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Current issue   Ukr. J. Phys. 2017, Vol. 62, N 1, p.33-38
https://doi.org/10.15407/ujpe62.01.0033    Paper

Azarenkov N.A., Gapon A.V., Dudin S.V.

V.N. Karazin Kharkiv National University
(31, Kurchatov Ave., Kharkiv 61108, Ukraine; e-mail: gapon@pht.univer.kharkov.ua)

Heuristic Solution of Langmuir Problem in Arbitrary Domain

Section: Plasmas and Gases
Original Author's Text: English

Abstract: The Langmuir problem for a collisionless plasma was formulated and solved for some simple domains at 1921. But, for more complicated cases, no robust method is known till now except for the macro particle simulation. We propose a new method applicable to domains with arbitrary boundary shape. The method is based on the solution of the well-known eigenvalue problem for diffusion-type equations. The comparison of test solutions obtained by this technique with the Particle-In-Cell method demonstrates an acceptable accuracy despite the lack of theoretical validation of this method.

Key words: collisionless plasma, Langmuir problem, free fall regime.