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Geometric Methods for Physics of Magnetized Plasmas

Course 0000002044 in WS 2022/3

General Data

Course Type lecture
Semester Weekly Hours 2 SWS
Organisational Unit Department of Mathematics
Lecturers Dominik Bell
Eric Sonnendrücker
Dates Mon, 10:15–11:45, MI 03.08.011

Assignment to Modules

Further Information

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.

additional remarks Many models in plasma physics have been shown to exhibit a Hamiltonian structure and can be derived from an action principle. This is true for the equations of motion of a particle in a given electromagnetic field, which is a finite dimensional Hamiltonian system, for which symplectic numerical integrators have been derived with a large success and a well developed theory. Many other, more complex models for plasma physics, disregarding dissipative effects, also fit into an infinite dimensional non canonical hamiltonian geometric structure. This geometric structure provides the basis for the conservation of some fundamental physics invariants like energy, momentum and some Casimir invariants like Gauss' law and div B=0. Therefore preserving it in asymptotic models, like for example the Gyrokinetic model for strongly magnetised plasmas, or numerical approximations can be very helpful. New numerical methods, like mimetic Finite Differences and Finite Element Exterior Calculus based on the discretisation of objects coming from differential geometry allow in a natural way to preserve the geometric structure of the continuous equations. Schemes derived on these concepts allow on the one hand to rederive very good well-known schemes that have previously been found in ad hoc way, like the Yee scheme for Maxwell's equations or charge conserving Particle In Cell methods. These concepts will be introduced and applied to some classical models from plasma physics: Maxwell's equations, a cold plasma model and the Vlasov-Maxwell equations.
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