Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T11:03:51.223Z Has data issue: false hasContentIssue false
  • English
  • Français

Detailed computation of hot-plasma atomic spectra

Published online by Cambridge University Press:  20 March 2015

Jean-Christophe Pain ,
Franck Gilleron  and
Thomas Blenski
Jean-Christophe Pain*
Affiliation:
CEA, DAM, DIF, Arpajon, France
Franck Gilleron
Affiliation:
CEA, DAM, DIF, Arpajon, France
Thomas Blenski
Affiliation:
CEA, DSM, IRAMIS, Gif-sur-Yvette, France
*
Address correspondence and reprint requests to: Jean-Christophe Pain, CEA, DAM, DIF, F-91297 Arpajon, France. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present recent evolutions of the detailed opacity code SCO-RCG which combines statistical modelings of levels and lines with fine-structure calculations. The code now includes the Partially Resolved Transition Array model, which allows one to replace a complex transition array by a small-scale detailed calculation preserving energy and variance of the genuine transition array and yielding improved higher-order moments. An approximate method for studying the impact of strong magnetic field on opacity and emissivity was also recently implemented. The Zeeman line profile is modeled by fourth-order Gram-Charlier expansion series, which is a Gaussian multiplied by a linear combination of Hermite polynomials. Electron collisional line broadening is often modeled by a Lorentzian function and one has to calculate the convolution of a Lorentzian with Gram-Charlier distribution for a huge number of spectral lines. Since the numerical cost of the direct convolution would be prohibitive, we propose, to obtain the resulting profile, a fast and precise algorithm, relying on a representation of the Gaussian by cubic splines.

