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Published on: November 7, 2017
Topological constraints on magnetic relaxation.
A R Yeates1, G Hornig, A L Wilmot-Smith
1Division of Mathematics, University of Dundee, Dundee, DD1 4HN, United Kingdom. anthony@maths.dundee.ac.uk
Physical Review Letters
|September 28, 2010
Summary
Turbulent magnetic relaxation in solar loops deviates from Taylor
Area of Science:
- Plasma physics
- Astrophysics
- Magnetohydrodynamics
Background:
- Taylor's hypothesis explains turbulent magnetic relaxation in reversed field pinches.
- Resistive-magnetohydrodynamic simulations of solar coronal loops show relaxed states deviating from the Taylor state.
- Helicity is conserved in these simulations.
Purpose of the Study:
- To investigate why solar coronal loop simulations deviate from Taylor states.
- To identify additional constraints on magnetic relaxation beyond helicity conservation.
- To propose a new topological invariant governing magnetic relaxation.
Main Methods:
- Analysis of resistive-magnetohydrodynamic simulations of braided solar coronal loops.
- Investigation of topological properties of magnetic fields within flux tubes.
- Calculation of the topological degree of field line mappings.
Main Results:
- Simulations yielded relaxed magnetic fields significantly different from the Taylor state.
- An additional topological invariant, the topological degree, was identified in non-zero magnetic fields within flux tubes.
- This invariant was shown to constrain the relaxation process.
Conclusions:
- The topological degree of the field line mapping is a crucial invariant in magnetic relaxation.
- This invariant explains why some simulations reach the Taylor state while others do not.
- The findings challenge the universality of Taylor's hypothesis for all magnetic relaxation scenarios, particularly in astrophysical contexts.
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