Applications of topology in magnetic fields.
Doctoral thesis, UCL (University College London).
This thesis concerns applications of topology in magnetic fields. First, we examine the influence of writhe in the stretch-twist-fold dynamo. We consider a thin flux tube distorted by simple stretch, twist, and fold motions and calculate the helicity and energy spectra. The writhe number assists in the calculations, as it tells us how much the internal twist changes as the tube is distorted. In addition it provides a valuable diagnostic for the degree of distortion. Non mirror-symmetric dynamos typically generate magnetic helicity of one sign on large-scales and of the opposite sign on small-scales. The calculations presented here confirm the hypothesis that the large-scale helicity corresponds to writhe and the small-scale corresponds to twist. In addition, the writhe helicity spectrum exhibits an interesting oscillatory behaviour. Second, we examine the effect of reconnection on the structure of a braided magnetic field. A prominent model for both heating of the solar corona and the source of small flares involves reconnection of braided magnetic flux elements. Much of this braiding is thought to occur at as yet unresolved scales, for example braiding of threads within an EUV or X-ray loop. However, some braiding may be still visible at scales accessible to Trace or the EIS imager on Hinode. We suggest that attempts to estimate the amount of braiding at these scales must take into account the degree of coherence of the braid structure. We demonstrate that simple models of braided magnetic fields which balance input of topological structure with reconnection evolve to a self-organized critical state. An initially random braid can become highly ordered, with coherence lengths obeying power law distributions. The energy released during reconnection also obeys a power law.
|Title:||Applications of topology in magnetic fields|
|Open access status:||An open access version is available from UCL Discovery|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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