19 and 20. The blue curve is the ideal case and the red curve accounts for an instrument spectral resolution .
Comparison of x-ray absorption spectra recorded on two different types of film, Kodak DEF and 101–07. The agreement between the two implies that the conversion of film density to film exposure was self-consistent.
Self-emission can contribute to the signal recorded by the spectrometer (a). A hypothetical situation is quantitatively illustrated in (b) using PrismSPECT (Ref. 18) calculations for iron plasma self-emission (green curve) and absorption spectra (red curve). The plasma temperature is assumed to be 125 eV and the backlighter is assumed to be a 170 eV Planckian. The most optically thick lines have self-emission that peaks at the blackbody limit, corresponding in this case to a 125 eV Planckian.
Self-emission grows with sample temperature and competes more strongly with a specified backlighter (a). The transmission calculated (Ref. 18) for a portion of the spectrum is illustrated both with and without self-emission in (b). The backlighter was assumed to be a 170 eV Planckian and the sample temperature was 150 eV. Both transmission spectra include convolution with instrument resolution.
Self-emission from iron plasma at 150 eV electron temperature is compared with 170 and 314 eV Planckian backlighter spectra in (a). The ideal transmission without self-emission and the transmission including self-emission are almost the same if the backlighter spectrum corresponds to a 314 eV Planckian (b). Both transmission spectra include convolution with instrument resolution.
Pioneering opacity experiments primarily used laser heated fibers coated with rare-earth elements to produce the backlighter. The La spectrum is adapted from Ref. 31 and the Nd spectrum is adapted from Ref. 34.
Dynamic Hohlraum backlighter diagram (a). The stagnation of a radiating shock on the pinch axis produces a bright continuum source. A time-gated x-ray pinhole image is shown in (b) and a plot of relative intensity as a function of photon energy is shown in (c).The equivalent brightness temperature is (Ref. 20).
Evaluation of transmission accuracy using experiments with different thickness samples (a). Examples of experiments that demonstrated high quality using the sample thickness scaling method are shown in (b) and (c), adapted from Refs. 19 and 62, respectively.
Calculated (Ref. 18) charge state distribution for Mg at 150 eV (black), 155 eV (red), and 160 eV (blue) electron temperatures. The electron density was in all cases. These ±5 eV temperature changes induce less than 1% change in the He-like population, but the H-like population changes by approximately ±40%. The Li-like population changes by a smaller amount.
Typical -shell absorption spectrum with features from H-, He-, and Li-like Mg (a). The spectrum in (a) represents the average transmission from the experiments in Ref. 19. PrismSPECT calculations of an expanded view of the to transitions in these three charge states and a simplified energy level diagram illustrate the energy shift from nuclear screening by additional spectator electrons in He-like and Li-like ions (b).
Calculated (Ref. 18) absorption from and at the three temperatures corresponding to Fig. 19 charge state distributions. The instrument resolution effect is included.
Calculated absorption line strength ratio as a function of electron temperature. The three curves correspond to three different electron densities. The horizontal line corresponds to the mean ratio value measured in the experiments in Refs. 19 and 20 and the dashed lines are the ratio uncertainties. The experimental temperature lies within the cross-hatched region.
Diagram of point projection radiography method used to measure sample expansion and thus measure the sample density. A dispersive element such as a crystal is often inserted in front of the detector to provide spectrally resolved information, greatly enhancing the radiograph contrast.
Example of Stark-broadened line profile calculations (Refs. 76 and 77) (a). The red, green, and blue curves correspond to 0.5, 1.0, and electron densities, respectively. These opacity profiles are converted to transmission and then convolved with the instrument resolution before comparing with the experiment (Ref. 20). The plot in (b) illustrates the full width at half maximum as a function of electron density. The areal density and instrument resolution in (b) correspond to the Z experiments in Refs. 19 and 20.
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