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\u27s equation above the photosphere to represent the corona. The PDE\u27s 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
