Low-dimensional chaos in the single wave model for self-consistent wave-particle Hamiltonian

Author(s)

Gomes, J. V. ^{[1, 2]} ; de Sousa, M. C. ^{[3, 2]} ; Viana, R. L. ^[1] ; Caldas, I. L. ^[3] ; Elskens, Y. ^[2]

Affiliation

^[1] Univ Fed Parana, Dept Fis, BR-81531980 Curitiba, PR - Brazil

^[2] Aix Marseille Univ, CNRS, PIIM UMR 7345, F-13397 Marseille - France

^[3] Univ Sao Paulo, Inst Fis, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: Chaos; v. 31, n. 8 AUG 2021.
• Web of Science Citations: 0

Abstract

We analyze nonlinear aspects of the self-consistent wave-particle interaction using Hamiltonian dynamics in the single wave model, where the wave is modified due to the particle dynamics. This interaction plays an important role in the emergence of plasma instabilities and turbulence. The simplest case, where one particle (N = 1) is coupled with one wave (M = 1), is completely integrable, and the nonlinear effects reduce to the wave potential pulsating while the particle either remains trapped or circulates forever. On increasing the number of particles (N = 2, M = 1), integrability is lost and chaos develops. Our analyses identify the two standard ways for chaos to appear and grow (the homoclinic tangle born from a separatrix, and the resonance overlap near an elliptic fixed point). Moreover, a strong form of chaos occurs when the energy is high enough for the wave amplitude to vanish occasionally. Published under an exclusive license by AIP Publishing. (AU)

• FAPESP's process: 15/05186-0 - Bifurcations and control of chaos in wave-particle interactions
• Grantee: Meirielen Caetano de Sousa
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 18/03211-6 - Non linear dynamics
• Grantee: Iberê Luiz Caldas
• Support Opportunities: Research Projects - Thematic Grants