Activity: Conferences and workshops › Participation in workshop, seminar or course
Lecture entitled "What do spinning tops and flowing plasmas have in common ?"
At a macroscopic level, a plasma is suitably described by magneto-hydrodynamics (MHD) equations or extensions thereof. The hotter a plasma, the less resistive it is (the opposite of a metal), becoming an ideal conductor in the infinite temperature limit. Ideal MHD equations are relevant to the modelling of magnetic confinement fusion plasmas, the heliosphere, solar flares, accretion disks, etc. They feature several structural properties leading to important conservation laws, in particular Alfvén's frozen-in theorem where the magnetic field is dragged along the plasma fluid motion. It is interesting to interpret the ideal MHD equations as the Euler-Poincaré equations obtained by reduction of geodesic motion on the Lie-Fréchet group of diffeomorphisms equipped with a right-invariant Riemannian metric. The advantages of attaching a variational problem to ideal MHD are theoretical (origins of relabelling symmetry and conservation laws) and computational (hints for better discretisation schemes). In this talk, we will review Euler-Poincaré reduction using rigid body dynamics as an example, we will apply the recipe to the ideal MHD problem, and discuss whether Multi-Region relaXed magnetohydrodynamics (MRxMHD) fits in this picture.