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Analytical solution of the Poisson-Boltzmann equation in cases of spherical and axial symmetry

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Abstract

An exact analytical solution of the Poisson-Boltzmann (PB) equation in cases of spherical, axial, and planar geometry has been obtained in the form of the logarithm of a power series. This solution describes an electrostatic potential distribution around a charged macroscopic particle (wire, plane) under conditions of thermal equilibrium at an arbitrary ratio of the density of charge borne by the particles (wires, planes) to the charge density in the surrounding plasma. Previously, an analytical solution of the PB equation was known only in the case of planar geometry.

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Authors and Affiliations

  1. Institute for High Energy Densities, Associated Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia

    L. G. D’yachkov

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  1. L. G. D’yachkov
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Translated from Pis’ma v Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 31, No. 5, 2005, pp. 58–66.

Original Russian Text Copyright © 2005 by D’yachkov.

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D’yachkov, L.G. Analytical solution of the Poisson-Boltzmann equation in cases of spherical and axial symmetry. Tech. Phys. Lett. 31, 204–207 (2005). https://doi.org/10.1134/1.1894433

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