Exact Solution of a Fully General Non-Local-Thermodynamic-Equilibrium Two-Level Atom
Brian G. Wilson1; Jean-Christophe Pain2
1 Lawrence Livermore National Laboratories, P.O. Box 808, Livermore, CA 94550, USA
2 CEA, DAM, DIF, 91297 Arpajon, France; Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, 91680 Bruyères-le-Châtel, France
MathematicS In Action, Special issue Maths and Industry, Volume 11 (2022) no. 1, pp. 259-267.

We describe an algorithm for the solution of a statistical/average atom non-local-thermodynamic-equilibrium atomic kinetics model of steady-state plasmas in which all one- and two-electron processes are included in full generality.

Published online:
DOI: 10.5802/msia.27
Mots-clés : Plasma spectroscopy, Opacity, Emissivity, Gröbner basis
Brian G. Wilson 1; Jean-Christophe Pain 2

1 Lawrence Livermore National Laboratories, P.O. Box 808, Livermore, CA 94550, USA
2 CEA, DAM, DIF, 91297 Arpajon, France; Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, 91680 Bruyères-le-Châtel, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Brian G. Wilson; Jean-Christophe Pain. Exact Solution of a Fully General Non-Local-Thermodynamic-Equilibrium Two-Level Atom. MathematicS In Action, Special issue Maths and Industry, Volume 11 (2022) no. 1, pp. 259-267. doi : 10.5802/msia.27. https://msia.centre-mersenne.org/articles/10.5802/msia.27/

[1] Mathematica, Version 12.3.1, 2021 (Wolfram Research, Inc., Champaign, IL, https://www.wolfram.com/mathematica)

[2] J. R. Albritton; B. G. Wilson NLTE ionization and energy balance in high-Z laser-plasmas including two-electron transitions, J. Quant. Spectrosc. Radiat. Transfer, Volume 65 (2000), pp. 1-13 | DOI

[3] L. Allen; J. H. Eberly Optical Resonance and Two-level Atoms, Dover books on physics and chemistry, Dover Publications, 1987

[4] A. Barchielli; M. Gregoratti A Two-Level Atom: General Setup, in Quantum Trajectories and Measurements in Continuous Time: The Diffusive Case, Springer, 2009, pp. 151-182

[5] C. Blancard; G. Faussurier; T. Kato; R. M. More Effective Boltzmann law and Prigogine theorem of minimum entropy production in highly charged ion plasmas, J. Quant. Spectrosc. Radiat. Transfer, Volume 99 (2006), pp. 75-83 | DOI

[6] D. Bouche; A. Decoster; L. Desvillettes; V. Ricci A Coherent Derivation of an Average Ion Model Including the Evolution of Correlations Between Different Shells, MathS In Action, Volume 6 (2013), pp. 1-14 | DOI | Numdam | MR | Zbl

[7] C. Bowen; P. Kaiser Dielectronic recombination in Au ionization temperature calculations, J. Quant. Spectrosc. Radiat. Transfer, Volume 81 (2001), pp. 85-95 | DOI

[8] B. Buchberger Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal (An Algorithm for Finding the Basis Elements in the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal), Ph. D. Thesis, Mathematical Institute, University of Innsbruck, Austria (1965) English translation in J. of Symb. Comput. (Special Issue on Logic, Mathematics, and Computer Science: Interactions) 41:475-511, 2006

[9] B. Buchberger Gröbner Bases and Systems Theory, Multidimensional Syst. Signal Process., Volume 12 (2001), pp. 223-251 | DOI | Zbl

[10] B. Buchberger; M. Kauers Groebner basis, Scholarpedia, Volume 5 (2010), pp. 7763-7783 | DOI

[11] M. Busquet Radiation-dependent ionization model for laser-created plasmas, Phys. Fluids B, Volume 5 (1993), pp. 4191-4206 | DOI

[12] M. S. Chaharbashloo; A. Basiri; S. Rahmany; S. Zarrinkamar An Application of Gröbner Basis in Differential Equations of Physics, Z. Naturforsch. A., Volume 68 (2013), pp. 646-650 | DOI

[13] N. Courtois; A. Klimov; J. Patarin; A. Shamir Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations, Advances in Cryptology — EUROCRYPT 2000 (2000), pp. 392-407 | DOI | Zbl

[14] D. Cox; J. Little; D. O’Shea Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer, 2007

[15] P. Dallot; G. Faussurier; A. Decoster; A. Mirone Average-ion level-population correlations in off-equilibrium plasmas, Phys. Rev. E, Volume 57 (1998), pp. 1017-1028 | DOI

[16] A. Decoster Onsager symmetry of the average ion near equilibrium, J. Quant. Spectrosc. Radiat. Transfer, Volume 71 (2001), pp. 295-303 | DOI

[17] L. Desvillettes; V. Ricci About the link between the detailed description of transitions in an ion and the average-ion models, Commun. Math. Sci., Volume 7 (2009), pp. 471-488 | MR | Zbl

[18] A. Djaoui; S. J. Rose Calculation of the time-dependent excitation and ionization in a laser-produced plasma, J. Phys. B: At. Mol. Opt. Phys., Volume 25 (1992), pp. 2745-2762 | DOI

[19] H. Fakhri; M. Sayyah-Fard The Jaynes-Cummings model of a two-level atom in a single-mode para-Bose cavity field, Sci. Rep., Volume 11 (2021), pp. 2045-2322 | DOI

[20] J.-C. Faugère A new efficient algorithm for computing Gröbner bases, J. Pure Appl. Algebra, Volume 139 (1999), pp. 61-88 | DOI | Zbl

[21] R. P. Feynman The Feynman Lectures on Physics, 3, Addison-Wesley Publishing Group, 1965

[22] E. T. Jaynes; F. W. Cummings Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proc. IEEE, Volume 51 (1964), pp. 89-109 | DOI

[23] N. Lauritzen Concrete Abstract Algebra: From Numbers to Gröbner Bases, Cambridge University Press, 2003

[24] M. Lax Fluctuations from the nonequilibrium steady state, Rev. Mod. Phys., Volume 32 (1960), pp. 25-64 | DOI | Zbl

[25] W. Lokke; W. Grassberger XSNQ-U: a non-LTE emission and absorption coefficient subroutine (1977) no. Report UCRL-52276 (Technical report)

[26] J. P. McKelvey Simple transcendental expressions for the roots of cubic equations, Am. J. Phys., Volume 52 (1984), pp. 269-270 | DOI | MR

[27] R. More; T. Kato Near-LTE Linear Response Calculations with a Collisional-Radiative Model for He-like Al Ions, Phys. Rev. Lett., Volume 81 (1998), pp. 814-817 | DOI

[28] H. S. Rag; J. Gea-Banacloche Two-level-atom excitation probability for single- and N-photon wave packets, Phys. Rev. A, Volume 96 (2017), p. 033817 | DOI

[29] B. L. van der Waerden A History of Algebra, Springer, 1985 | DOI

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