Ionization balance of non-LTE plasmas from an average-atom collisional-radiative model

Ovechkin A. A.; Loboda P. A.; Korolev A. S.; Kolchugin S. V.; Vichev I. Yu.; Solomyannaya A. D.; Kim D. A.; Grushin A. S.

doi:10.1063/5.0098814

Volume 7 Issue 6

Nov. 2022

Turn off MathJax

Article Contents

Article Navigation > Matter and Radiation at Extremes > 2022 > 7(6): 064401

Ovechkin A. A., Loboda P. A., Korolev A. S., Kolchugin S. V., Vichev I. Yu., Solomyannaya A. D., Kim D. A., Grushin A. S.. Ionization balance of non-LTE plasmas from an average-atom collisional-radiative model[J]. Matter and Radiation at Extremes, 2022, 7(6): 064401. doi: 10.1063/5.0098814

Citation:

Ovechkin A. A., Loboda P. A., Korolev A. S., Kolchugin S. V., Vichev I. Yu., Solomyannaya A. D., Kim D. A., Grushin A. S.. Ionization balance of non-LTE plasmas from an average-atom collisional-radiative model[J]. Matter and Radiation at Extremes, 2022, 7(6): 064401. doi: 10.1063/5.0098814

Citation:

Ovechkin A. A., Loboda P. A., Korolev A. S., Kolchugin S. V., Vichev I. Yu., Solomyannaya A. D., Kim D. A., Grushin A. S.. Ionization balance of non-LTE plasmas from an average-atom collisional-radiative model[J]. Matter and Radiation at Extremes, 2022, 7(6): 064401. doi: 10.1063/5.0098814

PDF( 4329 KB)

Ionization balance of non-LTE plasmas from an average-atom collisional-radiative model

doi: 10.1063/5.0098814

1.
Russian Federal Nuclear Center, Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Chelyabinsk Region, Snezhinsk, Russia
2.
Moscow Engineering Physics Institute (MEPhI), National Research Nuclear University, Moscow, Russia
3.
Keldysh Institute of Applied Mathematics RAS, Moscow, Russia

More Information

Corresponding author: a)Author to whom correspondence should be addressed: ovechkin.an@mail.ru
Received Date: 2022-05-12
Accepted Date: 2022-08-30

Available Online: 2022-11-01

Publish Date: 2022-11-01

Abstract

Abstract

We present a simplified version of an average-atom collisional-radiative model employing both local-thermodynamic-equilibrium average-atom and isolated-ion atomic data. The simplifications introduced do not lead to any substantial errors, and they significantly speed up calculations compared with the basic average-atom model involving direct solution of the self-consistent-field equations. Average ion charges, charge state distributions, and emission spectra of non-local-thermodynamic-equilibrium (NLTE) gold plasmas calculated using various modifications of the average-atom collisional-radiative model are compared with those obtained using the THERMOS model with the detailed configuration accounting approach. We also propose an efficient method to calculate thermodynamic functions of NLTE plasmas in the context of the simplified average-atom collisional-radiative model.

FullText(HTML)

References(59)

