Abstract
The ability to accurately model plasmas with the collisional-radiative approach typically depends on a number of factors. For example, the number of bound electrons per ion and the particular quantities to be modeled are two key determinants. When the dominant ion stages of a plasma contain only a few electrons per ion, it is possible to construct models in full fine-structure detail. The underlying list of configurations can be chosen to be sufficiently complete such that all quantities of interest, ranging from aggregate quantities such as the mean ion charge to detailed spectroscopic quantities such as the emission spectrum, can be calculated in a converged manner. For plasmas composed of more complex ions, it is often necessary to construct atomic models using an averaged scheme, such as the average-atom or configuration-average methods. In this case, quantities such as the mean ion charge and radiative power loss may still be accurately determined, but obtaining spectroscopically accurate line features can be computationally challenging or intractable. In this work, we use the Los Alamos suite of codes to illustrate some of the concepts associated with large-scale collisional-radiative modeling. Emphasis is placed on the use of fine-structure and configuration-average models with a significant level of detail in order to generate plasma quantities in an ab-initio, self-consistent fashion, with as little approximation as possible. This approach can be used as a benchmark for comparison with less detailed models or for comparison with experimental data.
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- 1.
We note the use of the word “states”, rather than “levels”, in the previous paragraph. We employ “states” in this work as a generic term, which could refer to well-defined concepts such as configurations or fine-structure levels, or some sort of averaged quantity. The word “levels” is reserved for fine-structure levels in this work.
References
D.R. Bates, A.E. Kingston, R.W.P. McWhirter, Recombination between electrons and atomic ions. I. Optically thin plasmas. Proc. R. Soc. (Lond.) A267, 297 (1962)
D.R. Bates, A.E. Kingston, R.W.P. McWhirter, Recombination between electrons and atomic ions. II. Optically thick plasmas. Proc. R. Soc. (Lond.) A270, 155 (1962)
R.D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, 1981)
D.H. Sampson, H.L. Zhang, C.J. Fontes, A fully relativistic approach for calculating atomic data for highly charged ions. Phys. Rep. 477, 111 (2009)
R.E.H. Clark, J. Abdallah Jr., Atomic data for titanium. Phys. Scr. T37, 28 (1991)
J. Abdallah Jr., R.E.H. Clark, J.M. Peek, C.J. Fontes, Kinetics calculations for near Ne-like ions. J. Quant. Spec. Rad. Trans. 51, 1 (1994)
N.H. Magee, J. Abdallah Jr., R.E.H. Clark, J.S. Cohen, L.A. Collins, G. Csanak, C.J. Fontes, A. Gauger, J.J. Keady, D.P. Kilcrease, A.L. Merts, in Astronomical Society of the Pacific Conference Proceedings ed. by S.J. Adelman, W.L Wiese, vol. 78, pp. 51–55. ASP, New York (1995)
C.J. Fontes, H.L. Zhang, J. Abdallah Jr., R.E.H. Clark, D.P. Kilcrease, J. Colgan, R.T. Cunningham, P. Hakel, N.H. Magee, M.E. Sherrill, The Los Alamos suite of relativistic atomic physics codes. J. Phys. B: At. Mol. Opt. Phys. 48, 144014 (2015)
R.E.H. Clark, J. Abdallah Jr., G. Csanak, S.P. Kramer, Electron-impact cross sections and coherence parameters for the \(6s^2 {^1}\!S-6s6p ^1\!P\) transition in neutral barium. Phys. Rev. A 40, 2935 (1989)
J. Abdallah Jr., R.E.H. Clark, X-ray transmission calculations for an aluminum plasma. J. Appl. Phys. 69, 23 (1991)
J. Abdallah Jr., R.E.H. Clark, J.M. Peek, Excited-state \(1s-2p\) absorption by aluminum ions with partially filled L shells. Phys. Rev. A 44, 4072 (1991)
T.S. Perry, S.J. Davidson, F.J.D. Serduke, D.R. Bach, C.C. Smith, J.M. Foster, R.J. Doyas, R.A. Ward, C.A. Iglesias, F.J. Rogers, J. Abdallah Jr., R.E. Steward, J.D. Kilkenny, R.W. Lee, Opacity measurements in hot dense medium. Phys. Rev. Lett. 67, 3784 (1991)
R.E.H. Clark, G. Csanak, J. Abdallah Jr., Theoretical studies on the electron-impact excitation of neutral magnesium. Phys. Rev. A 44, 2874 (1991)
R.E.H. Clark, J. Abdallah Jr., J.B. Mann, Integral and differential cross sections for electron impact ionization. Ap. J. 381, 597 (1991)
J. Abdallah Jr., R.E.H. Clark, J.M. Peek, Steady-state ionization balance calculations for a selenium plasma. Phys. Rev. A 45, 3980 (1992)
R.E.H. Clark, G. Csanak, J. Abdallah Jr., S. Trajmar, Differential cross sections for electron scattering by excited Ba \((\ldots 6s6p \,^1\!P_1)\) atoms. J. Phys. B: At. Mol. Opt. Phys. 25, 5233 (1992)
