Skip to main content
SpringerLink
Log in

Kinetic Equation for Systems with Resonant Captures and Scatterings

  • Chapter
  • First Online:
Nonlinear Dynamics, Chaos, and Complexity

Part of the book series: Nonlinear Physical Science ((NPS))

  • 625 Accesses

Abstract

We study a Hamiltonian system of type describing a charged particle resonant interaction with an electromagnetic wave. We consider an ensemble of particles that repeatedly pass through the resonance with the wave, and study evolution of the distribution function due to multiple scatterings on the resonance and trappings (captures) into the resonance. We derive the corresponding kinetic equation. Particular cases of this problem has been studied in our recent papers [1, 2].

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Artemyev AV, Neishtadt AI, Vasiliev AA, Mourenas D (2016) Kinetic equation for nonlinear resonant wave-particle interaction. Phys Plasmas 23:090701

    Article  Google Scholar 

  2. Artemyev AV, Neishtadt AI, Vasiliev AA, Mourenas D (2017) Probabilistic approach to nonlinear wave-particle resonant interaction. Phys Rev E 95:023204

    Article  Google Scholar 

  3. Neishtadt AI (1999) Hamiltonian systems with three or more degrees of freedom, NATO ASI Series C. 533:193–213; Kluwer Academic Publishers, Dordrecht. https://doi.org/10.1063/1.166236

  4. Neishtadt A (1975) Passage through a separatrix in a resonance problem with a slowly-varying parameter. J Appl Math Mech 39:594–605. https://doi.org/10.1016/0021-8928(75)90060-X

    Article  MathSciNet  Google Scholar 

  5. Arnold VI, Kozlov VV, Neishtadt AI (2006) Mathematical aspects of classical and celestial mechanics, 3rd edn. Dynamical systems III. Encyclopedia of mathematical sciences. Springer, New York

    Google Scholar 

  6. Neishtadt AI, Vasiliev AA (2006) Destruction of adiabatic invariance at resonances in slow-fast Hamiltonian systems. Nucl Instr Meth Phys Res A 561:158

    Article  Google Scholar 

  7. Itin AP, Neishtadt AI, Vasiliev AA (2000) Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave. Physica D: Nonlinear Phenomena 141:281–296. https://doi.org/10.1016/S0167-2789(00)00039-7

    Article  MathSciNet  MATH  Google Scholar 

  8. Vasiliev A, Neishtadt A, Artemyev A (2011) Nonlinear dynamics of charged particles in an oblique electromagnetic wave. Phys Lett A 375:3075–3079. https://doi.org/10.1016/j.physleta.2011.06.055

    Article  MATH  Google Scholar 

  9. Neishtadt A, Vasiliev A, Artemyev A (2011) Resonance-induced surfatron acceleration of a relativistic particle. Moscow Math J 11(3):531–545

    MathSciNet  MATH  Google Scholar 

  10. Vainchtein D, Mezić I (2004) Capture into resonance: a method for efficient control. Phys Rev Lett 93(8):084301. https://doi.org/10.1103/PhysRevLett.93.084301

  11. Artemyev AV, Neishtadt AI, Zelenyi LM, Vainchtein DL (2010) Adiabatic description of capture into resonance and surfatron acceleration of charged particles by electromagnetic waves. Chaos 20(4):043128. https://doi.org/10.1063/1.3518360

    Article  MathSciNet  MATH  Google Scholar 

  12. Artemyev AV, Vasiliev AA (2015) Resonant ion acceleration by plasma jets: effects of jet breaking and the magnetic-field curvature. Phys Rev E 91(5):053104. https://doi.org/10.1103/PhysRevE.91.053104

    Article  Google Scholar 

  13. Shklyar DR (1981) Stochastic motion of relativistic particles in the field of a monochromatic wave. Sov Phys JETP 53:1187–1192

    Google Scholar 

  14. Artemyev AV, Vasiliev AA, Mourenas D, Agapitov O, Krasnoselskikh V, Boscher D, Rolland G (2014) Fast transport of resonant electrons in phase space due to nonlinear trapping by whistler waves. Geophys Res Lett 41:5727–5733. https://doi.org/10.1002/2014GL061380

    Article  Google Scholar 

  15. Omura Y, Miyashita Y, Yoshikawa M, Summers D, Hikishima M, Ebihara Y, Kubota Y (2015) Formation process of relativistic electron flux through interaction with chorus emissions in the Earth’s inner magnetosphere. J Geophys Res 120:9545–9562. https://doi.org/10.1002/2015JA021563

Download references

Acknowledgements

The work was supported by the Russian Scientific Foundation, Project No. 19-12-00313.

Author information

Authors and Affiliations

  1. Institute of Geophysics and Planetary Physics, UCLA, Los Angeles, CA, USA

    A. V. Artemyev

  2. Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK

    A. I. Neishtadt

  3. Space Research Institute, RAS, Moscow, Russia

    A. V. Artemyev, A. I. Neishtadt & A. A. Vasiliev

Authors
  1. A. V. Artemyev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. I. Neishtadt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. A. Vasiliev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Vasiliev .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA

    Dimitri Volchenkov

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Higher Education Press

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Artemyev, A.V., Neishtadt, A.I., Vasiliev, A.A. (2021). Kinetic Equation for Systems with Resonant Captures and Scatterings. In: Volchenkov, D. (eds) Nonlinear Dynamics, Chaos, and Complexity. Nonlinear Physical Science. Springer, Singapore. https://doi.org/10.1007/978-981-15-9034-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-9034-4_10

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-9033-7

  • Online ISBN: 978-981-15-9034-4

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation