Leiden University Student Repository

Asseldonk, R.R.L.J. van (2015)

The Hopf Map in Magnetohydrodynamics

Bachelor thesis | Wiskunde (BSc)

In this thesis we will investigate the Hopf map, a differentiable map from the three-sphere to the two-sphere. Its fibres, the inverse images of points on the sphere, are circles that are all linked with every other fibre. Based on the Hopf map we will construct divergenceless vector fields that have a physical interpretation as the magnetic field in the theory of magnetohydrodynamics. The concept of linking relates to helicity in this theory, a quantity that will be used to exhibit self-stable configurations of plasma.

Author

Asseldonk, R.R.L.J. van

Faculty

Faculty of Science

Supervisors

Edixhoven, S.J.
Dalhuisen, J.W.

ECTS Credits

24

Language

en