J.J. Keady, J. Abdallah Jr., R.E.H. Clark, Accurate methods for calculating atomic processes in high temperature plasmas. Plasma Phys. Controll. Nuclear Fusion Res. 3, 205 (1993)
D.P. Kilcrease, J. Abdallah Jr., J.J. Keady, R.E.H. Clark, Atomic configuration average simulations for plasma spectroscopy. J. Phys. B: At. Mol. Opt. Phys. 26, L717 (1993)
J. Abdallah Jr., B.A. Bryunetkin, M.P. Kalashnikov, R.E.H. Clark, P. Nickels, S.A. Pikuz, I.Yu. Skobelev, A.Ya. Faenov, M. Shnurer, Identification of transitions from self-ionized levels of a beryllium-like Mg IX ion in a plasma heated by picosecond laser pulses. Quant. Electron. (Russian) 20, 1159 (1993)
J. Abdallah Jr., R.E.H. Clark, C.J. Keane, T.D. Shepard, L.J. Suter, Radiation field effects on the spectroscopic properties of seeded plasmas. J. Quant. Spec. Rad. Trans. 50, 91 (1993)
H.J. Beyer, H. Hamdy, E.I.M. Zohny, K.R. Mahmoud, M.A.K. El-Fayoumi, H. Kleinpoppen, J. Abdallah Jr., R.E.H. Clark, G. Csanak, Electron-impact coherence parameters for the excitation of the 5\(\,^1\!P\) State of Sr. Z. Phys. D 30, 91 (1994)
J. Abdallah Jr., R.E.H. Clark, Comparison of explicit and effective models for calculating ionic populations in argon plasmas. J. Phys. B: At. Mol. Opt. Phys. 27, 3589 (1994)
B.A. Bryunetkin, A.Ya. Faneov, M. Kalashnikov, P. Nickles, M. Schnuerer, I.Yu. Skobelev, J. Abdallah Jr., X-ray spectral investigations of a high irradiance picosecond laser produced plasma. J. Quant. Spect. Radiat. Transfer. 53, 45 (1995)
D. Post, J. Abdallah Jr., R.E.H. Clark, N. Putvinskaya, Calculations of energy losses due to atomic processes in tokamaks with applications to the International Thermonuclear Experimental Reactor divertor. Phys. Plasmas 2, 2328 (1995)
R.E.H. Clark, J. Abdallah Jr., D. Post, Radiation rates for low Z impurities in edge plasmas. J. Nuclear Mater. 220–222, 1028 (1995)
A.Ya. Faenov, I.Yu. Skobelev, S.A. Pikuz, G.A. Kyrala, R.D. Fulton, J. Abdallah Jr., D.P. Kilcrease, High-resolution X-ray spectroscopy of a subpicosecond-laser-produced silcon plasma. Phys. Rev. A 51, 3529 (1995)
J. Abdallah Jr., L.A. Collins, G. Csanak, A.G. Petschek, G.T. Schappert, Two-photon ionization of an inner shell electron of the Cl atom. Z. Phys. D 34, 233 (1995)
J. Abdallah Jr., A.Ya. Faenov, D. Hammer, S.A. Pikuz, G. Csanak, Electron beam effects on the spectroscopy of satellite lines in aluminum x-pinch experiments. Phys. Scripta 53, 705 (1996)
R.E.H. Clark, J. Abdallah Jr., Electron impact cross sections for beryllium and boron. Phys. Scripta T62, 7 (1996)
M.A. Khakoo, S. Trajmar, L.R. LeClair, I. Kanik, G. Csanak, C.J. Fontes, Differential cross sections for electron impact excitation of Xe: I. Excitation of the five lowest levels; experiment and theory. J. Phys. B: At. Mol. Opt. Phys. 29, 3455 (1996)
M.A. Khakoo, S. Trajmar, S. Wang, I. Kanik, A. Aguirre, C.J. Fontes, R.E.H. Clark, J. Abdallah Jr., Differential cross sections for electron impact excitation of Xe: II. Excitation of the sixth to twentieth lowest levels; experiment and theory. J. Phys. B: At. Mol. Opt. Phys. 29, 3477 (1996)
P.W. Zetner, S. Trajmar, S. Wang, I. Kanik, G. Csanak, R.E.H. Clark, J. Abdallah Jr., J.C. Nickel, Inelastic electron scattering by laser-excited barium atoms. J. Phys. B: At. Mol. Opt. Phys. 30, 5317 (1997)
A.W. Baerveldt, W.B. Westveld, J. van Eck, H.G.M. Heideman, G.D. Meneses, G. Csanak, R.E.H. Clark, J. Abdallah Jr., Cross sections, polarization and orientation in electron impact excitation to Ne\(^*\,(2p^5 3p)\) States. J. Phys. B: At. Mol. Opt. Phys. 31, 573 (1998)
J. Abdallah Jr., R.E.H. Clark, D.P. Kilcrease, G. Csanak, C.J. Fontes, in AIP Conference Proceedings Vol. 381, 10th APS Topical Conference on Atomic Processes in Plasmas, ed. by A.L. Osterheld, W.H. Goldstein, pp. 131–142 (AIP, New York, 1996)
A.Ya. Faenov, J. Abdallah Jr., R.E.H. Clark, J. Cohen, R.P. Johnson, G.A. Kyrala, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, M.D. Wilke, High-resolution X-ray spectroscopy of hollow atoms created in plasma heated by subpicosecond laser radiation. Proc. SPIE 3157, 10 (1997)
J. Abdallah Jr., A.Ya. Faenov, T.A. Pikuz, M.D. Wilke, G.A. Kyrala, R.E.H. Clark, Hot electron effects on the satellite spectrum of laser produced plasmas. J. Quant. Spec. Rad. Trans. 62, 1 (1999)
S.A. Pikuz, T.A. Shelkovenko, V.M. Romanova, J. Abdallah Jr., G. Csanak, R.E.H. Clark, A.Ya. Faenov, I.Yu. Skobelev, D.A. Hammer, Effect of an electron beam generated in an x-pinch plasma on the structure of the \(K\) spectra of multiply charged ions. J. Exp. Theor. Phys. 85, 484 (1997)
