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Stickiness in double-curl Beltrami magnetic fields
1Plasma Physics Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata 700064, India.
Chaos (Woodbury, N.Y.)
|January 3, 2019
Summary
This study explores the chaotic dynamics of double-curl Beltrami magnetic fields. Results reveal how a mean field influences magnetic field line behavior, transitioning from chaotic to mixed states with stickiness.
Area of Science:
- Plasma Physics
- Magnetohydrodynamics
- Dynamical Systems
Background:
- Double-curl Beltrami magnetic fields are non-force-free and represent physically interesting magnetic field configurations.
- Understanding the nonlinear dynamics of magnetic field lines is crucial in various astrophysical and fusion plasma contexts.
Purpose of the Study:
- To investigate the nonlinear dynamical behavior of magnetic field lines for double-curl Beltrami fields.
- To analyze the influence of a uniform mean field on the phase space structure and chaoticity.
- To characterize the transport properties of magnetic field lines based on their dynamical behavior.
Main Methods:
- Solving the double-curl Beltrami equation in three dimensions.
- Analyzing phase space structure, including regular and chaotic regions.
- Computing recurrence length statistics to quantify trajectory behavior.
- Examining transport characteristics of field lines.
Main Results:
- A specific 3D double-curl solution exhibits a wholly chaotic phase space.
- In the presence of a strong mean field, the phase space becomes mixed, featuring magnetic surfaces and weakly chaotic regions.
- Stickiness, or dynamical trapping, is observed at the boundaries of regular regions in the mixed phase space.
- Recurrence length statistics show a long-tail distribution for mixed phase spaces, contrasting with the rapid decay in wholly chaotic ones.
Conclusions:
- The mean field strength critically determines the transition from fully chaotic to mixed magnetic field line dynamics.
- Stickiness in mixed phase spaces leads to distinct trajectory behaviors and statistical properties.
- The study provides insights into magnetic field line transport and its connection to nonlinear dynamics, relevant for plasma confinement and astrophysical phenomena.
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