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Screened Cluster Expansions for Partially Ionized Gases

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Abstract

We consider a partially ionized gas at thermal equilibrium, in the Saha regime. The system is described in terms of a quantum plasma of nuclei and electrons. In this framework, the Coulomb interaction is the source of a large variety of phenomena occurring at different scales: recombination, screening, diffraction, etc. In this paper, we derive a cluster expansion adequate for a coherent treatment of those phenomena. The expansion is obtained by combining the path integral representation of the quantum gas with familiar Mayer diagrammatics. In this formalism, graphs have a clear physical interpretation: vertices are associated with recombined chemical species, while bonds describe their mutual interactions. The diagrammatical rules account exactly for all effects in the medium. Applications to thermodynamics, van der Waals forces and dielectric versus conductive behaviour will be presented in forthcoming papers.

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Authors and Affiliations

  1. Laboratoire de Physique, École Normale Supérieure de Lyon, UMR 5672 du CNRS, 46, allée d'Italie, 69364, Lyon Cedex 07, France

    A. Alastuey

  2. École Polytechnique Fédérale de Lausanne EPFL, Institut de Théorie des Phénomènes Physiques, CH-1015, Lausanne, Switzerland

    V. Ballenegger & Ph. A. Martin

  3. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, United Kingdom

    V. Ballenegger

  4. Laboratoire de Physique Théorique, Université Paris-Sud, UMR 8627 du CNRS, Bâtiment 210, 91405, Orsay, France

    F. Cornu

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  1. A. Alastuey
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  2. V. Ballenegger
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  3. F. Cornu
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  4. Ph. A. Martin
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Alastuey, A., Ballenegger, V., Cornu, F. et al. Screened Cluster Expansions for Partially Ionized Gases. Journal of Statistical Physics 113, 455–503 (2003). https://doi.org/10.1023/A:1026064617421

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