Description

Both the interior and the atmosphere of the Sun are strongly influenced by magnetic fields. When gases are heated to very high temperatures, molecules come apart leading to free electrons and ions (i.e., the gas becomes a plasma). Plasmas are excellent conductors of electricity and as a consequence they can support strong magnetic fields which can play an important role in the behavour of stars. Applied mathematicians study magnetic fields in a fluid dynamical framework known as magnetohydrodynamics (usually shortened to ‘MHD’). In this project, we will study aspects of MHD that are used in idealised mathematical models of stars.

To begin the project, we will review the governing equations of MHD and study some simple solutions. Following this, students will be encouraged to focus on a specific area of their choice. This could be something from the following list (but there is also plenty of flexibility here to follow the interests of the student):

• kinematic dynamo theory (the study of how large-scale magnetic fields can be generated by a given fluid flow).
• magnetoconvection (the interaction of convection with a magnetic field).
• magnetic equilibria (a special class of solution to the time independent governing equations which are often used in modelling the solar atmosphere).

Pre/Co-requisites

Analysis in Many Variables II is required. It is likely that projects in this area will require some numerical computation in Python (or similar) but you do not need to be an expert programmer, just an eagerness to learn and try things out! Fluid Mechanics III and/or Partial Differential Equations III would complement this project well.

Resources

• Magnetohydrodynamics of the Sun. Textbook by Priest providing an introduction to several areas of MHD.
• An introduction to Magnetohydrodynamics. Textbook by Davidson providing general backround to MHD.
• An overview of dynamo theory by Choudhuri.
• Self-exciting fluid dynamos. Textbook by Moffatt & Dormy which goes into much more detail on dynamo theory.
• Magnetoconvection. Textbook by Weiss & Proctor on magnetoconvection.
• A review article on magnetic equilibria by Wiegelmann & Sakurai.

For more information email: Laura Currie