Skip to main content
SpringerLink
Log in

Non-uniqueness of the multi-temperature law of mass action. Application to 2T plasma composition calculation by means of a collisional-radiative model

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

This work is devoted to the calculation of the composition for a monoatomic plasma (argon in the case presented) for which the assumption of thermal equilibrium is not realized. The plasma composition is obtained from a CR model, taking into account free electrons and a great number of electronic levels of Ar atoms and Ar+ ions. This model is based on a large set of transition probabilities and reaction rate coefficients for radiative processes (spontaneous emission and radiative recombination) and on an extended database of direct and reverse reaction rate coefficients for collisional processes (excitation/de-excitation and ionization/recombination mechanisms). Assuming Maxwellian energy distribution functions for electrons and heavy chemical species, detailed balance equations are determined for all kind of reactions in the frame of the micro reversibility principle. From these balance equations, reverse rate coefficients are calculated as a function of direct reaction rates and of electrons and heavy particles translation temperatures (T e and T h respectively). Particular attention is paid to problematic chemical reactions with electrons involved on one side and only heavy species on the other side such as: Ar + Ar → Ar + Ar+ + e. The detailed balance relations obtained for ionization/recombination processes demonstrate the non-uniqueness of the multi-temperature Saha-Eggert law (i.e. non-uniqueness of the multi-temperature law of mass action). Multi-temperature argon plasma compositions obtained in the present work exhibit abrupt density variations. These sharp variations are characteristic of the transition between the domination of heavy particle reactions (at low temperature) and the predominance of electron collisions (at high temperature).

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Gleizes, J.J. Gonzalez, P. Freton, J. Phys. D: Appl. Phys. 38, R153 (2005)

