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Decay of helical and nonhelical magnetic knots
Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
2011 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, no 1, 016406- p.Article in journal (Refereed) Published
Abstract [en]

We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call n-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and nonhelical triple-ring configurations. Unlike earlier nonhelical configurations, the present ones cannot trivially be reduced via flux annihilation to a single ring. For the n-foil knots the decay is described by power laws that range form t(-2/3) to t(-1/3), which can be as slow as the t(-1/3) behavior for helical triple-ring structures that were seen in earlier work. The two nonhelical configurations decay like t(-1), which is somewhat slower than the previously obtained t(-3/2) behavior in the decay of interlocked rings with zero magnetic helicity. We attribute the difference to the creation of local structures that contain magnetic helicity which inhibits the field decay due to the existence of a lower bound imposed by the realizability condition. We show that net magnetic helicity can be produced resistively as a result of a slight imbalance between mutually canceling helical pieces as they are being driven apart. We speculate that higher order topological invariants beyond magnetic helicity may also be responsible for slowing down the decay of the two more complicated nonhelical structures mentioned above.

Place, publisher, year, edition, pages
2011. Vol. 84, no 1, 016406- p.
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
URN: urn:nbn:se:su:diva-66558DOI: 10.1103/PhysRevE.84.016406ISI: 000293452500013OAI: oai:DiVA.org:su-66558DiVA: diva2:468962
Note

authorCount :2

Available from: 2011-12-22 Created: 2011-12-20 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Magnetic helicity in astrophysical dynamos
Open this publication in new window or tab >>Magnetic helicity in astrophysical dynamos
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The broad variety of ways in which magnetic helicity affects astrophysical systems, in particular dynamos, is discussed.

The so-called alpha effect is responsible for the growth of large-scale magnetic fields. The conservation of magnetic helicity, however, quenches the alpha effect, in particular for high magnetic Reynolds numbers. Predictions from mean-field theories state particular power law behavior of the saturation strength of the mean fields, which we confirm in direct numerical simulations. The loss of magnetic helicity in the form of fluxes can alleviate the quenching effect, which means that large-scale dynamo action is regained. Physically speaking, galactic winds or coronal mass ejections can have fundamental effects on the amplification of galactic and solar magnetic fields.

The gauge dependence of magnetic helicity is shown to play no effect in the steady state where the fluxes are represented in form of gauge-independent quantities. This we demonstrate in the Weyl-, resistive- and pseudo Lorentz-gauge. Magnetic helicity transport, however, is strongly affected by the gauge choice. For instance the advecto-resistive gauge is more efficient in transporting magnetic helicity into small scales, which results in a distinct spectrum compared to the resistive gauge.

The topological interpretation of helicity as linking of field lines is tested with respect to the realizability condition, which imposes a lower bound for the spectral magnetic energy in presence of magnetic helicity. It turns out that the actual linking does not affect the relaxation process, unlike the magnetic helicity content. Since magnetic helicity is not the only topological variable, I conduct a search for possible others, in particular for non-helical structures. From this search I conclude that helicity is most of the time the dominant restriction in field line relaxation. Nevertheless, not all numerical relaxation experiments can be described by the conservation of magnetic helicity alone, which allows for speculations about possible higher order topological invariants.

Place, publisher, year, edition, pages
Stockholm: Department of Astronomy, Stockholm University, 2012. 64 p.
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-81601 (URN)978-91-7447-593-7 (ISBN)
Public defence
2012-12-07, FD5, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:15 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 1: Submitted. 

Available from: 2012-11-15 Created: 2012-10-25 Last updated: 2012-10-29Bibliographically approved

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