Microscopic Theory of Resonant Radiative Transfer in Gas-discharge Plasma
DOI:
https://doi.org/10.24160/1993-6982-2026-3-160-170Keywords:
resonant radiation, gas-discharge plasma, radiative transfer, matrix Green's functions, Dyson equation, spectral line broadening, Keldysh formalism, absorption coefficientAbstract
A self-consistent microscopic approach to describing resonant radiative transfer in plasma is developed. It is based on the application of the Keldysh and Green matrix functions formalism to classical electrodynamics. Unlike the classical radiative transfer equation (RTE) and phenomenological broadening models (the Voigt profile), the proposed formalism allows for rigorous consideration of spatiotemporal correlations between absorption and re-emission events, as well as the mutual influence of various spectral line broadening mechanisms. A key result is a unified description of the field coherent and incoherent components, which is of critical importance for analyzing spectral line wings, in which the conventional approaches systematically underestimate the radiation brightness. It is shown, taking the hydrogen Hα resonance line (656.3 nm) as an example, that the taking into account of correlations between Doppler and Stark broadenings leads to an increase in the brightness in the wings by 1-2 orders of magnitude in comparison with the Voigt model, which is essential for accurate diagnostics of dense plasma. The proposed theory places no restrictions on the density of medium and opens new possibilities for modeling radiative transfer in optically dense and nonequilibrium plasma.
References
1. Hutchinson I.H. Principles of Plasma Diagnostics. Cambridge: Cambridge University Press, 2002.
2. Waymouth J.F. Electric Discharge Lamps. Cambridge: M.I.T. Press, 1971.
3. Роудз Ч., Хофф П., Кросс М. Эксимерные лазеры М.: Мир, 1981.
4. Mihalas D. Stellar Atmospheres. San Francisco: W.H. Freeman & Co., 1978.
5. Lieberman M.A., Lichtenberg A.J. Principles of Plasma Discharges and Materials Processing. Hoboken: John Wiley & Sons, Inc., 2005.
6. Baranger M. Problem of Overlapping Lines in the Theory of Pressure Broadening // Phys. Rev. 1958. V. 111(2). Pp. 494—504.
7. Keldysh L.V. Diagram Technique for Non-equilibrium Processes // Soviet Physics — JETP. 1965. V. 20(4). Pp. 1018—1028.
8. Danielewicz P. Quantum Theory of Non-equilibrium Processes, I // Annals Phys. 1984. V. 152(2), Pp. 239—304.
9. Biberman L.M., Vorob'ev V.S., Yakubov I.T. Kinetics of Non-equilibrium Low-temperature Plasmas. N.-Y.: Springer, 1987.
10. Bohm D., Pines D. A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas // Phys. Rev. 1953. V. 92(3). Pp. 609—625.
11. Blase H., Duchemin I., Jacquemin D., Loos P.-F. The Bethe-Salpeter Equation Formalism: from Physics to Chemistry // J. Phys. Chem. Lett. 2020. V. 11(17). Pp. 7371—7382.
12. Apresyan L.A., Kravtsov Yu.A. Radiation Transfer: Statistical and Wave Aspects. Amsterdam: Gordon and Breach, 1996.
13. Розенберг Г.В. Луч света (К теории светового поля) // Успехи физических наук. 1977. Т. 121. № 1. С. 97—138.
14. Mishchenko M.I. Directional Radiometry and Radiative Transfer: a New Paradigm // J. Quantitative Spectroscopy and Radiative Transfer. 2011. V. 112(13). Pp. 2079—2094.
15. Budak V.P., Veklenko B.A. Boson Peak, Flickering Noise, Backscattering Processes and Radiative Transfer in Random Media // J. Quantitative Spectroscopy and Radiative Transfer. 2011. V. 112(5). Pp. 864—875.
16. Sommerfeld A. Die Greensche Funktion der Schwingungsgleichung // Jahresbericht der Deutschen Mathematiker-vereinigung. 1912. V. 21. Pp. 309—353.
17. Dyson F.J. The S Matrix in Quantum Electrodynamics // Phys. Rev. 1949. V. 75(11). Pp. 1736—1755.
18. Wigner E.P. On the Quantum Correction for Thermodynamic Equilibrium // Phys. Rev. 1932. V. 40(5). Pp. 749—759.
19. Tsytovich V.N. e. a. From Plasma Crystals and Helical Structures Towards Inorganic Living Matter // New J. Phys. 2007. V. 9(8). P. 263.
