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Related Experiment Video

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Magnetic Tweezers for the Measurement of Twist and Torque

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Published on: May 19, 2014

Magnetic structures in the explicitly time-dependent nontwist map.

Dániel Jánosi^1,2, Anikó Horváth¹, Lili Édes^3,4

¹Department of Theoretical Physics, Eötvös Loránd University, 1117 Pázmány Péter sétány 1A, Budapest, Hungary.

Chaos (Woodbury, N.Y.)

|December 19, 2024

Summary

Plasma magnetic structures in tokamaks become chaotic when perturbed by ergodic magnetic limiters with time-varying parameters. This study reveals power-law relationships for chaos transition and Lyapunov exponents, offering insights into plasma confinement.

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Last Updated: Jun 4, 2025

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Published on: June 7, 2018

Area of Science:

Plasma Physics
Nonlinear Dynamics
Statistical Mechanics

Background:

Tokamak magnetic structures are crucial for plasma confinement.
Ergodic magnetic limiters are used to control plasma behavior.
Understanding transitions to chaos in dynamical systems is essential.

Purpose of the Study:

To investigate the impact of non-adiabatic parameter variations on tokamak magnetic structures.
To model the effects of ergodic magnetic limiter current changes over time.
To analyze the transition to chaos in perturbed magnetic systems.

Main Methods:

Utilizing the Ullmann-Caldas nontwist map with explicit time-dependence.
Applying tools for chaotic Hamiltonian systems with parameter drift.
Following trajectory ensembles (snapshot tori) and analyzing their evolution.
Calculating Lyapunov exponents and identifying critical instants for chaos transition.

Main Results:

Snapshot tori exhibit time-dependent shapes as the parameter drifts.
A transition to chaos is observed, characterized by a positive Lyapunov exponent.
Empirical power-law relationships were found between Lyapunov exponent, critical instant, and parameter drift rate.
The Lyapunov exponent increases, while the critical instant decreases with increasing drift rate.

Conclusions:

Coherent magnetic structures (tori, islands) tend to break up into chaos with increasing perturbation, similar to constant perturbations.
Continuous parameter drift allows some structures to persist longer than in static perturbation scenarios.
The findings provide insights into the dynamics of magnetic field perturbations in tokamaks under time-varying conditions.