Magnetic Helicity Flow in the Sun and Heliosphere
Date: 26 May 2020
University of Exeter
PhD in Mathematics
Magnetic helicity, the measure of entanglement within a magnetic field, has the capability to further our knowledge of the magnetic fields which are ubiquitous across the physical universe. Discovered half a century ago by Lodewijk Woltjer in 1958, it was only given physical meaning by Keith Moffatt in 1969. Progress was initially slow ...
Magnetic helicity, the measure of entanglement within a magnetic field, has the capability to further our knowledge of the magnetic fields which are ubiquitous across the physical universe. Discovered half a century ago by Lodewijk Woltjer in 1958, it was only given physical meaning by Keith Moffatt in 1969. Progress was initially slow due to the constraints on its calculation: it is assumed that the volume within which we wish to measure helicity does not have any magnetic field crossing its boundaries. But, in 1984, Mitchell Berger and George Field provided a resolution to this problem which allowed it to be applied to open astrophysical fields. From there, and particularly in the last two decades, interest in magnetic helicity has grown exponentially within the research community, resulting in this thesis. We will begin by providing a semi--formal introduction to the topic, in particular that of magnetohydrodynamics, which describes how a magnetic field and associated plasma co-interact. We provide a mathematical introduction to magnetic helicity, and demonstrate that unsolved problems remain in our understanding of the Sun's magnetic field that are associated with its magnetic helicity. With this knowledge in hand, we first tackle the topic of predicting the Solar Cycle, which has been an unachieved goal of the solar physics community for longer than we care to remember. We show that magnetic helicity, which is intrinsically linked to the emergence of sunspots, is a statistically stronger candidate for the predictor of activity than that of the polar field strength, which is the current 'best of the worst' of the known predictors. We then, for the first time, measure how much helicity is generated on the solar surface due to shear motions in a surface flux transport model, which is a method of modelling the magnetic field on the surface of the sun. We show that the results are not as obvious as we expect, and indeed that the flux of magnetic helicity within each hemisphere is carefully balanced between latitudes. We also provide an estimate of how much helicity is produced in a solar cycle, and correlate this with the dipole strength of that cycle. This is followed by the main result of the thesis: we demonstrate that helicity can be completely generalised for any physical system in terms of a two--point correlation, and fully described in terms of spatial scales and locality using wavelet analysis. In particular, we show that our generalised measure of helicity offers a physical meaning to this localisation. Our methods are demonstrated to have some notable advantages to that of Fourier analysis, which is shown to sometimes produce spurious results. Finally, we explore the hypothesis that the shape of a magnetic field domain can contribute to the magnetic helicity when using a toroidal--poloidal decomposition. Indeed, in some cases the asymmetry contains the entirety of the magnetic helicity, which we demonstrate numerically.
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