{"title":"Parametric representation, asymptotic and bifurcation analyses of the electronic plasma oscillations","authors":"Alexandr A. Barsuk, Florentin Paladi","doi":"10.1140/epjd/s10053-024-00949-w","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p><h3>Graphical abstract</h3><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":789,"journal":{"name":"The European Physical Journal D","volume":"79 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal D","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjd/s10053-024-00949-w","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPTICS","Score":null,"Total":0}
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Abstract
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.
期刊介绍：
The European Physical Journal D (EPJ D) presents new and original research results in:
Atomic Physics;
Molecular Physics and Chemical Physics;
Atomic and Molecular Collisions;
Clusters and Nanostructures;
Plasma Physics;
Laser Cooling and Quantum Gas;
Nonlinear Dynamics;
Optical Physics;
Quantum Optics and Quantum Information;
Ultraintense and Ultrashort Laser Fields.
The range of topics covered in these areas is extensive, from Molecular Interaction and Reactivity to Spectroscopy and Thermodynamics of Clusters, from Atomic Optics to Bose-Einstein Condensation to Femtochemistry.
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