Description

Magnetic reconnection is a fundamental plasma physical process that can rapidly release magnetic energy in astrophysical and laboratory plasmas. For instance, the intense radiation produced during a solar flare is due to magnetic energy released by reconnection. Reconnection can be thought of in a rough sense as the breaking and re-joining of magnetic field lines (the analogue of fluid velocity streamlines but for the magnetic field vector).

The arrow shows where reconnection is occuring in this solar eruption.

Reconnection relies upon a coupling between the fluid-like plasma and the magnetic field. Mathematically, this coupling is described by the equations of Magnetohydrodynamics (MHD). The MHD equations are coupled and non-linear and solutions that fully solve them are challenging to construct. In this project you will investigate the so-called "kinematic" method for finding solutions. Rather than solving the whole MHD problem, a magnetic field is specified and plasma flows consistent with maintaining it are solved for. Although not fully self consistent, solutions of this type provide an intuitive way to explore how magnetic reconnection occurs in three dimensions.

We will start by reviewing the MHD equations and early 2D reconnection models. Then we'll move on to constructing toy 2D kinematic models before beginning work on a fully 3D one. Two papers with kinematic solutions that could be used as a starting point for your 3D investigation are Wyper & Jain 2012 and Hornig & Priest 2003.

As we move on to 3D models, we'll also go through some fundamentals of how reconnection differs in 3D to help guide your interpretation of the results. Although the solutions are for the most part analytical, to develop a good physical understanding you will need to write some Python code to solve for field lines and to visualise and explore the solutions.

Prerequisites

Having taken Fluid Mechanics III is essential. Taking Topics of Applied Maths alongside this project would also be advisable.

Partial Differential Equations III and Special Relativity & Electromagnetism would also be useful, but not essential.

For the Python programming, knowledge beyond first year programming will not be assumed. But having the confidence to write your own plotting and analysis routines would be useful.

Resources

There is a vast amount of literature on magnetic reconnection. For a general introduction see for instace Wikipedia. Texbooks for background include chapter 6 of Magnetohydrodynamics of the Sun and chapter 8 of Magnetic Reconnection. MHD Theory and Applications.. See also this Living Review.

email: Peter Wyper