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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© 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
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