On problems solved in a quasi-linear approximation

Kos, Leon (author), Tskhakaya, David (author)

The complete analytic solution of the time-dependent Vlasov–Boltzmann kinetic equation is used to describe selected problems in plasma physics within the framework of the quasi-linear approximation. These problems usually include the relaxation of plasma oscillations and the relaxation of beam instability. Our kinetic equation is a first-order partial differential equation. The method of characteristics allows us to solve it analytically, while fully preserving the entire time dependence. Using the obtained analytic expression for the distribution function, the paper shows that the indicated relaxation processes do not occur in the approximation considered.

• Language: English
• Keywords: quasi-linear theory, Vlasov equation, plasma oscillations, beam instability, analytic solution, collisionless plasma
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 12 str.
• Numbering: Vol. 14, no. 6, art. 960
• PID: 20.500.12556/RUL-181223
• UDC: 51
• ISSN on article: 2227-7390
• DOI: 10.3390/math14060960
• COBISS.SI-ID: 272477699
• Publication date in RUL: 27.03.2026

Record is a part of a journal

• Title: Mathematics
• Shortened title: Mathematics
• Publisher: MDPI AG
• ISSN: 2227-7390
• COBISS.SI-ID: 523267865

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• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

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• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P2-0405-2019
• Name: Fuzijske tehnologije

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J2-60053-2025
• Name: Optimizacijsko ogrodje pridružene in umetne inteligence za optimizacijo kompleksnih večfizikalne simulacijskih modelom (A2FOMS)