A.M Urnov, J. Dubau, A.Ya. Faenov, T.A. Pikuz, I.Yu. Skobelev, J. Abdallah Jr., R.E.H. Clark, J.S. Cohen, R.P. Johnson, G.A. Kyrala, M.D. Wilke, A.L. Osterheld, X-ray spectra of multiply-charged hollow ions in the emission from a femtosecond laser plasma. J. Exp. Theor. Phys. Lett. 67, 489 (1998)
F.B. Rosmej, J. Abdallah Jr., Blue satellite structure near He \(\alpha \) and He \(\beta \) and redistribution of level populations. Phys. Lett. A 245, 548 (1998)
C.J. Fontes, The role of the \(5p^55d\) configuration and spin-orbit coupling in the electron impact excitation of the lowest lying \(J\)=0 and \(J\)=2 levels of xenon and krypton. J. Phys. B: At. Mol. Opt. Phys. 31, 175 (1998)
P.V. Johnson, Y. Li, P.W. Zetner, G. Csanak, R.E.H. Clark, J. Abdallah Jr., Electron-impact excitation of the \((\dots 6s6p\, ^{1}P_{1})\) level in ytterbium. J. Phys. B: At. Mol. Opt. Phys. 31, 3027 (1998)
J. Abdallah Jr., A.Ya. Faenov, M. Scholz, L. Karpinski, S.A. Pikuz, V.M. Romanova, M. Sadowski, A. Szydlowski, Electron beam effects on the spectroscopy of satellite lines in plasma focus experiments. J. Quant. Spec. Rad. Trans. 62, 85 (1999)
J. Abdallah Jr., N. Palmer, W. Gekelman, J. Maggs, R.E.H. Clark, Time dependent kinetics model for a helium discharge plasma. J. Phys. B: At. Mol. Opt. Phys. 32, 1001 (1999)
P.W. Zetner, S. Trajmar, S. Wang, I. Kanik, G. Csanak, R.E.H. Clark, J. Abdallah Jr., D. Fursa, I. Bray, Differential cross sections for electron-impact excitation out of the metastable levels of the barium atom. J. Phys. B: At. Mol. Opt. Phys. 32, 5123 (1999)
D. Fursa, I. Bray, S. Trajmar, I. Kanik, G. Csanak, R.E.H. Clark, J. Abdallah Jr., Integral cross sections for electron scattering by ground-state Ba atoms. Phys. Rev. A 60, 4590 (1999)
A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, S.A. Pikuz, A.M. Urnov, J. Abdallah Jr, R.E.H. Clark, J. Cohen, R.P. Johnson, G.A. Kyrala, M.D. Wilke, A. Maksimchuk, D. Umstadter, N. Nantel, R. Doron, E. Behar, P. Mandelbaum, J.J. Schwob, J. Dubau, F.B. Rosmej, A. Osterheld, High-resolved X-ray spectra of hollow atoms in a femtosecond laser-produced solid plasma. Phys. Scripta T80, 536 (1999)
X. Guo, M.A. Khakoo, D.F. Mathews, G. Mikaelian, A. Crowe, I. Kanik, S. Trajmar, V. Zeman, K. Bartschat, C.J. Fontes, Differential cross section ratios for low-energy electron-impact excitation of the 4p\(^5\)5s levels of krypton–sensitive tests of relativistic effects for heavy noble gases. J. Phys. B: At. Mol. Opt. Phys. 32, L155 (1999)
J. Abdallah Jr., I.Yu. Skobelev, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, F. Flora, S. Bollanti, P. Di Lazzaro, T. Letardi, E. Burattini, A. Grilli, A. Reale, L. Palladino, G. Tomasetti, A. Scafati, L. Reale, Spectra of multicharged hollow ions in plasma created by the shortwavelength laser. Quant. Electron. 30, 694 (2000)
T. Auguste, P. D’Oliveira, S. Hulin, P. Monot, J. Abdallah Jr., A.Ya. Faenov, I.Yu. Skobelev, A.I. Magunov, T.A. Pikuz, About the role of prepulse in the heating of clusters by high intensive femtosecond laser pulse. J. Exp. Theor. Phys. Lett. 72, 55 (2000)
J. Abdallah Jr., A.Ya. Faenov, I.Yu. Skobelev, A.I. Magunov, T.A. Pikuz, T. Auguste, P. D’Oliveira, S. Hulin, P. Monot, Hot electron influence on the X-ray emission spectra of Ar clusters heated by a high intensity 60 fs laser pulse. Phys. Rev. A 63, 032706 (2001)
T.S. Perry, S.J. Davidson, F.J.D. Serduke, D.R. Bach, C.C. Smith, J.M. Foster, R.J. Doyas, R.A. Ward, C.A. Iglesias, F.J. Rogers, J. Abdallah Jr., R.E. Stewart, R.J. Wallace, J.D. Kilkenny, R.W. Lee, Opacity measurements in hot dense medium. Astrophys. J. Suppl. Ser. 127, 433 (2000)
L. Karpinski, M. Paduch, M. Scholz, K. Tomaszewski, A. Szydlowski, S. Pikuz, V. Romanova, A.Ya. Faenov, J. Abdallah Jr., R.E.H. Clark, “Hot electrons” influence on argon \(K\)-spectrum emitted from plasma focus discharges. Czech. J. Phys. 50, 113 (2000)
C.J. Fontes, J. Abdallah Jr., R.E.H. Clark, D.P. Kilcrease, Non-LTE modeling of gold plasmas. J. Quant. Spec. Rad. Trans. 65, 223 (2000)
X. Guo, D.F. Mathews, G. Mikaelian, M.A. Khakoo, A. Crowe, I. Kanik, S. Trajmar, V. Zeman, K. Bartschat, C.J. Fontes, Differential cross sections for electron-impact excitation of krypton at low incident energies: I. Excitation of the 4p\(^5\)5s configuration. J. Phys. B: At. Mol. Opt. Phys. 33, 1895 (2000)
X. Guo, D.F. Mathews, G. Mikaelian, M.A. Khakoo, A. Crowe, I. Kanik, S. Trajmar, V. Zeman, K. Bartschat, C.J. Fontes, Differential cross sections for electron-impact excitation of krypton at Low incident energies: II. Excitation of the 4p\(^5\)5p, 4p\(^5\)4d and 4p\(^5\)6s configurations. J. Phys. B: At. Mol. Opt. Phys. 33, 1921 (2000)
