Courses are together with exams the building blocks for modules. Please keep in mind that information on the contents, learning outcomes and, especially examination conditions are given on the module level only – see section "Assignment to Modules" above.
||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. The basic "milestones" along the path are:
- 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.