MTH4343 · Magnetohydrodynamics and visualisation of scientific data

Overview

This unit briefly discusses plasma physics, covering single particle motion and kinetic plasma theory, and then introduces the fluid description to derive the equations of magnetohydrodynamics (MHD). It then explores basic MHD, including ideal and dissipative MHD, magnetic hydrostatics, and MHD waves. A detailed spectral theory of MHD waves is developed. Applications will be made to solar structures and observations. Stability and dynamics of solar features from the photosphere to corona will be analysed/simulated. These studies will be accompanied by the state-of-art visualisation techniques such as Python VTK, Mayavi and Paraview. Algorithms and ODE/PDE solvers to allow for Interactive MHD Visualisation will be an essential part of our tasks.

Areas of study: Master of Mathematics

Offerings

The Handbook publishes no offerings for this unit.

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Develop advanced knowledge of the terms in the governing equations of kinetic and fluid theories.
2. Identify the MHD equations and derive the associated mass and momentum conservation equations
3. Identify the terms in the MHD version of Ohm's Law and use the equation to explain convection electric fields and frozen-in magnetic fields
4. Demonstrate expert knowledge on magnetic pressure and tension forces
5. Derive the dispersion equation for the basic MHD wave modes and describe their properties, such as propagation of magnetohydrodynamic waves
6. Show using simple examples of how this system of equations can be applied to different astrophysical and laboratory phenomena.
7. Reach a high level of achievement in writing and presenting sophisticated visualisation methods of computational visualisation
8. Communicate complex information on waves and MHD theory with the use of visualisation methods.

Workload

• Three hours of seminars; • One hour applied class and • Eight hours independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.