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Abstract
A topological constraint on the dynamics of a magnetic field in a flux tube arises from the fixed point indices of its field line mapping. This can explain unexpected behaviour in recent resistivemagnetohydrodynamic simulations of magnetic relaxation. Here, we present the theory for a general periodic flux tube, representing, for example, a toroidal confinement device or a solar coronal loop. We show how an ideal dynamics on the side boundary of the tube implies that the sum of indices over all interior fixed points is invariant. This constraint applies to any continuous evolution inside the tube, which may be turbulent and/or dissipative. We also consider the analogous invariants obtained from periodic points (fixed points of the iterated mapping). Although there is a countably infinite family of invariants, we show that they lead to at most two independent dynamical constraints. The second constraint applies only in certain magnetic configurations. Several examples illustrate the theory.
Original language  English 

Article number  265501 
Number of pages  17 
Journal  Journal of Physics A: Mathematical and Theoretical 
Volume  44 
Issue number  26 
DOIs  
Publication status  Published  1 Jul 2011 
Keywords
 RECONNECTION
 MAPS
 SIMULATIONS
 RELAXATION
 INVARIANTS
 MECHANICS
 SYSTEMS
 CORONA
 INDEX
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Dive into the research topics of 'Dynamical constraints from field line topology in magnetic flux tubes'. Together they form a unique fingerprint.Projects
 1 Finished

Parallel Computing Resources UK MHD: Parallel computing resources
Science & Technology Facilities Council
1/12/09 → 30/11/12
Project: Standard