## Possible PhD Projects

This is a (non-exhaustive) list of potential projects that I would be willing to supervise.

For information about how to apply and funding, see our departmental webpages. Please note that I require you to have (or be expecting) a good First class degree (or equivalent) in Mathematics or a similar subject, whether you are applying for a funded or self-funded place.

### Testing the Babcock-Leighton model for the solar cycle

The origin (and variability) of the solar magnetic cycle is one of the central unsolved problems in solar physics. This project will use mathematical modelling and high-performance computation to attack this question. The new tool at our disposal is a three-dimensional kinematic code for the solar convection zone that implements the Babcock-Leighton model of the solar dynamo.

Unlike previous axisymmetric models, this code is able to self-consistently account for the conservation of magnetic flux during the Babcock-Leighton cycle, and is therefore - in principle - able to assess the viability of this mechanism for driving the solar activity cycle that we see. Although the Babcock-Leighton idea dates back to the 1960s, testing the idea numerically has had to wait for modern computers. The major aim of this project will be to determine (i) under which conditions the model produces a self-sustaining cycle, and (ii) whether this is possible while simultaneously matching observations of the real solar surface.

### Modelling of solar eruptions

This project will involve high-performance computer simulations of the magnetic field in the Sun's corona using a time-evolving magneto-frictional model. When the coronal magnetic field is driven continuously by magnetic footpoint motions inside the Sun, magnetic stresses build in the corona. Over time, these stresses become concentrated in twisted magnetic flux ropes, which can suddenly lose equilibrium and erupt. This is understood to cause coronal mass ejections, throwing plasma into interplanetary space and often impacting on the Earth's magnetic environment: an important aspect of space weather.

The idea is to build on recent progress where field-line helicity was used to automatically identify magnetic flux ropes in the 3D simulations. An important question to explore is how well the pre-eruption structure and/or orientation of a magnetic flux rope predicts the ejected helicity. Or, how do the statistical properties of flux rope eruptions depend on the helicity of emerging active regions on the Sun? The ultimate goal of this work is to improve space weather prediction tools used by the UK Met Office.

### Magnetic relaxation schemes for coronal modelling

This project is to develop a viscous relaxation model for the magnetic field in the Sun's corona, and study the improvement over an existing magneto-frictional model. This project will be primarily computational in nature, and will involve learning how to do parallel programming for computational fluid simulation. It will also involve developing simple analytical solutions with which to test the new model.

For more information about coronal magnetic field modelling, see this review. For an example of viscous relaxation applied to a magnetic field relaxation problem, see Bajer and Moffatt.