St Andrews Research Repository

St Andrews University Home
View Item 
  •   St Andrews Research Repository
  • Mathematics & Statistics (School of)
  • Mathematics & Statistics Theses
  • View Item
  •   St Andrews Research Repository
  • Mathematics & Statistics (School of)
  • Mathematics & Statistics Theses
  • View Item
  •   St Andrews Research Repository
  • Mathematics & Statistics (School of)
  • Mathematics & Statistics Theses
  • View Item
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.

Magnetic annihilation, null collapse and coronal heating

Thumbnail
View/Open
ChristopherMellorPhDThesis.pdf (19.46Mb)
Date
2004
Author
Mellor, Christopher
Supervisor
Priest, E. R. (Eric Ronald)
Metadata
Show full item record
Altmetrics Handle Statistics
Abstract
The problem of how the Sun's corona is heated is of central importance to solar physics research. In this thesis we model three main areas. The first, annihilation, is a feature of non-ideal MHD and focusses on how magnetic field of opposite polarity meets at a null point and annihilates, after having been advected with plasma toward a stagnation point in the plasma flow. Generally, the null point of the field and the stagnation point of the flow are coincident at the origin, but in chapter 2 a simple extension is considered where an asymmetry in the boundary conditions of the field moves the null point away from the origin. Chapter 3 presents a model of reconnective annihilation in three dimensions. It represents flux being advected through the fan plane of a 3D null, and diffusing through a thin diffusion region before being annihilated at the spine line, and uses the method of matched asymptotic expansions to find the solution for small values of the resistivity. The second area of the thesis covers null collapse. This is when the magnetic field in close proximity to a null point is disturbed, causing the field to fold up on itself and collapse. This is a feature of ideal MHD, and causes a strong current to build up, allowing non-ideal effects to become important. When using linearised equations for the collapse problem, we are in fact looking at a linear instability. If this instability initiates a collapse, this is only a valid model until non-linear effects become important. By talking about collapse in chapters 4 and 5 (as it is talked about in the literature), we mean that the linear instability initiates collapse, which in principle, non-linear effects could later stop. Chapter 4 introduces a two-dimensional model for collapse, using the ideal, compressible, linearised MHD equations. It is a general solution in which all spatially linear nulls and their supporting plasma flows and pressure gradients can be checked for susceptibility to collapse under open boundary conditions. Chapter 5 uses the model introduced in chapter 4 to investigate the collapse of three-dimensional, potential nulls (again, spatially linear) for all possible supporting plasma flows and pressure gradients. Using this model, all nulls under consideration are found to collapse and produce large currents, except for a group of 2D O-type nulls supported by highly super-Alfvenic plasma flows. The third area of this thesis involves numerically simulating a model of heating by coronal tectonics (Priest et al, 2002). A simple magnetic field is created and the boundary is driven, also in a simple manner. Current sheets which scale with grid resolution are seen to build up on the quasi-separatrix layers, and there is some evidence of magnetic reconnection.
Type
Thesis, PhD Doctor of Philosophy
Collections
  • Mathematics & Statistics Theses
URI
http://hdl.handle.net/10023/12946

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

Advanced Search

Browse

All of RepositoryCommunities & CollectionsBy Issue DateNamesTitlesSubjectsClassificationTypeFunderThis CollectionBy Issue DateNamesTitlesSubjectsClassificationTypeFunder

My Account

Login

Open Access

To find out how you can benefit from open access to research, see our library web pages and Open Access blog. For open access help contact: openaccess@st-andrews.ac.uk.

Accessibility

Read our Accessibility statement.

How to submit research papers

The full text of research papers can be submitted to the repository via Pure, the University's research information system. For help see our guide: How to deposit in Pure.

Electronic thesis deposit

Help with deposit.

Repository help

For repository help contact: Digital-Repository@st-andrews.ac.uk.

Give Feedback

Cookie policy

This site may use cookies. Please see Terms and Conditions.

Usage statistics

COUNTER-compliant statistics on downloads from the repository are available from the IRUS-UK Service. Contact us for information.

© University of St Andrews Library

University of St Andrews is a charity registered in Scotland, No SC013532.

  • Facebook
  • Twitter