Relativistic chaotic scattering: Unveiling scaling laws for trapped trajectories

Area of Science:

• Physics
• Astrophysics
• Dynamical Systems

Background:

• Relativistic chaotic scattering is crucial for understanding particle dynamics in various astrophysical contexts.
• Phase space structures, like exit basins, reveal complex behaviors in dynamical systems.
• The Hénon-Heiles Hamiltonian is a standard model for studying chaos, with relativistic effects introducing new dynamics.

Purpose of the Study:

• To investigate phase space structures in relativistic chaotic scattering.
• To compare relativistic dynamics with low-velocity Newtonian dynamics.
• To characterize escaping trajectories and identify scaling laws.

Main Methods:

• Numerical simulations of the relativistic Hénon-Heiles Hamiltonian.
• Analysis of exit basin topology in phase space, energy plane, and beta plane.
• Identification of fractal structures and scaling laws.

Main Results:

• Fractal structures are present in relativistic chaotic scattering.
• Escaping dynamics are characterized across different phase space representations.
• A scaling law was derived for trapped trajectories as a function of relativistic parameter beta and energy.

Conclusions:

• Relativistic effects significantly influence phase space structures in chaotic scattering.
• The identified scaling laws provide insights into particle trapping phenomena.
• Findings are relevant for understanding charged particle behavior in environments like the magnetosphere.