Statistics – Applications
Scientific paper
Nov 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000phdt.........2p&link_type=abstract
PhD Thesis, University of St Andrews, 2000.
Statistics
Applications
1
Solar Atmosphere, Mhd, Analytical Models
Scientific paper
We present in this thesis three-dimensional self-consistent solutions of the MHD equations which we then apply in giving simple models of magnetic structures in the solar atmosphere. Two classes of solution are presented. One class, steady-state equilibria with field-aligned incompressible flow, is calculated for the first time. These solutions are calculated by a transformation method which allows the construction of steady state MHD solutions with subalfvénic flow from known solutions of static MHD and of steady state MHD solutions with superalfvénic flow from known solutions of steady state hydrodynamics. For the first time this transformation method is applied to three-dimensional solutions of the steady state MHD equations. We discuss possible applications of particular solutions to flow phenomena in the solar atmosphere such as the Evershed flow in sunspots and flows in coronal arcades. For the second class of solutions, a special class of linear self-consistent three-dimensional solutions of the magnetohydrostatic (MHS) equations for which the current density is a combination of a linear force-free part and a part with non-force-free components, we succeed in deriving a Green's function method. This allows the construction of MHS solutions of this class with arbitrary photospheric boundary conditions for Bz. These solutions can be used to extrapolate coronal magnetic fields from known longitudinal photospheric field data and provide a self-consistent description of magnetic field, plasma pressure, plasma density and plasma temperature. The method therefore allows a better comparison of models with observations of solar coronal structures. We will demonstrate how the method works by giving an illustrative example. We continue this work by applying the Green's function method to several sets of observed line-of-sight photospheric magnetic field data and thereby calculating self-consistent plasma structures in the solar atmosphere. As far as possible we compare these calculated structures to near-simultaneous emission patterns. We conclude the thesis with a discussion recapping some strengths and weaknesses of the solutions and exploring some possibilities for extending the work.
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