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Coherent structures and self-consistent transport in a mean field Hamiltonian model
D. Del-Castillo-Negrete1, Marie-Christine Firpo
1Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-8071.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
This study explores coherent structures in plasma and fluid dynamics using a Hamiltonian mean field model. It reveals rotating dipole states and explains their stability through parametric resonance, while also detailing conditions for their chaotic destruction.
Area of Science:
- Plasma Physics
- Fluid Dynamics
- Statistical Mechanics
Background:
- The study investigates coherent structures and self-consistent transport within a Hamiltonian mean field, single wave model.
- This model captures the weakly nonlinear dynamics of marginally stable plasmas and fluids, relevant to long-range interacting systems.
Purpose of the Study:
- To analyze the dynamics of coherent structures, specifically rotating dipole states, in plasma and fluid systems.
- To understand the mechanisms of stability and destruction of these dipole states.
Main Methods:
- Utilized numerical simulations in finite-N and kinetic limits (N--> infinity).
- Approximated dipole states as two macroparticles (electron holes and clumps) in the N=2 limit.
- Employed perturbative solutions of a nontwist Hamiltonian to analyze dipole behavior.
Main Results:
- Confirmed the existence of coherent, rotating dipole states in simulations.
- Identified a family of integrable, rotating solutions in the N=2 limit.
- Explained dipole coherence via parametric resonance, creating islands of integrability shielding against chaotic transport.
Conclusions:
- Parametric resonance is key to maintaining dipole coherence and preventing chaotic transport.
- An elliptic-hyperbolic bifurcation can lead to dipole destruction through filamentation and chaotic mixing.
- The model provides insights into self-consistent transport and coherent structures in complex systems.