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Trapping scaling for bifurcations in the Vlasov systems
J Barré1, D Métivier2, Y Y Yamaguchi3
1Laboratoire J.-A. Dieudonné, Université de Nice-Sophia Antipolis, UMR CNRS 7351, Parc Valrose 06108 Nice Cedex 02, France and Institut Universitaire de France, 75005 Paris, France.
Physical Review. E
|May 14, 2016
Summary
We investigated bifurcations in the Vlasov equation, finding that initial perturbations can lead to small-scale saturation or large-scale system changes. Resonances are suppressed, altering dynamics compared to homogeneous cases.
Area of Science:
- Plasma Physics
- Astrophysics
- Nonlinear Dynamics
Background:
- The Vlasov equation describes systems like plasmas and galaxies.
- Nonhomogeneous steady states and their bifurcations are crucial for understanding system evolution.
- Bernstein-Greene-Kruskal modes are a key phenomenon in plasma physics.
Purpose of the Study:
- To analyze nonoscillating bifurcations of nonhomogeneous steady states in the Vlasov equation.
- To investigate the impact of initial perturbations on system dynamics.
- To explore the role of resonances in these bifurcations.
Main Methods:
- Utilized unstable manifold expansion for analytical insights.
- Performed direct numerical simulations with a cosine interaction potential.
- Focused on one spatial dimension for detailed analysis.
Main Results:
- System dynamics exhibit high sensitivity to initial perturbations.
- Instability can saturate at small amplitudes (generalizing plasma trapping scaling) or cause large-scale modifications.
- Resonances are significantly suppressed, leading to distinct phenomena compared to homogeneous systems.
Conclusions:
- Nonhomogeneous Vlasov equation dynamics are highly sensitive to initial conditions.
- The study reveals two distinct pathways for instability saturation.
- Suppressed resonances lead to unique behaviors in nonhomogeneous systems.
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