    Article  ADS  Google Scholar 

  2. J. Mostaghimi, P. Proulx, M.I. Boulos, J. Phys. D: Appl. Phys. 61, 1753 (1987)

    ADS  Google Scholar 

  3. M. El Morsli, P. Proulx, J. Phys. D: Appl. Phys. 40, 4810 (2007)

    Article  ADS  Google Scholar 

  4. Y. Tanaka, J. Phys. D: Appl. Phys. 37, 1190 (2004)

    Article  ADS  Google Scholar 

  5. R. Ye, A.B. Murphy, T. Ishigaki, Plasma Chem. Plasma Process. 27, 189 (2007)

    Article  Google Scholar 

  6. S.A. Al-Mamun, Y. Tanaka, Y. Uesugi, Plasma Chem. Plasma Process. 30, 141 (2010)

    Article  Google Scholar 

  7. S. Ghorui, J.V.R. Heberlein, E. Pfender, J. Phys. D: Appl. Phys. 40, 1966 (2007)

    Article  ADS  Google Scholar 

  8. M. Boselli, V. Colombo, E. Ghedini, M. Gherardi, P. Sanibondi, J. Phys. D: Appl. Phys. 46, 224009 (2013)

    Article  ADS  Google Scholar 

  9. J.P. Trelles, J.V.R. Heberlein, E. Pfender, J. Phys. D: Appl. Phys. 40, 5937 (2007)

    Article  ADS  Google Scholar 

  10. Y. Bartosiewicz, P. Proulx, Y. Mercadier, J. Phys. D: Appl. Phys. 35, 2139 (2002)

    Article  ADS  Google Scholar 

  11. A. Kaminska, B. Lopez, B. Izrar, M. Dudek, Plasma Sources Sci. Technol. 17, 035018 (2008)

    Article  ADS  Google Scholar 

  12. M. Baeva, D. Uhrlandt, J. Phys. D: Appl. Phys. 46, 325202 (2013)

    Article  Google Scholar 

  13. P. Freton, J.J. Gonzalez, Z. Ranarijoana, J. Mougenot, J. Phys. D: Appl. Phys. 45, 465206 (2012)

    Article  ADS  Google Scholar 

  14. V. Colombo, E. Ghedini, M. Boselli, P. Sanibondi, A. Concetti, J. Phys. D: Appl. Phys. 44, 194005 (2011)

    Article  ADS  Google Scholar 

  15. J. Park, J.V.R. Heberlein, E. Pfender, G. Candler, C.H. Chang, Plasma Chem. Plasma Process. 28, 213 (2008)

    Article  Google Scholar 

  16. M.S. Benilov, G.V. Naidis, J. Phys. D: Appl. Phys. 36, 1834 (2003)

    Article  ADS  Google Scholar 

  17. V. Rat, Ph.D. thesis, University of Limoges, France, 2001 (in French)

  18. V. Rat, P. André, J. Aubreton, M.F. Elchinger, P. Fauchais, D. Vacher, J. Phys. D: Appl. Phys. 35, 981 (2002)

    Article  ADS  Google Scholar 

  19. V. Rat, A.B. Murphy, J. Aubreton, M.F. Elchinger, P. Fauchais, J. Phys. D: Appl. Phys. 41, 183001 (2008)

    Article  ADS  Google Scholar 

  20. R.S. Devoto, Phys. Fluids 10, 2105 (1967)

    Article  ADS  Google Scholar 

  21. C. Bonnefoi, Ph.D. thesis no. 15-83, University of Limoges, France, 1983 (in French)

  22. H.X. Wang, S.Q. Chen, X. Chen, J. Phys. D: Appl. Phys. 45, 165202 (2012)

    Article  ADS  Google Scholar 

  23. J. Aubreton, M.F. Elchinger, P. Fauchais, Plasma Chem. Plasma Process. 18, 1 (1998)

    Article  Google Scholar 

  24. W.Z. Wang, M.Z. Rong, J.D. Yan, A.B. Murphy, J.W. Spencer, Phys. Plasmas 18, 113502 (2011)

    Article  ADS  Google Scholar 

  25. S. Ghorui, J.V.R. Heberlein, E. Pfender, Plasma Chem. Plasma Process. 27, 267 (2007)

    Article  Google Scholar 

  26. W.Z. Wang, M.Z. Rong, Y. Wu, J.W. Spencer, J.D. Yan, D.H. Mei, Phys. Plasmas 19, 083506 (2012)

    Article  ADS  Google Scholar 

  27. S. Ghorui, J.V.R. Heberlein, E. Pfender, Plasma Chem. Plasma Process. 28, 553 (2008)

    Article  Google Scholar 

  28. V. Colombo, E. Ghedini, P. Sanibondi, Plasma Sources Sci. Technol. 20, 035003 (2011)

    Article  ADS  Google Scholar 

  29. V. Colombo, E. Ghedini, P. Sanibondi, J. Phys. D: Appl. Phys. 42, 055213 (2009)

    Article  ADS  Google Scholar 

  30. J. Aubreton, M.F. Elchinger, V. Rat, P. Fauchais, J. Phys. D:Appl. Phys. 37, 34 (2004)

    Article  ADS  Google Scholar 

  31. V. Rat, P. André, J. Aubreton, M.F. Elchinger, P. Fauchais, A. Lefort, Plasma Chem. Plasma Process. 22, 453 (2002)

    Article  Google Scholar 

  32. V. Rat, P. André, J. Aubreton, M.F. Elchinger, P. Fauchais, A. Lefort, Plasma Chem. Plasma Process. 22, 475 (2002)

    Article  Google Scholar 

  33. J. Aubreton, M.F. Elchinger, J. Phys. D: Appl. Phys. 36, 1798 (2003)

    Article  ADS  Google Scholar 

  34. J. Aubreton, M.F. Elchinger, P. Fauchais, V. Rat, P. André, J. Phys. D: Appl. Phys. 37, 2232 (2004)

    Article  ADS  Google Scholar 

  35. W.B. White, S.M. Johnson, G.B. Dantzig, J. Chem. Phys. 28, 751 (1958)

    Article  ADS  Google Scholar 

  36. D. Godin, J.Y. Trépanier, Plasma Chem. Plasma Process. 24, 447 (2004)

    Article  Google Scholar 

  37. D.R. Bates, A.E. Kingston, R.W.P. McWhirter, Proc. R. Soc. Lond. Ser. A 267, 297 (1962)

    Article  ADS  Google Scholar 

  38. D.R. Bates, A.E. Kingston, R.W.P. McWhirter, Proc. R. Soc. Lond. Ser. A 270, 155 (1962)

    Article  ADS  Google Scholar 

  39. V. Rat, A.B. Murphy, J. Aubreton, M.F. Elchinger, P. Fauchais, J. Phys. D: Appl. Phys. 41, 183001 (2008)

    Article  ADS  Google Scholar 

  40. P. André, IEEE Trans. Plasma Sci. 23, 453 (1995)

    Article  ADS  Google Scholar 

  41. P. André, A. Lefort, J. Phys. D: Appl. Phys. 31, 717 (1998)

    Article  ADS  Google Scholar 

  42. X. Chen, P. Han, J. Phys. D: Appl. Phys. 32, 1711 (1999)

    Article  ADS  Google Scholar 

  43. P. André, J. Aubreton, M.F. Elchinger, V. Rat, P. Fauchais, A. Lefort, A.B. Murphy, Plasma Chem. Plasma Process. 24, 435 (2004)

    Article  Google Scholar 

  44. I. Prigogine, Bull. Cl. Sci. Acad. R. Belg. 26, 53 (1940)

    Google Scholar 

  45. A.V. Potapov, High Temp. 4, 48 (1966)

    Google Scholar 

  46. M.C.M. Van de Sanden, P.P.J.M. Schram, A.G. Peeters, J.A.M. Van der Mullen, G.M.W. Kroesen, Phys. Rev. E 40, 5273 (1989)

    Article  ADS  Google Scholar 

  47. Y. Tanaka, Y. Yokomizu, M. Ishikawa, T. Matsumura, IEEE Trans. Plasma Sci. 25, 991 (1997)

    Article  ADS  Google Scholar 

  48. A. Gleizes, B. Chervy, J.J. Gonzalez, J. Phys. D: Appl. Phys. 32, 2060 (1999)

    Article  ADS  Google Scholar 

  49. P. André, J. Aubreton, M.F. Elchinger, P. Fauchais, A. Lefort, Plasma Chem. Plasma Process. 21, 83 (2001)

    Article  Google Scholar 

  50. D. Giordano, M. Capitelli, Phys. Rev. E 65, 016401 (2001)

    Article  ADS  Google Scholar 

  51. J. Bacri, M. Lagreca, A. Médani, Physica B&C 113, 403 (1982)

    Article  ADS  Google Scholar 

  52. J.A. Kunc, W.H. Soon, Phys. Rev. A 40, 5822 (1989)

    Article  ADS  Google Scholar 

  53. L.C. Pierrot, C.O. Laux, C.H. Kruger, AIAA Paper AIAA 98-2664, in Proceedings of the 29th Plasmadynamics and Lasers Conference, 1998, June 15–18, Albuquerque, NM, USA (1998)

  54. A.M. Gomes, A. Essoltani, J. Bacri, J. Quant. Spectrosc. Radiat. Transf. 43, 471 (1990)

    Article  ADS  Google Scholar 

  55. W.H. Soon, J.A. Kunc, Phys. Rev. A 41, 825 (1990)

    Article  ADS  Google Scholar 

  56. C.O. Laux, L. Yu, D.M. Packan, R.J. Gessman, L.C. Pierrot, C.H. Kruger, R.N. Zare, AIAA Paper AIAA 99-3476, in Proceedings of the 30th Plasmadynamics and Lasers Conference, June 28–July 1, 1999, Norfolk, VA, USA (1999)

  57. Ph. Teulet, J.P. Sarrette, A.M. Gomes, J. Quant. Spectrosc. Radiat. Transf. 70, 159 (2001)

    Article  ADS  Google Scholar 

  58. M. Lino Da Silva, V. Guerra, J. Loureiro, Plasma Sources Sci. Technol. 18, 034023 (2009)

    Article  ADS  Google Scholar 

  59. A. Bultel, J. Annaloro, V. Morel, J. Phys.: Conf. Ser. 399, 012014 (2012)

    Google Scholar 

  60. C. Park, Nonequilibrium hypersonic aerothermodynamics (Wiley, New York, 1990)

  61. W.L. Hankey, Re-entry aerodynamics. AIAA education series (AIAA Inc., Washington, DC, 1988)

  62. J.D. Anderson, Hypersonic and high temperature gas dynamics (McGraw-Hill, New York, 1989)

  63. A. Bultel, B.G. Chéron, A. Bourdon, O. Motapon, I.F. Schneider, Phys. Plasmas 13, 043502 (2006)

    Article  ADS  Google Scholar 

  64. J. Annaloro, A. Bultel, Phys. Plasmas 21, 123512 (2014)

    Article  ADS  Google Scholar 

  65. A. Bultel, J. Annaloro, Plasma Sources Sci. Technol. 22, 025008 (2013)

    Article  ADS  Google Scholar 

  66. D.J. Drake, S. Popovic, L. Vuskovic, T. Dinh, IEEE Trans. Plasma Sci. 37, 1646 (2009)

    Article  ADS  Google Scholar 

  67. A.M. Brandis, C.O. Laux, T. Magin, T.J. McIntyre, R.G. Morgan, J. Thermophys. Heat Transf. 28, 32 (2014)

    Article  Google Scholar 

  68. P. André, Contrib. Plasma Phys. 37, 23 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  69. P. André, M. Abbaoui, R. Bessege, A. Lefort, Plasma Chem. Plasma Process. 17, 207 (1997)

