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).

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 rare. However, when written in a certain form a symmetry in the equations can be exploited to produce exact analytical solutions.

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

In this project you will study some of these solutions and where possible look to extend them. We will start by reviewing the MHD equations and early 2D reconnection models. Then we’ll move on to more complex exact 2D and 3D solutions. Along the way, you will also learn about the topological structure of null points in the magnetic field (where B = 0). Although the solutions are for the most part analytical, to develop a good physical understanding you will be encouraged to write some Python code (to solve for field lines) to visualise and explore the the solutions.

Prerequisites

The only essential prerequisite is Analysis of Many Variables II, although it is recommended that you also have taken Partial Differential Equations III.

Continuum Mechanics III and Special Relativity & Electromagnetism would be useful. So too would Dynamical Systems II for studying the topology of null points (describable as Hyperbolic fixed points).

For the Python programming, knowledge beyond first year programming will not be assumed.

Resources

There is a vast amount of literature on magnetic reconnection. For a general introduction see for instace Wikipedia. For a more detailed look see chapter 6 of Magnetohydrodynamics of the Sun (in particular section 6.4 describes the methodology we will follow, calling it reconnective annihilation). For an example of an exact 3D reconnection solution see Craig et al. 1995.