20. Boyd R.W. Nonlinear Optics. London: Academic Press, 2020.
21. Calisti A. e. a. Model for the Line Shapes of Complex Ions in Hot and Dense Plasmas // Phys. Rev. A. 1990. V. 42(9). Pp. 5433—5440.
22. Березина Г.П., Файнберг Я.Б., Березин А.Л., Назаренко O.K. Использование модулированного электронного пучка для генерации и переноса электромагнитных волн в плотной плазме // Физика плазмы. 1994. Т. 20. Вып. 9. С. 828—835.
23. Talin B. e. a. Frequency-fluctuation Model for Line-shape Calculations in Plasma Spectroscopy // Phys. Rev. A. 1995. V. 51(3). P. 1918.
24. Гавриков М.Б. Основные положения электромагнитной гидродинамики плазмы (ЭМГД) // Препринты ИПМ им. М.В. Келдыша. 2019. № 65. С. 1—36.
25. Zheleznov I.I., Popov O.A. Electrodeless Source of UV Radiation Based on Low Pressure Microwave Mercury Discharge // Light & Eng. 2023. V. 31(3). Pp. 36—42.
26. Грим Х.Р. Уширение спектральных линий в плазме. М.: Мир, 1978.
27. Решенов С.П. Генерация и перенос излучения в плазме. М.: Изд-во МЭИ, 1989.
28. Heisenberg W. Über den Anschaulichen Inhalt der Quantentheoretischen Kinematik und Mechanik // Zeitschrift für Physik. 1927. V. 43. Pp. 172—198.
29. Lorenz L.V. On the Identity of the Vibrations of Light with Electrical Currents // Phil. Mag. 1867. Ser. 4. V. XXVI. Pp. 287—301.
30. Gyenis B. Maxwell and the Normal Distribution: a Colored Story of Probability, Independence, and Tendency Towards Equilibrium // Studies in History and Phil. Modern Phys. 2017. V. 57. Pp. 53—65.
31. Дзялошинский И.Е., Лифшиц Е.М., Питаевский Л.П. Общая теория Ван-дер-Ваальсовых сил // Успехи физических наук. 1961. Т. 73. № 3. С. 381—422.
32. Stark J. Beobachtungen über den Effekt des Elektrischen Feldes auf Spektrallinien I. Quereffekt // Annalen der Physik. 2006. V. 348(7). Pp. 965—982.
33. Holtsmark J. Über die Verbreiterung von Spektrallinien // Annalen der Physik. 1919. V. 363(7). Pp. 577—630
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Для цитирования: Будак ВП., Железнов И.И. Микроскопическая теория переноса резонансного излучения в газоразрядной плазме // Вестник МЭИ. 2026. № 3. С. 160—170. DOI: 10.24160/1993-6982-2026-3-160-170
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Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
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1. Hutchinson I.H. Principles of Plasma Diagnostics. Cambridge: Cambridge University Press, 2002.
2. Waymouth J.F. Electric Discharge Lamps. Cambridge: M.I.T. Press, 1971.
3. Roudz Ch., Hoff P., Kross M. Eksimernye Lazery M.: Mir, 1981. (in Russian).
4. Mihalas D. Stellar Atmospheres. San Francisco: W.H. Freeman & Co., 1978.
5. Lieberman M.A., Lichtenberg A.J. Principles of Plasma Discharges and Materials Processing. Hoboken: John Wiley & Sons, Inc., 2005.
6. Baranger M. Problem of Overlapping Lines in the Theory of Pressure Broadening. Phys. Rev. 1958;111(2):494—504.
7. Keldysh L.V. Diagram Technique for Non-equilibrium Processes. Soviet Physics — JETP. 1965;20(4):1018—1028.
8. Danielewicz P. Quantum Theory of Non-equilibrium Processes, I. Annals Phys. 1984;152(2):239—304.
9. Biberman L.M., Vorob'ev V.S., Yakubov I.T. Kinetics of Non-equilibrium Low-temperature Plasmas. N.-Y.: Springer, 1987.
10. Bohm D., Pines D. A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas. Phys. Rev. 1953;92(3):609—625.
11. Blase H., Duchemin I., Jacquemin D., Loos P.-F. The Bethe-Salpeter Equation Formalism: from Physics to Chemistry. J. Phys. Chem. Lett. 2020;11(17):7371—7382.