G.C. Junkel-Vives, J. Abdallah Jr., F. Blasco, C. Stenz, F. Salin, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, T. Auguste, P. D’Oliveira, S. Hulin, P. Monot, S. Dobosz, High-resolution X-ray spectroscopy investigations of fs laser irradiated Ar clusters by varying cluster size and laser flux density. J. Quant. Spec. Rad. Trans. 71, 417 (2001)
G.C. Junkel-Vives, J. Abdallah Jr., F. Blasco, C. Stenz, F. Salin, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, Observation of H-like ions within Ar clusters irradiated by 35-fs laser via high-resolution X-ray spectroscopy. Phys. Rev. A 64, 021201(R) (2001)
M.E. Sherrill, R.C. Mancini, J.E. Bailey, A. Filuk, B. Clark, P. Lake, J. Abdallah Jr., Spectroscopy diagnostics of a low temperature laser ablated LiAg plasma plume. Rev. Sci. Inst. 72, 957 (2001)
D. Fursa, I. Bray, G. Csanak, R.E.H. Clark, J. Abdallah Jr., I. Kanik, S. Trajmar, Electron impact excitation of excited barium. Phys. Rev. A 65, 032723 (2002)
G.C. Junkel-Vives, J. Abdallah Jr., T. Auguste, P. D’Oliveira, S. Hulin, P. Monot, S. Dobosz, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, A.S. Boldarev, V.A. Gasilov, Spatially resolved X-ray spectroscopy investigations of femtosecond laser irradiated Ar clusters. Phys. Rev. E 65, 036410 (2002)
G.C. Junkel-Vives, J. Abdallah Jr., F. Blasco, C. Stenz, F. Salin, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, Evidence of supercritical density in 45-fs-laser-irradiated Ar-cluster plasmas. Phys. Rev. A 66, 033204 (2002)
P.W. Zetner, P.V. Johnson, Y. Li, G. Csanak, R.E.H. Clark, J. Abdallah Jr., Electron-impact excitation of the \((\ldots 6s6p\, ^3\!P_J\) levels in ytterbium. J. Phys. B: At. Mol. Opt. Phys. 34, 1619 (2001)
A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, A.Ya. Faenov, F. Blasco, F. Dorchies, T. Caillaud, C. Bonte, F. Salin, C. Stenz, P.A. Loboda, I.A. Litvinenko, V.V. Popova, G.V. Baidin, G.C. Junkel-Vives, J. Abdallah Jr., Influence of ultrashort laser pulse duration on the X-ray emission spectrum of plasma produced in cluster target. J. Exp. Theor. Phys. Lett. 74, 375 (2001)
A.Ya. Faenov, I.Yu. Skobelev, A.I. Magunov, T.A. Pikuz, J. Abdallah Jr., G.C. Junkel-Vives, F. Blasco, F. Dorchies, C. Stenz, F. Salin, T. Auguste, S. Dobosz, P. Monot, P. D’Oliveira, S. Hulin, A. Boldurev, V.A. Gasilov, X-ray radiation properties of clusters heated by fs laser pulses. Proc. SPIE 4504, 121 (2001)
J. Abdallah Jr., H.L. Zhang, C.J. Fontes, D.P. Kilcrease, B.J. Archer, Model comparisons for high-Z non-LTE steady-state calculations. J. Quant. Spec. Rad. Trans. 71, 107 (2001)
S.A. Pikuz, T.A. Shelkovenko, D.B. Sinars, D.A. Hammer, S.V. Lebedev, S.N. Bland, I.Yu. Skobelev, J. Abdallah Jr., C.J. Fontes, H.L. Zhang, Space, time and spectral characteristics of an x-pinch. J. Quant. Spec. Rad. Trans. 71, 581 (2001)
I.Yu. Skobelev, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, A.S. Boldarev, V.A. Gasilov, J. Abdallah Jr., G.C. Junkel-Vives, T. Auguste, P. D’Oliveira, S. Hulin, P. Monot, F. Blasco, F. Dorchies, T. Caillaud, C. Bonte, C. Stenz, F. Salin, B.Yu. Sharkov, On the interaction of femtosecond laser pulses with cluster targets. J. Exp. Theor. Phys. 94, 73 (2002)
I.Yu. Skobelev, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, A.S. Boldarev, V.A. Gasilov, J. Abdallah Jr., G.C. Junkel-Vives, T. Auguste, S. Dobosz, P. D’Oliveira, S. Hulin, P. Monot, F. Blasco, F. Dorchies, T. Caillaud, C. Bonte, C. Stenz, F. Salin, P.A. Loboda, I.A. Litvinko, V.V. Popova, G.V. Baidin, B.Yu. Sharkov, X-ray spectroscopy diagnostic of a plasma produced by femtosecond laser pulses Irradiating a Cluster Target. J. Exp. Theor. Phys. 94, 966 (2002)
M.E. Sherrill, R.C. Mancini, J.E. Baily, A. Filuk, B. Clark, P. Lake, J. Abdallah Jr., in AIP Conference Proceedings 13th APS Topical Conference on Atomic Processes in Plasmas, ed. by D.R. Schultz, F.W. Meyer, F. Ownby, vol. 635, pp. 32–41 (AIP, New York, 2002)
G.C. Junkel-Vives, J. Abdallah Jr., F. Blasco, F. Dorchies, C. Stenz, F. Salin, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, T. Auguste, S. Dobosz, P. D’Oliveira, S. Hulin, P. Monot, in AIP Conference Proceedings, 13th APS Topical Conference on Atomic Processes in Plasmas, D.R. Schultz, F.W. Meyer, F. Ownby, vol. 635, pp. 82–91 (AIP, New York, 2002)
G.D. Meneses, R.E.H. Clark, J. Abdallah Jr., G. Csanak, Cross sections for the excitation of \(3s, 3p,3d, 4s\) and \(4p\) manifolds in e-Ne collisional. J. Phys. B: At. Mol. Opt. Phys. 35, 3119 (2002)
U. Andiel, K. Eidmann, P. Hakel, R.C. Mancini, G.C. Junkel-Vives, J. Abdallah Jr., K. Witte, Demonstration of aluminum \(K\)-shell line shifts in isochorically heated targets driven by ultrashort laser pulses. Europhys. Lett. 60, 861 (2002)
