Opacity of iron, nickel, and copper plasmas in the x-ray wavelength range: Theoretical interpretation of $2p-3d$ absorption spectra

This paper deals with theoretical studies on the $2p-3d$ absorption in iron, nickel, and copper plasmas related to LULI2000 (Laboratoire pour l'Utilisation des Lasers Intenses, 2000J facility) measurements in which target temperatures were of the order of 20 eV and plasma densities were in the range 0.004–0.01 ${\mathrm{g}/\mathrm{cm}}^3$. The radiatively heated targets were close to local thermodynamic equilibrium (LTE). The structure of $2p-3d$ transitions has been studied with the help of the statistical superconfiguration opacity code sco and with the fine-structure atomic physics codes hullac and fac. A new mixed version of the sco code allowing one to treat part of the configurations by detailed calculation based on the Cowan’s code rcg has been also used in these comparisons. Special attention was paid to comparisons between theory and experiment concerning the term features which cannot be reproduced by sco. The differences in the spin-orbit splitting and the statistical (thermal) broadening of the $2p-3d$ transitions have been investigated as a function of the atomic number $Z$. It appears that at the conditions of the experiment the role of the term and configuration broadening was different in the three analyzed elements, this broadening being sensitive to the atomic number. Some effects of the temperature gradients and possible non-LTE effects have been studied with the help of the radiative-collisional code scric. The sensitivity of the $2p-3d$ structures with respect to temperature and density in medium-$Z$ plasmas may be helpful for diagnostics of LTE plasmas especially in future experiments on the $\Delta n=0$ absorption in medium-$Z$ plasmas for astrophysical applications.

Figure 1

Scheme of the LULI2000 experiment

Figure 2

Density (a) and temperature (b) profiles versus the Lagrangian coordinate for the iron foil of 20 $\mu$g/cm${}^2$ given by the numerical simulations at probing time. Three different radiation temperature data have been used corresponding to the average (mid) measurements of $\mu$DMX and to its lower (min) and upper (max) bounds (one standard deviation). Temperature and density are plotted as a function of the mesh number. Laser energy and three maximum radiative temperatures are presented in Table (shot 28).

Figure 3

Same as in Fig. 2 in the case of the shot 38 with a nickel sample of areal mass 20 $\mu$g/cm${}^2$.

Figure 4

Same as in Fig. 2 in the case of the shot 31 with a copper sample of areal mass 40 $\mu$ g/cm${}^2$.

Figure 5

Spectral transmissions of iron, nickel, and copper samples with areal mass of 20 $\mu$g/cm${}^2$ measured at LULI2000 laser facility. $2p-3d$ structures are indicated by thicker lines.

Figure 6

Comparison of two spectral transmissions of copper samples with areal mass of 40 $\mu$g/cm${}^2$ (shots 21 and 31) measured at LULI2000 laser facility. The laser energy at these two shots was respectively 80 and 64 J. We display also the absolute value of the difference between these transmissions.

Figure 7

Two measured spectral transmissions of iron. The areal mass of the target was 20 $\mu$g/cm${}^2$. For comparison we also display three transmissions calculated using the sco code taking the same areal mass, at plasma density 4 mg/cm${}^3$ and at three values of temperature: 18, 22, and 25 eV. $Z$* values for the conditions of the three calculated curves are given in Table .

Figure 8

Measured spectral transmissions of iron plasma (shot 28) of areal mass 20 $\mu$g/cm${}^2$ with hullac, fac, scorcg, and sco calculated transmission curves. In all calculations the temperature was 22 eV and plasma density was 4 mg/cm${}^3$. $Z$* value from all the codes is practically the same (7.12 from the sco and scorcg codes, and 7.13 from the hullac and fac codes).

