%0 Thesis
%9 Doctoral
%A Asgari-Targhi, M.
%B Department of Mathematics
%D 2009
%F discovery:18900
%I UCL (University College London)
%P 181
%T Applications of topology in magnetic fields
%U https://discovery.ucl.ac.uk/id/eprint/18900/
%X 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.