References

[1]	J. Bauche, C. Bauche-Arnoult, and O. Peyrusse, Atomic Properties in Hot Plasmas: From Levels to Superconfigurations (Springer International Publishing, Editions Grenoble Sciences, 2015).
[2]	A. Bar-Shalom, J. Oreg, W. H. Goldstein, D. Shvarts, and A. Zigler, “Super-transition arrays: A model for the spectral analysis of hot, dense plasma,” Phys. Rev. A 40, 3183–3193 (1989).10.1103/physreva.40.3183
[3]	A. Bar-Shalom, J. Oreg, and M. Klapisch, “Collisional radiative model for heavy atoms in hot non-local-thermodynamical-equilibrium plasmas,” Phys. Rev. E 56, R70–R73 (1997).10.1103/physreve.56.r70
[4]	A. Bar-Shalom, J. Oreg, and M. Klapisch, “Non-LTE superconfiguration collisional radiative model,” J. Quant. Spectrosc. Radiat. Transfer 58, 427–439 (1997).10.1016/s0022-4073(97)00050-2
[5]	A. Bar-Shalom, J. Oreg, and M. Klapisch, “Recent developments in the SCROLL model,” J. Quant. Spectrosc. Radiat. Transfer 65, 43–55 (2000).10.1016/s0022-4073(99)00054-0
[6]	O. Peyrusse, “A superconfiguration model for broadband spectroscopy of non-LTE plasmas,” J. Phys. B: At. Mol. Opt. Phys. 33, 4303–4321 (2000).10.1088/0953-4075/33/20/308
[7]	M. Busquet, “Radiation-dependent ionization model for laser-created plasmas,” Phys. Fluids B 5, 4191–4206 (1993).10.1063/1.860586
[8]	C. Bowen, “NLTE emissivities via an ionisation temperature,” J. Quant. Spectrosc. Radiat. Transfer 71, 201–214 (2001).10.1016/s0022-4073(01)00068-1
[9]	C. Bowen and P. Kaiser, “Dielectronic recombination in Au ionisation temperature calculations,” J. Quant. Spectrosc. Radiat. Transfer 81, 85–95 (2003).10.1016/s0022-4073(03)00062-1
[10]	M. Busquet, D. Colombant, M. Klapisch, D. Fyfe, and J. Gardner, “Improvements to the RADIOM non-LTE model,” High Energy Density Phys. 5, 270–275 (2009).10.1016/j.hedp.2009.05.005
[11]	R. M. More, “Electronic energy levels in dense plasmas,” J. Quant. Spectrosc. Radiat. Transfer 27, 345–357 (1982).10.1016/0022-4073(82)90127-3
[12]	P. Dallot, G. Faussurier, A. Decoster, and A. Mirone, “Average-ion level-population correlations in off-equilibrium plasmas,” Phys. Rev. E 57, 1017–1028 (1998).10.1103/physreve.57.1017
[13]	G. Faussurier, C. Blancard, and E. Berthier, “Nonlocal thermodynamic equilibrium self-consistent average-atom model for plasma physics,” Phys. Rev. E 63, 026401 (2001).10.1103/PhysRevE.63.026401
[14]	G. Faussurier, C. Blancard, and A. Decoster, “New screening coefficients for the hydrogenic ion model including l-splitting for fast calculations of atomic structure in plasmas,” J. Quant. Spectrosc. Radiat. Transfer 58, 233–260 (1997).10.1016/s0022-4073(97)00018-6
[15]	H. A. Scott and S. B. Hansen, “Advances in NLTE modeling for integrated simulations,” High Energy Density Phys. 6, 39–47 (2010).10.1016/j.hedp.2009.07.003
[16]	B. F. Rozsnyai, “Collisional-radiative average-atom model for hot plasmas,” Phys. Rev. E 55, 7507–7521 (1997).10.1103/physreve.55.7507
[17]	B. F. Rozsnyai, “Hot plasma opacities in the presence or absence of local thermodynamic equilibrium,” High Energy Density Phys. 6, 345–355 (2010).10.1016/j.hedp.2010.02.003
[18]	A. F. Nikiforov, V. G. Novikov, and V. B. Uvarov, “Quantum-statistical models of hot dense matter,” in Methods for Computation Opacity and Equation of State (Birkhauser, Basel, 2005).
[19]	A. A. Ovechkin, P. A. Loboda, V. G. Novikov, A. S. Grushin, and A. D. Solomyannaya, “RESEOS—A model of thermodynamic and optical properties of hot and warm dense matter,” High Energy Density Phys. 13, 20–33 (2014).10.1016/j.hedp.2014.09.001
[20]	A. A. Ovechkin, P. A. Loboda, and A. L. Falkov, “Transport and dielectric properties of dense ionized matter from the average-atom RESEOS model,” High Energy Density Phys. 20, 38–54 (2016).10.1016/j.hedp.2016.08.002
[21]	D. A. Liberman, “Self-consistent field model for condensed matter,” Phys. Rev. B 20, 4981–4989 (1979).10.1103/physrevb.20.4981