M.A. Khakoo, J. Wrkich, M. Larsen, G. Kleiban, I. Kanik, S. Trajmar, M.J. Brunger, P.J.O. Teubner, A. Crowe, C.J. Fontes, R.E.H. Clark, V. Zeman, K. Bartschat, D.H. Madison, R. Srivastava, A.D. Stauffer, Differential cross sections and cross-section ratios for the electron-impact excitation of the neon \(2p^53s\) configuration. Phys. Rev. A 65, 062711 (2002)
J. Abdallah Jr., G.C. Junkel-Vives, A.Ya. Faenov, I.Yu. Skobelev, T.A. Pikuz, A.I. Magunov, F. Blasco, C. Bonte, F. Dorchies, T. Caillaud, F. Salin, C. Stenz, Time-dependent study of \(K\)-shell satellite line structure from L-shell ions in ultra-short laser argon cluster experiments. J. Quant. Spec. Rad. Trans. 81, 3 (2003)
Y. Fukuda, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, K. Yamakawa, J. Abdallah Jr., G. Csanak, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, A.S. Boldarev, V.A. Gasilov, X-ray observations of microdroplet plasma formation under super-intense laser radiation. J. Exp. Theor. Phys. Lett. 78, 146 (2003)
J. Abdallah Jr., G. Csanak, Y. Fukuda, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, K. Yamakawa, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, Time-dependent Boltzmann kinetic model of X-rays produced by the ultrashort-pulse laser irradiation of argon clusters. Phys. Rev. A 68, 063201 (2003)
R.E.H. Clark, J. Abdallah Jr., Comparison calculations of radiated power loss for silicon and iron. At. Plasma-Mater. Interact. Data Fusion 11, 1 (2003)
J. Abdallah Jr., R.E.H. Clark, Calculated radiated power loss for neon, silicon, argon, titanium, and iron. At. Plasma-Mater. Interact. Data Fusion 11, 21 (2003)
R.E.H. Clark, J. Abdallah Jr., C.J. Fontes, Effective rates for calculation of steady-state and time dependent plasmas. At. Plasma-Mater. Interact. Data Fusion 11, 49 (2003)
Y. Fukuda, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, Y. Kishimoto, K. Yamakawa, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, J. Abdallah Jr., G. Csanak, A.S. Boldarev, V.A. Gasilov, X-ray radiation of clusters irradiated by ultrafast, high intensity laser pulses. Proc. SPIE 5196, 234 (2003)
C.J. Fontes, H.L. Zhang, J. Abdallah Jr., in AIP Conference Proceeding, 14th APS Topical Conference on Atomic Processes in Plasmas, ed. by J.S. Cohen, S. Mazevet, D.P. Kilcrease, vol. 730, pp. 41–49 (AIP, New York, 2004)
K. Eidmann, U. Andiel, F. Pisani, P. Hakel, R.C. Mancini, J. Abdallah Jr., G.C. Junkel-Vives, K. Witte, in AIP Conference Proceeding, 14th APS Topical Conference on Atomic Processes in Plasmas, ed. by J.S. Cohen, S. Mazevet, D.P. Kilcrease, vol. 730, pp. 81–93 (AIP, New York, 2004)
N.H. Magee, J. Abdallah Jr., J. Colgan, P. Hakel, D.P. Kilcrease, S. Mazevet, M.E. Sherrill, C.J. Fontes, H.L. Zhang, in AIP Conference Proceeding, 14th APS Topical Conference on Atomic Processes in Plasmas, ed. by J.S. Cohen, S. Mazevet, D.P. Kilcrease, vol. 730, pp. 168–179 (AIP, New York, 2004)
M.A. Khakoo, P. Vandeventer, J.G. Childers, I. Kanik, C.J. Fontes, K. Bartschat, V. Zeman, D.H. Madison, S. Saxena, R. Srivastava, A.D. Stauffer, Electron impact excitation of the argon \(3p^5 4s\) configuration: differential cross-sections and cross-section ratios. J. Phys. B: At. Mol. Opt. Phys. 37, 247 (2004)
S.D. Loch, C.J. Fontes, J. Colgan, M.S. Pindzola, C.P. Ballance, D.C. Griffin, M.G. O’Mullane, H.P. Summers, Collisional-radiative study of lithium plasmas. Phys. Rev. E 69, 066405 (2004)
C.J. Fontes, J. Colgan, H.L. Zhang, J. Abdallah Jr., Large-scale kinetics modeling of non-LTE plasmas. J. Quant. Spec. Rad. Trans. 99, 175 (2006)
P. Hakel, M.E. Sherrill, S. Mazevet, J. Abdallah Jr., J. Colgan, D.P. Kilcrease, N.H. Magee, C.J. Fontes, H.L. Zhang, The new Los Alamos opacity code ATOMIC. J. Quant. Spec. Rad. Trans. 99, 265 (2006)
M.E. Sherrill, J. Abdallah Jr., G. Csanak, D.P. Kilcrease, Y. Fukuda, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, K. Yamakawa, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time dependent X-ray spectra. J. Quant. Spec. Rad. Trans. 99, 584 (2006)
M.E. Sherrill, J. Abdallah Jr., G. Csanak, E.S. Dodd, Y. Fukuda, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, K. Yamakawa, A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, Spectroscopic characterization of an ultrashort laser driven Ar cluster target incorporating both Boltzmann and particle in cell models. Phys. Rev. E 73, 066404 (2006)
S. Mazevet, J. Abdallah Jr., Mixed UTA and detailed line treatment for mid-Z opacity and spectral calculations. J. Phys. B: At. Mol. Opt. Phys. 39, 3419 (2006)
J. Colgan, C.J. Fontes, J. Abdallah Jr., Collisional-radiative studies of carbon plasmas. High Energy Density Phys. 2, 90 (2006)
J. Colgan, C.J. Fontes, H.L. Zhang, Inner-shell electron-impact ionization of neutral atoms. Phys. Rev. A 73, 062711 (2006)
