# A mathematical introduction to Magnetohydrodynamics (MA5902)

The course provides a basic introduction to magnetohydrodynamics (MHD), with emphasis on its mathematical aspects (as opposite to physical phenomena). Essentially, MHD is the theory of electrically conducting fluids in presence of a magnetic field. Since MHD is one of the two building blocks (together with kinetic theory) of theoretical plasma physics, its understanding is of paramount importance for applied mathematicians who deal with plasma physics and nuclear fusion applications.

## Content

- Basic concepts and quantities of fluid dynamics.
- Reynolds transport theorem and the equation of fluid dynamics.
- Relation to kinetic theory.
- Multi-fluid description of plasmas and quasi-neutral limit.
- Derivation of MHD equations from multi-fluid theories.
- Global conservation theorems for MHD.
- Topology of the magnetic field lines.
- Conservation of the magnetic flux.
- Qualitative aspects of the solutions of MHD equations.
- Reduced MHD equations and conservation theorems.
- Variational formulation of MHD.
- Hamiltonian formulation of MHD and reduced MHD.

Prerequisites are basic calculus, basic mathematical analysis, and the theory of ordinary differential equations. Understanding of partial differential equations and basic numerical methods for their solution are an advantage but not a prerequisite.
## News

## Lecture notes

## Literature

- A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Dynamics, Springer-Verlag (1993).
- D. D. Schnack, Lectures on Magnetohydrodynamics, Springer (2009).
- E. Priest, Magnetohydrodynamics of the Sun, Cambridge University Press (2014).

## Lecturer

- Dr. Omar Maj. Wednesday 12:15-13:45 MI 03.08.011

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StefanPossanner - 18 Apr 2019