[22]	R. Piron and T. Blenski, “Variational-average-atom-in-quantum-plasmas (VAAQP) code and virial theorem: Equation-of-state and shock-Hugoniot calculations for warm dense Al, Fe, Cu, and Pb,” Phys. Rev. E 83, 026403 (2011).10.1103/PhysRevE.83.026403
[23]	A. Bar-Shalom, J. Oreg, and W. H. Goldstein, “Effect of configuration widths on the spectra of local thermodynamic equilibrium plasmas,” Phys. Rev. E 51, 4882–4890 (1995).10.1103/physreve.51.4882
[24]	V. G. Novikov, “Average atom approximation in non-LTE level kinetics,” in Modern Methods in Collisional-Radiative Modeling of Plasmas, edited by Y. Ralchenko (Springer International Publishing, Switzerland, 2016), Chap. 5, pp. 105–126.
[25]	I. Y. Vichev, A. D. Solomyannaya, A. S. Grushin, and D. A. Kim, “On certain aspects of the THERMOS toolkit for modeling experiments,” High Energy Density Phys. 33, 100713 (2019).10.1016/j.hedp.2019.100713
[26]	R. F. Heeter, S. B. Hansen, K. B. Fournier, M. E. Foord, D. H. Froula, A. J. Mackinnon, M. J. May, M. B. Schneider, and B. K. F. Young, “Benchmark measurements of the ionization balance of non-local thermodynamic equilibrium gold plasmas,” Phys. Rev. Lett. 99, 195001 (2007).10.1103/physrevlett.99.195001
[27]	M. E. Foord, S. H. Glenzer, R. S. Thoe, K. L. Wong, K. B. Fournier, J. R. Albritton, B. G. Wilson, and P. T. Springer, “Accurate determination of the charge state distribution in a well characterized highly ionized Au plasma,” J. Quant. Spectrosc. Radiat. Transfer 65, 231–241 (2000).10.1016/s0022-4073(99)00070-9
[28]	H. van Regemorter, “Rate of collisional excitation in stellar atmospheres,” Astrophys. J. 136, 906–915 (1962).10.1086/147445
[29]	R. D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, 1981).
[30]	H. R. Griem, M. Blaha, and P. C. Kepple, “Stark-profile calculations for Lyman-series lines of one-electron ions in dense plasmas,” Phys. Rev. A 19, 2421–2432 (1979).10.1103/physreva.19.2421
[31]	Using the relation l∼2meε/q, valid at high free-electron energies, one can rewrite the restriction q ≳ ℏ/d in a more evident form: ρ ≲ d, where ϱ≃ℏl/2meε is the classical impact parameter.
[32]	W. Lotz, “Electron-impact ionization cross-sections and ionization rate coefficients for atoms and ions,” Astrophys. J. Suppl. 14, 207 (1967).10.1086/190154
[33]	G. Faussurier and C. Blancard, “Degeneracy and relativistic microreversibility relations for collisional-radiative equilibrium models,” Phys. Rev. E 95, 063201 (2017).10.1103/PhysRevE.95.063201
[34]	I. Sobelman, Introduction to the Theory of Atomic Spectra (Pergamon Press, 1972).
[35]	In the present work, we do not allow for the change of the m-subshell occupation number brought about by two-electron transitions like (j → c, m → i) and (i → c, j → m) as well as by their inverse counterparts.¹³ In general, the inclusion of these transitions would suggest the use of more accurate approximations to evaluate transition rates Ajimc than the dipole approximation employed in Eq. (23), e.g., the distorted-wave approximation.¹ This is evidenced merely by the fact that Eq. (23) yields different values of the m → c, j → i (Ajimc) and j → c, m → i (Amijc) transition rates (so that one of these may even be equal to zero), although in the distorted-wave approximation these rates appear to be the same.
[36]	In practice, the occupation numbers in Eqs. (22) and (25) are updated only when one goes from one external iteration to another, i.e., variation of those in the internal iterations is not allowed.
[37]	V. Eyert, “A comparative study on methods for convergence acceleration of iterative vector sequences,” J. Comput. Phys. 124, 271–285 (1996).10.1006/jcph.1996.0059
[38]	D. A. Liberman and B. I. Bennett, “Atomic vibrations in a self-consistent-field atom-in-jellium model of condensed matter,” Phys. Rev. B 42, 2475–2484 (1990).10.1103/physrevb.42.2475
[39]	C. E. Starrett, N. M. Gill, T. Sjostrom, and C. W. Greeff, “Wide ranging equation of state with tartarus: A hybrid Green’s function/orbital based average atom code,” Comp. Phys. Commun. 235, 50–62 (2019).10.1016/j.cpc.2018.10.002
