Date of Award

Winter 2001

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

John A. Adam

Committee Member

Gary E. Copeland

Committee Member

J. Mark Dorrepaal

Committee Member

David G. Lasseigne

Committee Member

Stanley E. Weinstein

Abstract

Magnetic fields in the solar atmosphere suspend and insulate dense regions of cool plasma known as prominences. The convection zone may be the mechanism that both generates and expels this magnetic flux through the photosphere in order to make these formations possible. The connection is examined here by modeling the convection zone as both one-dimensional, then more realistically, two-dimensional.

First a Dirichlet problem on a semi-infinite strip is solved using conformal mapping and the method of images. The base of the strip represents the photosphere where a current distribution can be given as a boundary condition, and the strip extends into a current free atmosphere. Secondly a diffusion equation with convection terms is assigned to a two-dimensional region below the photosphere to represent the convection zone, and this is matched to Laplace's equation above the photosphere to represent the corona. The PDE's are solved numerically to find the magnetic field lines.

In both cases the solutions obtained resemble classic magnetic topologies that have been used to model quiescent prominences. Some of the solutions even have the feet observed to drop into supergranule boundaries.

DOI

10.25777/dh52-5y22

ISBN

9780493565194

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