https://doi.org/10.1140/epjd/s10053-024-00949-w
Regular Article - Plasma Physics
Parametric representation, asymptotic and bifurcation analyses of the electronic plasma oscillations
Department of Theoretical Physics and ePhysMCS Lab, Faculty of Physics and Engineering, Moldova State University, A. Mateevici Str. 60, MD-2009, Chisinau, Republic of Moldova
Received:
4
November
2024
Accepted:
26
December
2024
Published online:
27
January
2025
Real (non-damped) solutions of the dispersion equation first derived by A.A. Vlasov for the oscillations of the electronic plasma are studied. We present the exact solutions of the Vlasov’s dispersion equation in the parametric form. It is shown that the value of the singular integral entering the dispersion equation coincides with the calculated one obtained in the sense of Cauchy principal value. The frequency values of the oscillations are derived in the parametric representation without prior assumptions, which supports the fundamental concept of self-consistent field of charged particles leading to the Vlasov decay of spatial oscillations. Ultimately, this helps in understanding the historical controversy on Vlasov modes and Landau damping as relaxation mechanisms in the electronic plasma. Bifurcation values of parameters and the asymptotic representations for the obtained solutions in the parametric form are also discussed.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.