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Maximum Entropy Description of Plasma Equilibrium

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Maximum Entropy and Bayesian Methods

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 39))

Abstract

The self-consistent equation for the potential φ in an equilibrium plasma is found by combining Poisson’s equation ε0∇2 φ= −ρ with the Maximum Entropy formula relating the charge density ρ to the potential. On ignoring interparticle correlations this takes the form of the Boltzmann distribution, ρ α exp(−β q φ). The resulting ‘Poisson-Boltzmann’ equation for the potential is studied in various geometries with differing combinations of charge species. It is nonlinear, inducing a surprising result: a fixed line charge immersed in plasma may attract a non-zero amount of charge of opposite polarity arbitrarily close to it; neutralisation of fixed point charges is exact; and a fixed point dipole causes the entire plasma to condense onto it! Failure of these results in practice is due to particle correlations and the non-zero size of real multipoles.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK

    A. J. M. Garrett

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  1. A. J. M. Garrett
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Editors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Paul F. Fougère

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© 1990 Kluwer Academic Publishers

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Garrett, A.J.M. (1990). Maximum Entropy Description of Plasma Equilibrium. In: Fougère, P.F. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0683-9_15

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  • DOI: https://doi.org/10.1007/978-94-009-0683-9_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6792-8

  • Online ISBN: 978-94-009-0683-9

  • eBook Packages: Springer Book Archive

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