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Adiabatic chaos in a two-dimensional mapping.

D. L. Vainshtein1, A. A. Vasiliev, A. I. Neishtadt

  • 1Space Research Institute, Russian Academy of Sciences, 84/32 Profsoyuznaya St., 117810, Moscow, Russia.

Chaos (Woodbury, N.Y.)
|December 1, 1996
PubMed
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A study on charged particle dynamics reveals that even small deviations from identity in symplectic mappings create large chaotic regions. This chaos arises from quasirandom changes in the adiabatic invariant when crossing resonance curves.

Area of Science:

  • Plasma Physics
  • Nonlinear Dynamics
  • Charged Particle Motion

Background:

  • Charged particles in electrostatic waves exhibit complex dynamics.
  • Symplectic mappings approximate particle behavior in wave fields.
  • Understanding chaotic dynamics is crucial for plasma physics.

Purpose of the Study:

  • To analyze a symplectic mapping for charged particle dynamics in an electrostatic wave packet.
  • To investigate the emergence and characteristics of chaotic regions.
  • To quantify the relationship between mapping deviation and chaos width.

Main Methods:

  • Analysis of a near-identity symplectic mapping.
  • Study of phase cylinder dynamics.
  • Derivation of an asymptotic formula for adiabatic invariant jumps.

Related Experiment Videos

  • Estimation of chaos region width and invariant curve density.

    • Main Results:

    • A large region of chaotic dynamics emerges even with small deviations from identity.
    • Chaos is linked to quasirandom changes in the adiabatic invariant at resonance crossings.
    • An asymptotic formula for adiabatic invariant jumps was derived.
    • Estimates for chaos region width and invariant curve density were obtained.

    Conclusions:

    • The study elucidates the mechanism of chaos generation in charged particle dynamics.
    • The findings provide insights into the stability and behavior of particles in wave fields.
    • The derived formulas and estimates are valuable for further theoretical and experimental investigations.