    Article  Google Scholar 

  70. E. Richley, D.T. Tuma, J. Appl. Phys. 53, 8537 (1982)

    Article  ADS  Google Scholar 

  71. G.J. Cliteur, K. Suzuki, Y. Tanaka, T. Sakuta, T. Matsubara, Y. Yokomizu, T. Matsumura, J. Phys. D: Appl. Phys. 32, 1851 (1999)

    Article  ADS  Google Scholar 

  72. V. Rat, P. André, J. Aubreton, M.F. Elchinger, P. Fauchais, A. Lefort, J. Phys. D: Appl. Phys. 34, 2191 (2001)

    Article  ADS  Google Scholar 

  73. http://www.nist.gov/pml/data/asd.cfm

  74. Y.B. Zel’dovich, Y.P. Raizer, Physics of shock waves and high-temperature hydrodynamic phenomena (Dover Mineola, New York, 2002)

  75. H.W. Drawin, Collision and transport cross sections, Report EUR-CEA-FC 383, 1966

  76. A. Bultel, B. Van Ootegem, A. Bourdon, P. Vervisch, Phys. Rev. E 65, 046046 (2002)

    Article  Google Scholar 

  77. H.W. Drawin, F. Emard, Phys. Lett. 43A, 333 (1973)

    Article  ADS  Google Scholar 

  78. C.O. Laux, Ph.D. thesis, Stanford University, HTGL Report T-288, 1993

  79. A.R. Hochstim, Kinetic processes in gases and plasmas (Academic Press, New York, 1969)

  80. J. Oxenius, Kinetic theory of particles and photons (Springer-Verlag, Berlin, 1986)

  81. C.B. Collins, Phys. Rev. 158, 94 (1967)

    Article  ADS  Google Scholar 

  82. D.R. Bates, S.P. Khare, Proc. Phys. Soc. (Lond.) 85, 231 (1965)

    Article  ADS  Google Scholar 

  83. P.N. Brown, G.D. Byrne, A.C. Hindmarsh, SIAM J. Sci. Stat. Comput. 10, 1038 (1989)

    Article  Google Scholar 

  84. R. Goldstein, Numerical calculation of electron-atom excitation and ionization rates using Gryzinski cross sections, NASA Technical Report 32-1372, Jet Propulsion Laboratory, Pasadena, California, USA, 1969

  85. R.J. Giannaris, F.P. Incropera, J. Quant. Spectrosc. Radiat. Transf. 11, 291 (1971)

    Article  ADS  Google Scholar 

  86. H.V.R. Van Regemorter, Astrophys. J. 136, 906 (1962)

    Article  ADS  Google Scholar 

  87. P. Mansbach, J. Keck, Phys. Rev. 181, 275 (1969)

    Article  ADS  Google Scholar 

  88. J.J. Lowke, E.R. Capriotti, J. Quant. Spectrosc. Radiat. Transf. 9, 207 (1969)

    Article  ADS  Google Scholar 

  89. J.J. Lowke, J. Quant. Spectrosc. Radiat. Transf. 14, 111 (1974)

    Article  ADS  Google Scholar 

  90. R.W. Libermann, J.J. Lowke, J. Quant. Spectrosc. Radiat. Transf. 16, 253 (1976)

    Article  ADS  Google Scholar 

  91. R. Hannachi, Y. Cressault, D. Salem, Ph. Teulet, L. Beji, Z. Ben Lakhdar, J. Phys. D: Appl. Phys. 45, 485206 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Toulouse, UPS, INPT, LAPLACE (Laboratoire Plasma et Conversion d’Energie), 118 Route de Narbonne, 31062, Toulouse Cedex 9, France

    Julien Annaloro, Philippe Teulet, Yann Cressault & Alain Gleizes

  2. CORIA, UMR CNRS 6614, Université de Rouen, Site universitaire du Madrillet, BP 12, 76801, Saint-Etienne du Rouvray, France

    Julien Annaloro & Arnaud Bultel

Authors
  1. Julien Annaloro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Philippe Teulet
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arnaud Bultel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yann Cressault
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alain Gleizes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philippe Teulet.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Annaloro, J., Teulet, P., Bultel, A. et al. Non-uniqueness of the multi-temperature law of mass action. Application to 2T plasma composition calculation by means of a collisional-radiative model. Eur. Phys. J. D 71, 342 (2017). https://doi.org/10.1140/epjd/e2017-80284-5

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2017-80284-5

Keywords

Search

Navigation