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Hamiltonian chaos for one particle with two waves: Self-consistent dynamics.

Matheus J Lazarotto^1,2, Iberê L Caldas², Yves Elskens¹

¹Aix-Marseille Université, CNRS, UMR 7345, PIIM, F-13397, Marseille cedex 13, France.

Chaos (Woodbury, N.Y.)

|May 15, 2025

Summary

This summary is machine-generated.

This study explores wave-particle interactions in a self-consistent model, revealing how energy exchange can lead to chaotic dynamics and multiple wave equilibria. Regularity dominates, but specific parameters trigger chaos.

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Area of Science:

Plasma physics
Nonlinear dynamics
Computational physics

Background:

Wave-particle interactions are fundamental in many physical systems.
Understanding self-consistent models, where particles influence wave dynamics, is crucial.
Previous models often simplified the feedback mechanisms between waves and particles.

Purpose of the Study:

To investigate a simple self-consistent model of wave-particle interaction.
To analyze the emergence of locked solutions (equilibria) and chaotic behavior.
To understand the role of energy-momentum exchange in inducing chaos.

Main Methods:

Mathematical analysis of locked solutions and equilibria.
Exploration of the system's non-linearity.
Parameter variation to study transitions between regularity and chaos.

Main Results:

Identified the mathematical structure underlying locked states.
Demonstrated how non-linearity allows for multiple wave equilibrium amplitudes.
Observed a predominance of regularity with parameter variation.
Characterized the specific parameter ranges that lead to chaotic behavior.

Conclusions:

The self-consistent model exhibits complex dynamics, including stable equilibria and chaos.
Energy-momentum exchange is a key driver for chaotic transitions.
Non-linearity plays a critical role in determining the system's possible states and behaviors.