Figure 9

Transmission of an iron plasma around the $2p-3d$ array calculated with the hullac detailed code. The temperature is 22 eV, density is 4 mg/cm${}^3$, and areal mass is 20 $\mu$g/cm${}^2$. Convolution by Gaussian curve with $\lambda /\delta \lambda =400$ has been performed. Fe vi to Fe xi ions are accounted for. Computation includes only the complete $3p^6$ subshell (red curve), $3p^6$ and $3p^5$ subshells (green), or $3p^6$, $3p^5$, and $3p^4$ subshells (blue). Collisional broadening is included in the main figure. The inset shows the plasma transmission around 17 Å with (solid lines) and without (broken lines) collisions.

Figure 10

Transmission of an iron plasma with an areal mass of 20 $\mu$g/cm${}^2$. Experimental data (shot 28) are presented together with predictions from sco (Sec. 3c) with a $\Delta E=4\text{eV}$ average, hullac and fac with $\lambda /\delta \lambda =400$ average. In calculations 22 eV temperature and 4 mg/cm${}^3$ density is assumed. Collisional broadening is not included in hullac and fac calculations. fac data with and without autoionization are both presented.

Figure 11

Effect of configuration interaction in an iron plasma as computed with hullac. Subshells $3p^4$, $3p^5$, $3p^6$ are included. Collisional broadening is accounted for. The plasma parameters are the same as in Fig. 9

Figure 12

Measured spectral transmissions of iron plasma of areal mass 20 $\mu$g/cm${}^2$ compared with calculated transmission curves obtained using the scric code in which convolution with the hydrodynamic profiles of temperature and density has been performed. The maximum radiative temperatures correspond to the $\mu$DMX measurements; see text.

Figure 13

Transmission of iron ions at 20 eV and 4 mg/cm${}^3$ obtained from the hullac code. Each spectrum is calculated assuming 100% of the relevant ion.

Figure 14

Measured spectral transmission for nickel sample with an areal mass of 20 $\mu$g/cm${}^2$ and calculated sco transmissions at 22 eV temperature and at 10 mg/cm${}^3$ mass density.

Figure 15

Measured spectral transmissions of nickel plasma of areal mass 20 $\mu$g/cm${}^2$ compared with calculated transmission curves obtained using the scorcg code without and with the experimental width corresponding to the resolution of $\lambda /\delta \lambda =400$. The sco code results are also displayed. The theoretical transmission curves have been obtained assuming 21-eV temperature and 4-mg/cm${}^3$ density.

Figure 16

Two measured spectral transmissions for copper samples with an areal mass of 40 $\mu$g/cm${}^2$ and comparison with the sco and scorcg calculations at 16 eV temperature and 5 mg/cm${}^3$ mass density.

Figure 17

Measured spectral transmissions for copper sample with an areal mass of 20 $\mu$g/cm${}^2$ (shot 25) and comparison with transmission calculated with sco assuming 16 eV temperature, 5 mg/cm${}^3$ mass density, and 20 $\mu$g/cm${}^2$ areal mass (two models of RCI), and with transmission measured in the sample of 40 $\mu$g/cm${}^2$ areal mass (shot 31).

Figure 18

Comparison of measured spectral transmissions for copper sample with an areal mass of 40 $\mu$g/cm${}^2$ (shots 31 and 21) with transmissions calculated with hullac assuming mass density of 5 mg/cm${}^3$ and two values of temperature: 15 and 20 eV. $Z$* values calculated by hullac are 5.646 and 6.789 at temperatures 15 and 20 $\text{eV}$, respectively.

Figure 19

Transmission of copper ions at 16 eV and 5 mg/cm${}^3$ obtained from the scorcg code, for an areal mass of a copper plasma 40 $\mu$g/cm${}^2$. Each spectrum is calculated assuming 100% of the relevant ion.

Figure 20

Temperature dependence of iron and copper transmission in the spectral wavelength domain corresponding to $\Delta n=0$ transitions at 3.4 mg/cm${}^3$ mass density. Areal mass of both samples is 10 $\mu$g/cm${}^2$. Nonrelativistic Configuration Interaction is not taken into account.

Figure 21

Temperature dependence of copper and iron transmission from the sco code in the spectral wavelength domain corresponding to $2p-3d$ transitions. The conditions are the same as those of Fig. 20.