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

TL;DR

This paper investigates a self-consistent wave-particle interaction model, revealing how non-linearity and feedback mechanisms lead to multiple equilibria and chaos, with implications for understanding complex dynamical systems.

Contribution

It introduces a self-consistent model of wave-particle interaction, analyzing equilibrium states and the conditions under which chaos emerges due to non-linearity and feedback.

Findings

Multiple equilibrium amplitudes for waves due to non-linearity

Chaos emerges under limited parameter ranges

Regularity dominates as control parameters vary

Abstract

A simple model of wave-particle interaction is studied in its self-consistent form, that is, where the particles are allowed to feedback on the waves dynamics. We focus on the configurations of locked solutions (equilibria) and how the energy-momentum exchange mechanism induces chaos in the model. As we explore the system, we analyse the mathematical structure that gives rise to locked states and how the model's non-linearity enables multiple equilibrium amplitudes for waves. We also explain the predominance of regularity as we vary the control parameters and the mechanism behind the emergence of chaos under limited parameter choices.