Electrostatic interaction between two macroparticles in the Poisson-Boltzmann model

A. V. Filippov, A. F. Pal, A. N. Starostin, A. S. Ivanov

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Considering the electrostatic energy of the system of two macroparticles in a plasma in the Poisson-Boltzmann model, Resendes et al. [Phys. Lett. A 239, 181 (1998)], Ivanov [Phys. Lett. A 290, 304 (2001)], Gerasimov and Sinkevich {Teplofiz. Vys. Temp. 37, 853 (1999) [High Temp. 37, 823 (1999)]}, and D'achkov {Teplofiz. Vys. Temp. 43, 331 (2005) [High Temp. 43, 322 (2005)]} conclude that attraction between identically charged macroparticles is possible. In the Poisson-Boltzmann model, the distribution of electrons and ions has the Boltzmann form in a self-consistent field that is determined by the Poisson equation. In this work, on the basis of the analysis of the force between two macroparticles in a plasma by using the Maxwell stress tensor, it has been shown that two macroparticles with the same charge always repulse each other in both isothermal and nonisothermal plasmas. The interaction between macroparticles at distances, where Boltzmann exponentials can be linearized, is completely described by the Debye-Hückel theory. The free energy of the system of two particles has been found. It coincides with the Yukawa potential and has no minimum; therefore, such a system is thermodynamically unstable. Since the interaction energy obtained by integrating the interaction force coincides with the free energy of the electric field, the interaction between two macroparticles in the equilibrium plasma is potential.

Original languageEnglish
Pages (from-to)546-552
Number of pages7
JournalJETP Letters
Volume83
Issue number12
DOIs
StatePublished - Aug 2006
Externally publishedYes

Funding

We are grateful to L.G. D’yachkov for stimulating discussions. This work was supported by the Russian Foundation for Basic Research, project nos. 05-02-17258a and 05-02-08158-ofi_a.

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