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Influence of Partition Function and Interaction Potential on Transport Properties of Thermal Plasmas

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Abstract

This paper, divided into two parts, is devoted to the transport properties at local thermodynamic equilibrium: the first part shows the influences of partition functions through the plasma composition and the second part the influence of interaction potentials. In the first part, for complex chemical mixtures the determination of the partition functions of different species is considered: monatomic, diatomic and polyatomic. In the plasmas the monatomic species are important; we study thoroughly the partition functions of monatomic neutrals and ions. We introduce two cut-off criteria. We test the influence of the two criteria on the partition functions and consequently onto the plasma composition and transport properties. We applied the study to Ar–Cu mixtures. In the second part, an historic study shows that the collision integrals used in calculating the transport properties become more accurate leading to more reliable values of the transport coefficients: application to N2 plasma. Now we have to calculate transport properties of complex mixtures and in these cases, for numerous interactions, a lack of data means that model potentials have to be used to determine collision integrals. In this paper, we have used two potential models: the first, for neutral–neutral and ion–neutral interactions, is an improvement of the Lennard-Jones function and the second is developed, from Stockmayer potential, for polar gases. We compare, for the collision integrals, the results obtained by these two models with those determined with more accurate potentials: applications to CO2 plasma and H2–N2 mixtures.

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Authors and Affiliations

  1. CNRS, SPCTS (UMR7315), Université de Limoges, 12 rue Atlantis, 87068, Limoges Cedex, France

    J. Aubreton & M. F. Elchinger

  2. Clermont Université, Université Blaise Pascal, LAEPT, BP 10448, 63000, Clermont-Ferrand, France

    P. André

Authors
  1. J. Aubreton
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  3. P. André
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Correspondence to P. André.

Appendix

Appendix

The second sum of (relation 4) introduces discontinuities in the plasma composition (when the values of n max increase or decrease) as the temperature varies and these discontinuities will appear also in the calculated transport coefficients. Therefore we are obliged to remedy to this drawback having no physical justification. We have, with simplified notation and for neutral atomic species as an example, the following procedure: where n is the principal quantum number, E n (id. for E n−1 and E n+1) is the hydrogenic energy with statistical weight of 2n 2 g f and for \( E_{I} - \Updelta E_{I}^{0} \). We have defined \( E_{1} = (E_{n} + E_{n - 1} )/2 \) (id for E 2). Then, for this last state, the statistical weight is calculated using \( 2n^{2} g_{c} \frac{\Updelta E}{{E_{2} - E_{1} }} \). Our partition function Q ours is greater than classical calculated Q c for \( E_{I} - \Updelta E_{I}^{0} \) < E n and in the reverse order for \( E_{I} - \Updelta E_{I}^{0} \) > E n . Notice that the continuity of the first and second derivatives of the partition function are not ensured.

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Aubreton, J., Elchinger, M.F. & André, P. Influence of Partition Function and Interaction Potential on Transport Properties of Thermal Plasmas. Plasma Chem Plasma Process 33, 367–399 (2013). https://doi.org/10.1007/s11090-012-9427-3

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