[40]	R. Karazija, The Theory of X-Ray and Electronic Spectra of Free Atoms: An Introduction (Mokslas, Vilnius, 1987) (in Russian).
[41]	G. Massacrier and J. Dubau, “A theoretical approach to N-electron ionic structure under dense plasma conditions: I. Blue and red shift,” J. Phys. B: At. Mol. Opt. Phys. 23, 2459S–2469S (1990).10.1088/0953-4075/23/13/033
[42]	M. F. Gu, “The flexible atomic code,” Can. J. Phys. 86(5), 675–689 (2008).10.1139/p07-197
[43]	A basic configuration is built by successively filling subshells in order of increasing quantum numbers n, l, and j.
[44]	X. Li and F. B. Rosmej, “Quantum-number-dependent energy level shifts of ions in dense plasmas: A generalized analytical approach,” Europhys. Lett. 99, 33001 (2012).10.1209/0295-5075/99/33001
[45]	M. Poirier, “A study of density effects in plasmas using analytical approximations for the self-consistent potential,” High Energy Density Phys. 15, 12–21 (2015).10.1016/j.hedp.2015.03.008
[46]	X. Li, F. B. Rosmej, V. S. Lisitsa, and V. A. Astapenko, “An analytical plasma screening potential based on the self-consistent-field ion-sphere model,” Phys. Plasmas 26, 033301 (2019).10.1063/1.5055689
[47]	C. A. Iglesias, “On spectral line shifts from analytic fits to the ion-sphere model potential,” High Energy Density Phys. 30, 41–44 (2019).10.1016/j.hedp.2019.01.001
[48]	J.-C. Pain, “On the Li-Rosmej analytical formula for energy level shifts in dense plasmas,” High Energy Density Phys. 31, 99–100 (2019).10.1016/j.hedp.2019.03.003
[49]	X. Li and F. B. Rosmej, “Analytical approach to level delocalization and line shifts in finite temperature dense plasmas,” Phys. Lett. A 384, 126478 (2020).10.1016/j.physleta.2020.126478
[50]	J.-C. Pain and D. Benredjem, “Simple electron-impact excitation cross-sections including plasma density effects,” High Energy Density Phys. 38, 100923 (2019).10.1016/j.hedp.2021.100923
[51]	J. C. Stewart and K. D. Pyatt, “Lowering of ionization potentials in plasmas,” Astrophys. J. 144, 1203–1211 (1966).10.1086/148714
[52]	In fact, THERMOS calculates atomic-process rates using the differences of average configuration energies rather than one-electron transition energies as is done in RESEOS. This distinction, however, plays no significant role in the comparisons of the RESEOS and THERMOS results presented and is therefore omitted in the following discussion.
[53]	J. R. Albritton and B. G. Wilson, “NLTE ionization and energy balance in high-Z laser-plasmas including two-electron transitions,” J. Quant. Spectrosc. Radiat. Transfer 65, 1–13 (2000).10.1016/s0022-4073(99)00050-3
[54]	K. L. Wong, M. J. May, P. Beiersdorfer, K. B. Fournier, B. Wilson, G. V. Brown, P. Springer, P. A. Neill, and C. L. Harris, “Determination of the charge state distribution of a highly ionized coronal Au plasma,” Phys. Rev. Lett. 90, 235001 (2003).10.1103/physrevlett.90.235001
[55]	P. Beiersdorfer, M. J. May, J. H. Scofield, and S. B. Hansen, “Atomic physics and ionization balance of high-Z ions: Critical ingredients for characterizing and understanding high-temperature plasmas,” High Energy Density Phys. 8, 271–283 (2012).10.1016/j.hedp.2012.03.003
[56]	F. Gilleron and J.-C. Pain, “Stable method for the calculation of partition functions in the superconfiguration approach,” Phys. Rev. E 69, 056117 (2004).10.1103/PhysRevE.69.056117
[57]	J. G. Rubiano, R. Florido, C. Bowen, R. W. Lee, and Y. Ralchenko, “Review of the 4th NLTE code comparison workshop,” High Energy Density Phys. 3, 225–232 (2007).10.1016/j.hedp.2007.02.027
[58]	A. A. Ovechkin, P. A. Loboda, A. L. Falkov, and P. A. Sapozhnikov, “Equation of state modeling with pseudoatom molecular dynamics,” Phys. Rev. E 103, 053206 (2021).10.1103/PhysRevE.103.053206
[59]	N. Wetta, J.-C. Pain, and O. Heuzé, “D’yakov-Kontorovitch instability of shock waves in hot plasmas,” Phys. Rev. E 98, 033205 (2018).10.1103/physreve.98.033205