Centre de Physique Théorique


Mercredi 19 avril 2017

14h00 – 15h00, Amphi 5 du CPT

Slow Manifold Reduction of the Two-Fluid Maxwell System

Joshua Burby (Courant Institute, New York)


The two-fluid Maxwell system couples frictionless electron and ion
fluids via Maxwell’s equations. When the frequencies of light waves,
Langmuir waves, and single-particle cyclotron motion are scaled to be
asymptotically large, the two-fluid Maxwell system becomes a fast-slow
dynamical system. The slow manifold for this fast-slow system is an
invariant set in the two-fluid Maxwell phase space on which solutions
are free of high-frequency oscillations. In this talk, I will present
expressions for the (asymptoticallly-scaled) two-fluid Maxwell system
restricted to its slow manifold. In the leading order approximation, the
slow dynamics are given by magnetohydrodynamics (MHD). Higher order
approximations of the slow dynamics give an infinite hierarchy of
conservative extensions to MHD, which include Hall MHD and inertial MHD.
The slow dynamics obey a variational principle and possess a
noncanonical Hamiltonian structure. By employing infinite-dimensional
Lie transforms, the Poisson structure may be obtained in closed form.