Classification and Properties of Solutions for the System of Equations of Classical Electrode Effect Theory
| Autor: | A. A. Zhidkov, A. M. Terent’ev, E. E. Grigor’ev, A. V. Kalinin |
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| Rok vydání: | 2014 |
| Předmět: |
Physics
Nuclear and High Energy Physics Turbulent diffusion Phase portrait Plane (geometry) Mathematical analysis Charge density Astronomy and Astrophysics Statistical and Nonlinear Physics System of linear equations Electronic Optical and Magnetic Materials symbols.namesake Continuity equation Electric field symbols Gauss's law Electrical and Electronic Engineering |
| Zdroj: | Radiophysics and Quantum Electronics. 56:747-768 |
| ISSN: | 1573-9120 0033-8443 |
| DOI: | 10.1007/s11141-014-9478-9 |
| Popis: | We study a one-dimensional stationary system of equations comprising the continuity equation for the ion concentration with the recombination effects taken into account and the Gauss law for the electric field. This system gives a simplified description of various phenomena in ionized medium theory and is used, in particular, for modeling of the electrode effect in the atmospheric surface layers with the turbulent diffusion effects neglected. Using the integral of the system and a phase portrait in the ion concentration plane, we offer a complete classification of types of solutions of the system, examine their properties, and deduce some analytical relations between the ion concentration and the electric field. The basic equations of classical electrode effect theory are obtained for some classes of solutions within the framework of this approach. Correct formulations of the problems are discussed. New classes of solutions, for which there are layers with infinitely increasing conductivity and charge density are described. The Appendix illustrates, in both analytical and graphical form, the results obtained in the main part of this paper on the basis of qualitative reasoning for parameters close to real. Analytical expressions for the fields and ion concentrations are given for all types of solutions. Relations for the distances between electrodes and analytical relations describing the properties of the spatially localized solutions are presented. |
| Databáze: | OpenAIRE |
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