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Magnetic helicity in astrophysical dynamos
Stockholm University, Faculty of Science, Department of Astronomy.
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: urn:nbn:se:su:diva-81601ISBN: 978-91-7447-593-7 (print)OAI: oai:DiVA.org:su-81601DiVA: diva2:562767
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
List of papers
1. The kinetic helicity needed to drive large-scale dynamos
Open this publication in new window or tab >>The kinetic helicity needed to drive large-scale dynamos
(English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376Article in journal (Refereed) Submitted
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-81643 (URN)
Available from: 2012-10-29 Created: 2012-10-29 Last updated: 2017-12-07Bibliographically approved
2. Small-scale magnetic helicity losses from a mean-field dynamo
Open this publication in new window or tab >>Small-scale magnetic helicity losses from a mean-field dynamo
2009 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 398, no 3, 1414-1422 p.Article in journal (Refereed) Published
Abstract [en]

Using mean-field models with a dynamical quenching formalism, we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity density or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong for both large- and small-scale fields. In the presence of shear, there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region, there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behaviour emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain.

Keyword
hydrodynamics, magnetic fields, MHD, turbulence
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-32536 (URN)10.1111/j.1365-2966.2009.15188.x (DOI)000269731500030 ()
Available from: 2009-12-12 Created: 2009-12-12 Last updated: 2017-12-12Bibliographically approved
3. Equatorial magnetic helicity flux in simulations with different gauges
Open this publication in new window or tab >>Equatorial magnetic helicity flux in simulations with different gauges
Show others...
2010 (English)In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 331, no 1, 130-135 p.Article in journal (Refereed) Published
Abstract [en]

% We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small-scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo-Lorenz gauge, where the speed of light is replaced by the sound speed, and the `resistive gauge' in which the Laplacian of the magnetic vector potential acts as a resistive term. We find that, in the statistically steady state, the time-averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges.

Keyword
Sun: magnetic fields, magnetohydrodynamics (MHD)
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-36130 (URN)10.1002/asna.200911308 (DOI)000273944200016 ()
Available from: 2010-01-22 Created: 2010-01-22 Last updated: 2017-12-12Bibliographically approved
4. Magnetic helicity transport in the advective gauge family
Open this publication in new window or tab >>Magnetic helicity transport in the advective gauge family
2011 (English)In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 18, no 1, 012903- p.Article in journal (Refereed) Published
Abstract [en]

Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e., when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential.

National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-68666 (URN)10.1063/1.3533656 (DOI)000286900000033 ()
Note

authorCount :4

Available from: 2012-01-05 Created: 2012-01-04 Last updated: 2017-12-08Bibliographically approved
5. Magnetic-field decay of three interlocked flux rings with zero linking number
Open this publication in new window or tab >>Magnetic-field decay of three interlocked flux rings with zero linking number
2010 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 81, no 3, 36401- p.Article in journal (Refereed) Published
Abstract [en]

The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.

National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-49938 (URN)10.1103/PhysRevE.81.036401 (DOI)000276199400076 ()
Note

authorCount :3

Available from: 2010-12-20 Created: 2010-12-20 Last updated: 2017-12-11Bibliographically approved
6. Decay of helical and nonhelical magnetic knots
Open this publication in new window or tab >>Decay of helical and nonhelical magnetic knots
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.

National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-66558 (URN)10.1103/PhysRevE.84.016406 (DOI)000293452500013 ()
Note

authorCount :2

Available from: 2011-12-22 Created: 2011-12-20 Last updated: 2017-12-08Bibliographically approved

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