J.A. Cobble, T.E. Tierney, J. Abdallah Jr., Kilovolt radiation from a laser-produced Al plasma. J. Appl. Phys. 102, 023303 (2007)
J. Abdallah Jr., D. Batani, T. Desai, G. Lucchini, A. Faenov, T. Pikuz, A. Maganov, V. Narayanan, High resolution X-ray emission spectra from picosecond laser irradiated Ge targets. Laser Part. Beams 25, 245 (2007)
J. Abdallah Jr., D.P. Kilcrease, N.H. Magee, S. Mazevet, P. Hakel, M.E. Sherrill, Spectral line strength binning method for opacity calculations. High Energy Density Phys. 3, 1 (2007)
M.E. Sherrill, R.C. Mancini, J. Bailey, A. Filuk, B. Clark, P. Lake, J. Abdallah Jr., Spectroscopic modeling and characterization of a collisionally confined laser-ablated plasma plume. Phys. Rev. E 76, 056401 (2007)
J.E. Bailey, G.A. Rochau, C.A. Iglesias, J. Abdallah Jr., J.J. MacFarlane, I. Golovkin, P. Wang, R.C. Mancini, P.W. Lake, T.C. Moore, M. Bump, O. Garcia, S. Mazevet, Iron opacity measurements at temperatures above 150 eV. Phys. Rev. Lett. 99, 265002 (2007)
J. Colgan, C.J. Fontes, J. Abdallah Jr., B. Streufert, in AIP Conference Proceeding, 15th International Conference on Atomic Processes in Plasmas, ed. by J.D. Gillaspy, J.J. Curry, W.L. Wiese, vol. 926, pp. 180–189 (AIP, New York, 2007)
J. Oelgoetz, C.J. Fontes, H.L. Zhang, M. Montenegro, S.N. Nahar, A.K. Pradhan, High-temperature behavior of the helium-like K\(\alpha \,G\) ratio: the effect of improved recombination rate coefficients for calcium, iron and nickel. Mon. Not. R. Astron. Soc. 382, 761 (2007)
J. Oelgoetz, C.J. Fontes, H.L. Zhang, A.K. Pradhan, A study of the breakdown of the quasi-static approximation at high densities and its effect on the helium-like K\(\alpha \) complex of nickel, iron, and calcium. Phys. Rev. A 76, 062504 (2007)
J. Colgan, J. Abdallah Jr., A.Ya. Faenov, A.I. Magunov, T.A. Pikuz, I.Yu. Skobelev, Y. Fukuda, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, K. Yamakawa, The role of hollow atoms in the spectra of an ultrashort-pulse-laser-driven Ar cluster target. Laser Part. Beams 26, 83 (2008)
J. Colgan, J. Abdallah Jr., A. Faenov, T.A. Pikuz, I.Yu. Skobelev, MUTA calculations of a laser produced Mg hollow atom spectrum. Phys. Scripta 78, 015302 (2008)
J. Abdallah Jr., M.E. Sherrill, The reduced detailed configuration accounting (RDCA) model for NLTE plasma calculations. High Energy Density Phys. 4, 124 (2008)
J. Colgan, H.L. Zhang, C.J. Fontes, Electron-impact excitation and ionization cross sections for the Si, Cl and Ar isonuclear sequences. Phys. Rev. A 77, 062704 (2008)
J. Colgan, J. Abdallah Jr., M.E. Sherrill, J. Foster, C.J. Fontes, U. Feldman, Radiative losses of solar coronal plasmas. Astrophys. J. 689, 585 (2008)
T.C. Berkelbach, J. Colgan, J. Abdallah Jr., A.Ya. Faenov, T.A. Pikuz, Y. Fukuda, K. Yamakawa, Modeling energy dependence of the inner-shell X-ray emission produced by femtosecond-pulse laser irradiation of xenon clusters. Phys. Rev. E 79, 016407 (2009)
P. Hakel, R.C. Mancini, J. Abdallah Jr., M.E. Sherrill, H.L. Zhang, X-ray line polarization spectroscopy of Li-like Si satellite line spectra. J. Phys. B: At. Mol. Opt. Phys. 42, 085701 (2009)
J. Oelgoetz, C.J. Fontes, H.L. Zhang, S.N. Nahar, A.K. Pradhan, On the importance of satellite lines to the He-like K\(\alpha \) complex and the \(G\) ratio for calcium, iron, and nickel. Mon. Not. R. Astron. Soc. 394, 742 (2009)
J. Abdallah Jr., M.E. Sherrill, D.P. Kilcrease, C.J. Fontes, H.L. Zhang, J. Oelgoetz, The reduced detailed configuration accounting (RDCA) model for NLTE plasma spectral calculations. High Energy Density Phys. 5, 204 (2009)
P. Hakel, R.C. Mancini, U. Andiel, K. Eidmann, F. Pisani, G. Junkel-Vives, J. Abdallah Jr., X-ray line emissions from tamped thin aluminum targets driven by subpicosecond-duration laser pulses. High Energy Density Phys. 5, 35 (2009)
Yu. Ralchenko, J. Abdallah Jr., A. Bar-Shalom, J. Bauche, C. Bauche-Arnoult, C. Bowen, M. Busquet, H.-K. Chung, J. Colgan, G. Faussurier, C.J. Fontes, M. Foster, F. de Dortan, I. Golovkin, S.B. Hansen, M. Klapsich, R.W. Lee, V. Novikov, J. Oreg, O. Peyrusse, M. Poirier, A. Sasaki, H. Scott, H.L. Zhang, in AIP Conference Proceeding, 16th International Conference on Atomic Processes in Plasmas, ed. by K.B. Fournier, vol. 1161, pp. 242–250 (AIP, New York, 2009)
J. Colgan, J. Abdallah Jr., C.J. Fontes, R.E.H. Clark, Non-LTE studies of boron plasma. J. Phys. B: At. Mol. Opt. Phys. 43, 144021 (2010)
J. Colgan, J. Abdallah Jr., C.J. Fontes, D.P. Kilcrease, J. Dunn, R.W. Lee, Non-LTE and gradient effects in \(K\)-shell oxygen emission laser-produced plasma. High Energy Density Phys. 6, 295 (2010)