12. Apresyan L.A., Kravtsov Yu.A. Radiation Transfer: Statistical and Wave Aspects. Amsterdam: Gordon and Breach, 1996.
13. Rozenberg G.V. Luch Sveta (K Teorii Svetovogo Polya). Uspekhi Fizicheskih Nauk. 1977;121(1):97—138. (in Russian).
14. Mishchenko M.I. Directional Radiometry and Radiative Transfer: a New Paradigm. J. Quantitative Spectroscopy and Radiative Transfer. 2011;112(13):2079—2094.
15. Budak V.P., Veklenko B.A. Boson Peak, Flickering Noise, Backscattering Processes and Radiative Transfer in Random Media. J. Quantitative Spectroscopy and Radiative Transfer. 2011;112(5):864—875.
16. Sommerfeld A. Die Greensche Funktion der Schwingungsgleichung. Jahresbericht der Deutschen Mathematiker-vereinigung. 1912;21:309—353.
17. Dyson F.J. The S Matrix in Quantum Electrodynamics. Phys. Rev. 1949;75(11):1736—1755.
18. Wigner E.P. On the Quantum Correction for Thermodynamic Equilibrium. Phys. Rev. 1932;40(5):749—759.
19. Tsytovich V.N. e. a. From Plasma Crystals and Helical Structures Towards Inorganic Living Matter. New J. Phys. 2007;9(8):263.
20. Boyd R.W. Nonlinear Optics. London: Academic Press, 2020.
21. Calisti A. e. a. Model for the Line Shapes of Complex Ions in Hot and Dense Plasmas. Phys. Rev. A. 1990;42(9):5433—5440.
22. Berezina G.P., Faynberg Ya.B., Berezin A.L., Nazarenko O.K. Ispol'zovanie Modulirovannogo Elektronnogo Puchka dlya Generatsii i Perenosa Elektromagnitnyh Voln v Plotnoy Plazme. Fizika Plazmy. 1994;20(9):828—835. (in Russian).
23. Talin B. e. a. Frequency-fluctuation Model for Line-shape Calculations in Plasma Spectroscopy. Phys. Rev. A. 1995;51(3):1918.
24. Gavrikov M.B. Osnovnye Polozheniya Elektromagnitnoy Gidrodinamiki Plazmy (EMGD). Preprinty IPM im. M.V. Keldysha. 2019;65:1—36. (in Russian).
25. Zheleznov I.I., Popov O.A. Electrodeless Source of UV Radiation Based on Low Pressure Microwave Mercury Discharge. Light & Eng. 2023;31(3):36—42.
26. Grim H.R. Ushirenie Spektral'nyh Liniy v Plazme. M.: Mir, 1978. (in Russian).
27. Reshenov S.P. Generatsiya i Perenos Izlucheniya v Plazme. M.: Izd-vo MEI, 1989. (in Russian).
28. Heisenberg W. Über den Anschaulichen Inhalt der Quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik. 1927;43:172—198.
29. Lorenz L.V. On the Identity of the Vibrations of Light with Electrical Currents. Phil. Mag. 1867;4(XXVI):287—301.
30. Gyenis B. Maxwell and the Normal Distribution: a Colored Story of Probability, Independence, and Tendency Towards Equilibrium. Studies in History and Phil. Modern Phys. 2017;57:53—65.
31. Dzyaloshinskiy I.E., Lifshits E.M., Pitaevskiy L.P. Obshchaya Teoriya Van-der-Vaal'sovyh Sil. Uspekhi Fizicheskih Nauk. 1961;73(3):381—422. (in Russian).
32. Stark J. Beobachtungen über den Effekt des Elektrischen Feldes auf Spektrallinien I. Quereffekt. Annalen der Physik. 2006;348(7):965—982.
33. Holtsmark J. Über die Verbreiterung von Spektrallinien. Annalen der Physik. 1919;363(7):577—630
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For citation: Budak V.P., Zheleznov I.I. Microscopic Theory of Resonant Radiative Transfer in Gas-discharge Plasma. Bulletin of MPEI. 2026;3:160—170. (in Russian). DOI: 10.24160/1993-6982-2026-3-160-170
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Conflict of interests: the authors declare no conflict of interest