Keywords

E1 linesFine structureHot plasmasOpacityRadiative propertiesStatistical methods
Type
Research Article
Information
Laser and Particle Beams , Volume 33 , Issue 2 , June 2015 , pp. 201 - 210
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bailey, J.E., Rochau, G.A., Iglesias, C.A., Abdallah, J. Jr., Macfarlane, J.J., Golovkin, I., Wang, P., Mancini, R.C., Lake, P.W., Moore, T.C., Bump, M., Garcia, O. & Mazevet, S. (2007). Iron-plasma transmission measurements at temperatures above 150 eV. Phys. Rev. Lett. 99, 265002.CrossRefGoogle ScholarPubMed
Bancewicz, M. & Karwowski, J. (1987). On moment-generated spectra of atoms. Physica 145C, 241–248.Google Scholar
Baranger, M. (1958). Problem of overlapping lines in the theory of pressure broadening. Phys. Rev. 111, 494–504.CrossRefGoogle Scholar
Bar-Shalom, A., Oreg, J., Goldstein, W.H., Shvarts, D. & Zigler, A. (1989). Super-transition-arrays: A model for the spectral analysis of hot, dense plasmas. Phys. Rev. A 40, 3183–3193.CrossRefGoogle Scholar
Bauche-Arnoult, C., Bauche, J. & Klapisch, M. (1979). Variance of the distributions of energy levels and of the transition arrays in atomic spectra. Phys. Rev. A 20, 2424–2439.CrossRefGoogle Scholar
Bauche-Arnoult, C., Bauche, J. & Klapisch, M. (1985). Variance of the distributions of energy levels and of the transition arrays in atomic spectra. III. Case of spin-orbit-split arrays. Phys. Rev. A 31, 2248–2259.CrossRefGoogle ScholarPubMed
Bauche, J. & Bauche-Arnoult, C. (1987). Level and line statistics in atomic spectra. J. Phys. B: At. Mol. Opt. Phys. 20, 1659–1677.CrossRefGoogle Scholar
Bauche, J. & Bauche-Arnoult, C. (1990). Statistical properties of atomic spectra. Comput. Phys. Rep. 12, 3–28.CrossRefGoogle Scholar
Bauche, J., Bauche-Arnoult, C. & Klapisch, M. (1988). Transition arrays in the spectra of ionized atoms. Adv. At. Mol. Opt. Phys. 23, 131–195.CrossRefGoogle Scholar
Blenski, T., Grimaldi, A. & Perrot, F. (2000). A superconfiguration code based on the local density approximation. J. Quant. Spectrosc. Radiat. Transfer 65, 91–100.CrossRefGoogle Scholar
Blenski, T., Loisel, G., Poirier, M., Thais, F., Arnault, P., Caillaud, T., Fariaut, J., Gilleron, F., Pain, J.-C., Porcherot, Q., Reverdin, C., Silvert, V., Villette, B., Bastiani-Ceccotti, S., Turck-Chieze, S., Foelsner, W. & De Gaufridy De Dortan, F. (2011 a). Opacity of iron, nickel and copper plasmas in the X-ray wavelength range: Theoretical interpretation of the 2p-3d absorption spectra measured at the LULI2000 facility. Phys. Rev. E 84, 036407.CrossRefGoogle Scholar
Blenski, T., Loisel, G., Poirier, M., Thais, F., Arnault, P., Caillaud, T., Fariaut, J., Gilleron, F., Pain, J.-C., Porcherot, Q., Reverdin, C., Silvert, V., Villette, B., Bastiani-Ceccotti, S., Turck-Chieze, S., Foelsner, W. & De Gaufridy De Dortan, F. (2011 b). Theoretical interpretation of X-rays photo-absorption in medium-Z elements plasmas measured at LULI2000 facility. High Energy Density Phys. 7, 320–326.CrossRefGoogle Scholar
Blinnikov, S. & Moessner, R. (1998). Expansions for nearly Gaussian distributions. Astron. Astrophys. Suppl. Ser. 130, 193–205.CrossRefGoogle Scholar
Cowan, R.D. (1981). The Theory of Atomic Structure and Spectra. Berkeley: University of California.CrossRefGoogle Scholar
Darby, M.I. (1967). Tables of the Brillouin function and of the related function for the spontaneous magnetization. Br. J. Appl. Phys. 18, 1415–1417.CrossRefGoogle Scholar
Davis, A.W. (2005). Gram–Charlier series. In Encyclopedia of Statistical Sciences. 2nd edn., Vol. 3. New York: Wiley-Interscience.Google Scholar
De Boor, C. (1978). A Practical Guide to Splines Series: Applied Mathematical Sciences, 27. New York: Springer-Verlag.CrossRefGoogle Scholar
Di Marco, V.B. & Bombi, G.G. (2001). Mathematical functions for the representation of chromatographic peaks. J. Chromatogr. A 931, 1–30.CrossRefGoogle ScholarPubMed
Dimitrijevic, M.S. & Konjevic, N. (1987). Simple estimates for Stark broadening of ion lines in stellar plasmas. Astron. Astrophys. 172, 345–349.Google Scholar
Doron, R., Mikitchuk, D., Stollberg, C., Rosenzweig, G., Stambulchik, E., Kroupp, E., Maron, Y. & Hammer, D.A. (2014). Determination of magnetic fields based on the Zeeman effect in regimes inaccessible by Zeeman-splitting spectroscopy. High Energy Density Phys. 10, 56–60.CrossRefGoogle Scholar
Gilles, D., Turck-Chieze, S., Loisel, G., Piau, L., Ducret, J.-E., Poirier, M., Blenski, T., Thais, F., Blancard, C., Cosse, P., Faussurier, G., Gilleron, F., Pain, J.-C., Porcherot, Q., Guzik, J.A., Kilcrease, D.P., Magee, N.H., Harris, J., Busquet, M., Delahaye, F., Zeippen, C.J. & Bastiani-Ceccotti, S. (2011). Comparison of Fe and Ni opacity calculations for a better understanding of pulsating stellar envelopes. High Energy Density Phys. 7, 312–319.Google Scholar
Ginocchio, J.N. (1973). Operator averages in a shell-model basis. Phys. Rev. C 8, 135–145.CrossRefGoogle Scholar
Griem, H.R. (1968). Semi-empirical formulas for the electron-impact widths and shifts of isolated ion lines in a plasma. Phys. Rev. 165, 258–266.CrossRefGoogle Scholar
Griem, H.R., Baranger, M., Kolb, A.C. & Oertel, G.K. (1962). Stark broadening of neutral helium lines in a plasma. Phys. Rev. 125, 177–195.CrossRefGoogle Scholar
