Stability Analysis of Solar Atmospheric Models

               

Principal Investigator

Warren Wood

Department of Mathematics,

University of Newcastle

This project is studying the stability of equilibrium magnetic fields evaluated from mathematical
models of the solar atmosphere. The models display many of the gross features of the Sun's atmospheric magnetic structures and this investigation aims to establish the stability behaviour of such fields. The lack of stability in the magnetic fields is thought to give rise to eruptive phenomena such as solar flares and coronal mass ejection. In particular we wish to establish those magnetic topologies which are the most unstable.
   

Co-Investigators

     

Murray Sciffer

Department of Physics,

University of Newcastle

     
             

     

Projects

g90 - VPP

           
               

What are the results to date and the future of this work?

As part of the total project we have completed calculations analysing the normal mode behaviour of two dimensional equilibrium fields. These calculations show that the fields exhibit growth times to instability which are the correct order of magnitude when compared with observation. These models, being two dimensional, are not directly applicable to the solar atmosphere. In calculations to follow we plan to study the normal modes of more realistic three dimensional structures. For 2D models the resulting matrices are real whereas for 3D models they are complex.

What computational techniques are used?

To study the problem a system of partial differential equations are discretized resulting in an eigenvalue problem in which the eigenvalues give information as to the stability of the equilibrium system. To completely analyse the problem all the eigenvalues need to be determined which means that a QR algorithm is appropriate. In these calculations we are using the NAG routines. At this stage we have only considered the eigenvalues for real matrices of order 7500. To study realistic 3D models then the eigenvalues for complex matrices must be computed.

Publications

M. D Sciffer, Magnetic Structures in the Solar Atmosphere, PhD Thesis, Submitted February,1998.

               
- Appendix B