## MAS6450 Waves and Magnetohydrodynamics

 Both semesters, 2021/22 20 Credits Lecturer: Dr Yi Li Timetable Aims Outcomes Assessment

Studying wave phenomena has had a great impact on Applied Mathematics. This module looks at some important wave motions with a view to understanding them by developing from first principles the key mathematical tools. In the second part it gives an introduction to classical magnetohydrodynamics. Magnetohydrodynamics has been successfully applied to a number of astrophysical problems (e.g., to problems in Solar and Magnetospheric Physics), as well as to problems related to laboratory physics, especially to fusion devices.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.

## Outline syllabus

• Waves on strings. D'Alembert solution. Standing and propagating waves. Normal modes.
• Use of Fourier series for solving one-dimensional wave problems.
• Sound waves. Plane, cylindrical and spherical sound waves.
• Water waves. Wave dispersion. Group velocity.
• Traffic waves.
Semester 2:
• The system of magnetohydrodynamic equations and its main properties.
• Magnetohydrodynamics equilibria.
• Propagation of magnetohydrodynamic waves.
• Magnetohydrodynamic stability.
• Magnetic dynamo.

## Office hours

1pm Friday or by appointments

## Aims

• develop the concept of standing and progressive waves, and normal modes;
• consider examples of linear waves on strings, sound waves and water waves and nonlinear waves like “traffic waves”;
• introduce the system of magnetohydrodynamic equations and describe its main properties;
• apply this system of equations to different astrophysical and laboratory phenomena.

## Learning outcomes

By the end of the unit, a candidate will be able to demonstrate the ability to, the capability for... 1. using Fourier series to solve problems relating to waves on strings and membranes; 2. understanding the system of magnetohydrodynamic equations and main theorems that follow from this system (e.g., conservation laws, anti-dynamo theorem); 3. recognizing magnetic equilibrium configurations and magnetohydrodynamic stability.

40 lectures, no tutorials

## Assessment

The module will be assessed by a formal, closed book, two hour examination at the end of each semester.