J. Colgan, J. Abdallah Jr., A.Ya. Faenov, T.A. Pikuz, I.Yu. Skobelev, F. Flora, M. Francucci, S. Martellucci, Model calculations of the emission of barium plasma in the spectral range of high-\(n\) Rydberg levels in a near Ni-like state. J. Phys. B: At. Mol. Opt. Phys. 43, 175701 (2010)
J. Abdallah Jr., J. Colgan, R.E.H. Clark, C.J. Fontes, H.L. Zhang, A collisional-radiative study of low temperature tungsten plasma. J. Phys. B: At. Mol. Opt. Phys. 44, 075701 (2011)
J. Colgan, J. Abdallah Jr., A.Ya. Faenov, T.A. Pikuz, I.Yu. Skobelev, Y. Fukuda, Y. Hayashi, A. Pirozhkov, K. Kawase, Y. Kato, S.V. Bulanov, M. Kando, Observation and modeling of high resolution spectral features of the inner-shell X-ray emission produced by \(10^{-10}\) contrast femtosecond-pulse laser irradiation of argon clusters. High Energy Density Phys. 7, 77 (2011)
C.J. Fontes, J. Colgan, H.L. Zhang, J. Abdallah Jr., A.L. Hungerford, C.L. Fryer, D.P. Kilcrease, Atomic data and the modeling of supernova light curves. J. Phys.: Conf. Ser. 388, 012022 (2012)
J. Abdallah Jr., J. Colgan, Time dependent calculations of electron energy distribution functions for cold argon gas in the presence of intense black body radiation. J. Phys. B: At. Mol. Opt. Phys. 45, 035701 (2012)
L.H. Frey, W. Even, D.J. Whelan, C.L. Fryer, A.L. Hungerford, C.J. Fontes, J. Colgan, The Los Alamos supernova light-curve project: computational methods. Astrophys. J. Suppl. Ser. 204, 16 (2013)
J. Colgan, D.P. Kilcrease, N.H. Magee Jr, G.S.J. Armstrong, J. Abdallah Jr, M.E. Sherrill, C.J. Fontes, H.L. Zhang, P. Hakel, Light element opacities from ATOMIC. High Energy Density Phys. 9, 369 (2013)
S. Turck-Chièze, D. Gilles, M. Le Pennec, T. Blenski, F. Thais, S. Bastiani-Ceccotti, C. Blancard, M. Busquet, T. Caillaud, J. Colgan, P. Cossé, F. Delahaye, J.E. Ducret, G. Faussurier, C.J. Fontes, F. Gilleron, J. Guzik, J.W. Harris, D.P. Kilcrease, G. Loisel, N.H. Magee, J.C. Pain, C. Reverdin, V. Silvert, B. Villette, C.J. Zeippen, Radiative properties of stellar envelopes: comparison of asteroseismic results to opacity calculations and measurements for iron and nickel. High Energy Density Phys. 9, 473 (2013)
J. Colgan, J. Abdallah Jr., A.Ya. Faenov, S.A. Pikuz, N. Booth, O. Culfa, R.J. Dance, R.G. Evans, R.J. Gray, T. Kaempfer, K.L. Lancaster, P. McKenna, A.L. Rossall, I.Yu. Skobelev, K.S. Schulze, I. Uschmann, A.G. Zhidkov, N.C. Woolsey, Exotic dense matter states pumped by relativistic laser plasma in the radiation dominant regime. Phys. Rev. Lett. 110, 125001 (2013)
S.A. Pikuz, A.Ya. Faenov, J. Colgan, R.J. Dance, J. Abdallah Jr., E. Wagenaars, N. Booth, O. Culfa, R.G. Evans, R.J. Gray, T. Kaempfer, K.L. Lancaster, P. McKenna, A.L. Rossall, I.Yu. Skobelev, K.S. Schulze, I. Uschmann, A.G. Zhidkov, N.C. Woolsey, Measurement and simulations of hollow atom X-ray spectra of solid-density relativistic plasma created by high-contrast PW optical laser pulses. High Energy Density Phys. 9, 560 (2013)
J. Colgan, D.P. Kilcrease, N.H. Magee Jr., G.S.J. Armstrong, J. Abdallah Jr., M.E. Sherrill, C.J. Fontes, H.L. Zhang, P. Hakel, in AIP Conference Proceeding, Eighth International Conference on Atomic and Molecular Data and their Applications, ed. by J.D. Gillaspy, W.L. Wiese, Y.A. Podpaly, vol. 1545, pp. 17–26 (AIP, New York, 2013)
S. Hansen, G.S.J. Armstrong, S. Bastiani-Ceccotti, C. Bowen, H.-K. Chung, J.P. Colgan, F. de Dortan, C.J. Fontes, F. Gilleron, J.-R. Marquès, R. Piron, O. Peyrusse, M. Poirier, Yu. Ralchenko, A. Sasaki, E. Stambulchik, F. Thais, Testing the reliability of non-LTE spectroscopic models for complex ions. High Energy Density Phys. 9, 523 (2013)
J. Abdallah Jr., J. Colgan, N. Rohringer, Time-dependent calculations of electron energy distribution functions for neon gas in the presence of intense XFEL radiation. J. Phys B 46, 235004 (2013)
G.S.J. Armstrong, J. Colgan, D.P. Kilcrease, N.H. Magee Jr., Ab initio calculation of the non-relativistic free-free Gaunt factor incorporating plasma screening. High Energy Density Phys. 10, 61 (2014)
C.J. Fontes, K.A. Eriksen, J. Colgan, H.L. Zhang, J.P. Hughes, Spectral modeling of supernova remnants. High Energy Density Phys. 10, 43 (2013)
P. Hakel, G.A. Kyrala, P.A. Bradley, N.S. Krasheninnikova, T.J. Murphy, M.J. Schmitt, I.L. Tregillis, R.J. Kanzleieter, S.H. Batha, C.J. Fontes, M.E. Sherrill, D.P. Kilcrease, S.P. Regan, X-ray spectroscopic diagnostics and modeling of polar-drive implosion experiments on national ignition facility. Phys. Plasmas 21, 063306 (2014)