Hald, A. (2000). The early history of the cumulants and the Gram–Charlier series. Int. Stat. Rev. 68, 137–153.Google Scholar
Ida, T., Ando, M. & Toraya, H. (2000). Extended pseudo-Voigt function for approximating the Voigt profile. J. Appl. Crystallogr. 33, 1311–1316.CrossRefGoogle Scholar
Iglesias, C.A., Lebowitz, J.L. & Macgowan, D. (1983). Electric microfield distributions in strongly coupled plasmas. Phys. Rev. A 28, 1667–1672.CrossRefGoogle Scholar
Iglesias, C.A. & Sonnad, V. (2012). Partially resolved transition array model for atomic spectra. High Energy Density Phys. 8, 154–160.CrossRefGoogle Scholar
Inglis, D.R. & Teller, E. (1939). Ionic depression of series limits in one-electron spectra. Astrophys. J. A90, 439–448.CrossRefGoogle Scholar
Jondeau, E. & Rockinger, M. (2001). Gram–Charlier densities. J. Econ. Dyn. Control 25, 1457–1483.CrossRefGoogle Scholar
Karazija, R. & Kucas, S. (2013). Average characteristics of the configuration interaction in atoms and their applications. J. Quant. Spectrosc. Radiat. Transfer 129, 131–144.CrossRefGoogle Scholar
Kendall, M.G. & Stuart, A. (1969). The Advanced Theory of Statistics, 3rd edn.London: Griffin.Google Scholar
Kucas, S., Jonauskas, V. & Karazija, R. (2005). Calculation of HCI spectra using their global characteristics. Nucl. Instrum. Methods Phys. Res. B 235, 155–159.CrossRefGoogle Scholar
Kucas, S. & Karazija, R. (1993). Global characteristics of atomic spectra and their use for the analysis of spectra. I. energy level spectra. Phys. Scr. 47, 754–764.CrossRefGoogle Scholar
Kucas, S. & Karazija, R. (1995). Global characteristics of atomic spectra and their use for the analysis of spectra. II. characteristic emission spectra. Phys. Scr. 51, 566–577.CrossRefGoogle Scholar
Loisel, G., Arnault, P., Bastiani-Ceccotti, S., Blenski, T., Caillaud, T., Fariaut, J., Foelsner, W., Gilleron, F., Pain, J.-C., Poirier, M., Reverdin, C., Silvert, V., Thais, F., Turck-Chieze, S. & Villette, B. (2009). Absorption spectroscopy of mid and neighboring Z plasmas: Iron, nickel, copper and germanium. High Energy Density Phys. 5, 173–181.CrossRefGoogle Scholar
Mathys, G. & Stenflo, J.O. (1987). Anomalous Zeeman effect and its influence on the line absorption and dispersion coefficients. Astron. Astrophys. 171, 368–377.Google Scholar
Matveev, V.S. (1972). Approximate representation of absorption coefficient and equivalent widths of lines with Voigt profile. Zhurnal Prikladnoi Spectroskopii 16, 228–233.Google Scholar
Matveev, V.S. (1981). Approximate representations of the refractive index of a medium in the region of a Voigt-profile absorption line. Zhurnal Prikladnoi Spectroskopii 35, 528–532.Google Scholar
Moszkowski, S.A. (1962). On the energy distribution of terms and line arrays in atomic spectra. Progr. Theor. Phys. 28, 1–23.CrossRefGoogle Scholar
O'brien, M.C.M. (1992). Using the Gram–Charlier expansion to produce vibronic band shapes in strong coupling. J. Phys.: Condens. Matter 4, 2347–2359.Google Scholar
Pain, J.-C. & Gilleron, F. (2012 a). Description of anomalous Zeeman patterns in stellar astrophysics. EAS Publications Series 58, 43–50.CrossRefGoogle Scholar
Pain, J.-C. & Gilleron, F. (2012 b). Characterization of anomalous Zeeman patterns in complex atomic spectra. Phys. Rev. A 85, 033409.CrossRefGoogle Scholar
Pain, J.-C., Gilleron, F., Porcherot, Q. & Blenski, T. (2013). The hybrid opacity code SCO-RCG: Recent developments. Proc. of the 40th EPS Conf. on Plasma Physics, P4.403 (2013). http://ocs.ciemat.es/EPS2013PAP/pdf/P4.403.pdf.Google Scholar
Pain, J.-C., Gilleron, F., Porcherot, Q. & Blenski, T. (2015). The Hybrid Detailed/Statistical opacity code SCO-RCG: New developments and applications. Proc. of the 18th Conf. on Atomic Physics in Plasmas. AIP Conf. Proc., in press.Google Scholar
Porcherot, Q., Pain, J.-C., Gilleron, F. & Blenski, T. (2011). A consistent approach for mixed detailed and statistical calculation of opacities in hot plasmas. High Energy Density Phys. 7, 234–239.CrossRefGoogle Scholar
Rozsnyai, B.F. (1977). Spectral lines in hot dense matter. J. Quant. Spectrosc. Radiat. Transfer 17, 77–88.CrossRefGoogle Scholar
Subramanian, P.R. (1986). Evaluation of Tr(J λ2p) using the Brillouin function. J. Phys. A: Math. Gen. 19, 1179–1187.CrossRefGoogle Scholar
Szego, G. (1939). Orthogonal Polynomials. Rhode Island, Providence: American Mathematical Society.Google Scholar
Thole, B.T., Van Der Laan, G. & Sawatzky, G.A. (1985). Strong magnetic dichroïsm predicted in the M 4,5 X-ray absorption spectra of magnetic rare-earth materials. Phys. Rev. Lett. 55, 2086–2088.CrossRefGoogle ScholarPubMed
Turck-Chieze, S., Loisel, G., Gilles, D., Piau, L., Blancard, C., Blenski, T., Busquet, M., Cosse, P., Delahaye, F., Faussurier, G., Gilleron, F., Guzik, J., Harris, J., Kilcrease, D.P., Magee, N.H. Jr., Pain, J.-C., Porcherot, Q., Poirier, M., Zeippen, C., Bastiani-Ceccotti, S., Reverdin, C., Silvert, V. & Thais, F. (2011). Radiative properties of stellar plasmas and open challenges. Astrophys. Space Sci. 336, 103–109.CrossRefGoogle Scholar
Voigt, W. (1912). Sitzber. K. B. Akad. Wiss. München, p. 603.Google Scholar