Skip to main content
Log in

Dispersion Relationship and Spectrum in the Collisionless Plasma Kinetic Model

  • Research Articles
  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

The topic of the paper is the spectral analysis of a dynamical system representing a kinetic model for two-component rarefied plasma. In the present paper, we restrict ourselves to the case of two-dimensional one-particle phase space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. D. Landau, “On the Vibrations of the Electronic Plasma”, J. Phys. USSR, 10:1 (1946), 25–34.

    MathSciNet  MATH  Google Scholar 

  2. V. P. Maslov and M. V. Fedoryuk, “The Linear Theory of Landau Damping”, Sb. Math., 55:2 (1986), 437–465.

    Article  Google Scholar 

  3. T. H. Stix, Waves in Plasmas, American Institute of Physics, New York, 1992.

    Google Scholar 

  4. A. B. Mikhailovski, Theory of Plasma Instabilities, Atomizdat, Moscow, 1970 (Russian).

    Google Scholar 

  5. A. A. Arseniev, Lectures on Kinetic Equations, Nauka, Moscow, 1992 (Russian).

    Google Scholar 

  6. P. Degond, “Spectral Theory of the Linearized Vlasov-Poisson Equation”, Trans. Amer. Math. Soc., 294:2 (1986), 435–453.

    Article  MathSciNet  Google Scholar 

  7. S. A. Stepin, “Wave Operators for the Linearized Boltzmann Equation in One-Speed Transport Theory”, Sb. Math., 192:1 (2001), 141–162.

    Article  ADS  MathSciNet  Google Scholar 

  8. I. B. Bernstein, J. M. Green, and M. D. Kruskal, “Exact Nonlinear Plasma Oscillations”, Phys. Rev., 108:3 (1957), 546–551.

    Article  ADS  MathSciNet  Google Scholar 

  9. P. R. Halmos, A Hilbert Space Problem Book, Springer-Verlag, 1982.

    Book  Google Scholar 

  10. R. von Mises, Mathematical Theory of Probability and Statistics, Academic Press, New York, 1964.

    MATH  Google Scholar 

  11. T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, 1966.

    Book  Google Scholar 

  12. M. A. Lavrentiev and B. V. Shabat, Methods of the Theory of Functions of the Complex Variable, Nauka, Moscow, 1973 (Russian).

    Google Scholar 

  13. O. Penrose, “Electrostatic Instabilities of a Uniform Non-Maxwellian Plasma”, Phys. Fluids, 2:2 (1960), 258–264.

    Article  ADS  Google Scholar 

Download references

Funding

The reported study was funded by RFBR, project number 19-01-00474.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. A. Stepin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stepin, S.A. Dispersion Relationship and Spectrum in the Collisionless Plasma Kinetic Model. Russ. J. Math. Phys. 28, 107–120 (2021). https://doi.org/10.1134/S106192082101012X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106192082101012X

Navigation