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Low-dimensional chaos in the single wave model for self-consistent wave-particle Hamiltonian
J V Gomes1, M C de Sousa2, R L Viana1
1Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil.
Chaos (Woodbury, N.Y.)
|September 2, 2021
Summary
Nonlinear wave-particle interactions in plasma can lead to instabilities. Chaos emerges with multiple particles, driven by homoclinic tangles or resonance overlap, impacting wave amplitude.
Area of Science:
- Plasma Physics
- Nonlinear Dynamics
- Computational Physics
Background:
- Wave-particle interaction is fundamental to plasma behavior, driving instabilities and turbulence.
- Understanding nonlinear dynamics is crucial for predicting plasma phenomena.
- The single wave model provides a simplified yet insightful framework for studying these interactions.
Purpose of the Study:
- To analyze the nonlinear aspects of self-consistent wave-particle interactions.
- To investigate the transition from integrable to chaotic dynamics in plasma systems.
- To identify the mechanisms responsible for chaos generation in wave-particle systems.
Main Methods:
- Utilizing Hamiltonian dynamics to model wave-particle interactions.
- Analyzing the N=1, M=1 (single particle, single wave) integrable case.
- Investigating the N=2, M=1 (two particles, single wave) non-integrable case to observe chaos.
Main Results:
- The N=1, M=1 system exhibits integrable behavior with pulsating wave potential and particle trapping or circulation.
- Integrability is lost for N=2, M=1, leading to the development of chaos.
- Chaos emerges through homoclinic tangle formation and resonance overlap near fixed points.
- A strong form of chaos is observed when high energy causes occasional wave amplitude vanishing.
Conclusions:
- The transition to chaos in wave-particle interactions is dependent on the number of particles involved.
- Homoclinic tangles and resonance overlap are key mechanisms driving chaotic behavior.
- The study highlights the complex dynamics that can arise even in simplified plasma models, with implications for understanding plasma instabilities and turbulence.
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