S.B. Hansen, J. Colgan, A.Ya. Faenov, J. Abdallah Jr., S.A. Pikuz Jr., I.Yu. Skobelev, E. Wagenaars, N. Booth, O. Culfa, R.J. Dance, G.J. Tallents, R.G. Evans, R.J. Gray, T. Kaempfer, K.L. Lancaster, P. McKenna, A.L. Rossall, K.S. Schulze, I. Uschmann, A.G. Zhidkov, N.C. Woolsey, Detailed analysis of hollow ions spectra from dense matter pumped by X-ray emission of relativistic laser plasma. Phys. Plasmas 21, 031213 (2014)
J. Colgan, E.J. Judge, D.P. Kilcrease, J.E. Barefield, Ab-initio modeling of an iron laser-induced plasma: comparison between theoretical and experimental atomic emission spectra. Spectrochimica Acta B 97, 65 (2014)
J.E. Bailey, T. Nagayama, G.P. Loisel, G.A. Rochau, C. Blancard, J. Colgan, Ph Cosse, G. Faussurier, C.J. Fontes, F. Gilleron, I. Golovkin, S.B. Hansen, C.A. Iglesias, D.P. Kilcrease, J.J. MacFarlane, R.C. Mancini, C. Orban, J.-C. Pain, A.K. Pradhan, M. Sherrill, B.G. Wilson, A higher-than-predicted measurement of iron opacity at solar interior temperatures. Nature 517, 56 (2015)
J. Colgan, D.P. Kilcrease, N.H. Magee Jr., J. Abdallah Jr, M.E. Sherrill, C.J. Fontes, P. Hakel, H.L. Zhang, Light element opacities of astrophysical interest from ATOMIC. High Energy Density Phys. 14, 33 (2015)
J. Colgan, C.J. Fontes, H.L. Zhang, J. Abdallah Jr., Collisional-radiative modeling of tungsten at temperatures of 1200–2400 eV. Atoms 3, 76 (2015)
R.W. Lee, J.K. Nash, Y. Ralchenko, J. Quant. Spec. Rad. Trans. 58, 737 (1997)
C. Bowen, A. Decoster, C.J. Fontes, C.J. Fournier, O. Peyrusse, Yu. Ralchenko, J. Quant. Spec. Rad. Trans. 81, 71 (2003)
C. Bowen, R.W. Lee, YuJ Ralchenko, Quant. Spec. Rad. Trans. 99, 102 (2006)
J.G. Rubiano, R. Florido, C. Bowen, R.W. Lee, Yu. Ralchenko, High Energy Density Phys. 3, 225 (2007)
C.J. Fontes, J. Abdallah Jr., C. Bowen, R.W. Lee, Yu. Ralchenko, High Energy Density Phys. 5, 15 (2009)
The NLTE-6 Code Comparison Workshop http://nlte.nist.gov/NLTE6/ (unpublished)
H.-K. Chung, C. Bowen, C.J. Fontes, S.B. Hansen, Yu. Ralchenko, High Energy Density Phys. 9, 645 (2013)
The NLTE-8 Code Comparison Workshop http://nlte.nist.gov/NLTE8/ (unpublished)
A. Kramida, Yu. Ralchenko, J. Reader, NIST ASD Team: NIST Atomic Spectra Database (ver. 5.2) (National Institute of Standards and Technology, Gaithersburg, MD, 2015). http://physics.nist.gov/asd
H.-K. Chung, M.H. Chen, W.L. Morgan, Y. Ralchenko, R.W. Lee, FLYCHK: generalized population kinetics and spectral model for rapid spectroscopic analysis for all elements. High Energy Density Phys. 1, 3 (2005)
D. Layzer, Ann. Phys. (New York) 8, 271 (1959)
J.M. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics (Dover Publications, New York, 1991)
R.H. Fowler, Statistical Mechanics (Cambridge University Press, Cambridge, 1936)
H. Bethe, Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie. Ann. Phys. 397, 325 (1930)
H.A. Kramers, On the theory of X-ray absorption and of the continuous X-ray spectrum. Philos. Mag. 46, 836 (1923)
C.W. Gear, Numerical initial value problems in ordinary differential equations (Prentice Hall, New Jersey, 1971)
E. Isaacson, H.B. Keller, Analysis of Numerical Methods (Chapter 2.3) (Wiley, New York, 1966)
Y. Saad, M.H. Schultz, SIAM J. Sci. Stat. Comput. 7, 856 (1986)
Y. Saad, Iterative methods for sparse linear systems, 2nd edn. (Society for Industrial and Applied Mathematics, Philadelphia, 2003)
W.D. Joubert, LAMG: Los Alamos multigrid code reference manual. Los Alamos National Laboratory Report LA-UR-03-6183, Dec 2003 (unpublished)
X.S. Li, J.W. Demmel, ACM Trans. Math. Softw. 29, 110 (2003)
http://www-01.ibm.com/support/knowledgecenter/SSFHY8/essl_welcome.html
J. Bauche, C. Bauche-Arnoult, M. Klapisch, Transition arrays in the spectra of ionized atoms. Adv. At. Mol. Phys. 23, 131 (1988)
C. Bauche-Arnoult, J. Bauche, M. Klapisch, 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 (1985)
J. Bauche, C. Bauche-Arnoult, M. Klapisch, Breakdown of \(jj\) coupling in spinorbit-split atomic transition arrays. J. Phys. B: At. Mol. Opt. Phys. 24, 1 (1991)
S.B. Hansen, J. Bauche, C. Bauche-Arnoult, M.F. Gu, Hybrid atomic models for spectroscopic plasma diagnostics. High Energy Density Phys. 3, 109 (2007)
Acknowledgments
Helpful conversations with Yu. Ralchenko, D.P. Kilcrease and P. Hakel are gratefully acknowledged. This work was carried out under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory and supported by contract no DE-AC52-06NA25396.
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Fontes, C.J., Colgan, J., Abdallah, J. (2016). Self-consistent Large-Scale Collisional-Radiative Modeling. In: Ralchenko, Y. (eds) Modern Methods in Collisional-Radiative Modeling of Plasmas. Springer Series on Atomic, Optical, and Plasma Physics, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-27514-7_2
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