Magneto-Fluid Dynamics Seminar

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Metriplectic dynamics -- a framework for plasma kinetic theory and numerics

Speaker: Eero Hirvijoki, Princeton Plasma Physics Laboratory

Location: Warren Weaver Hall 905

Date: Tuesday, October 3, 2017, 11 a.m.

Synopsis:

In dissipationless systems, Hamiltonian mechanics, culminating in a Poisson bracket and a Hamiltonian, provides a convenient framework for both theoretical and numerical studies. In systems that obey both the First and the Second Law of Thermodynamics, the dissipationless dynamics can often be extended with a symmetric bracket and an entropy to account for the dissipation. The resulting, so-called metriplectic framework captures many interesting models, including the Navier-Stokes equations, non-isothermal kinetic polymer models, and the Vlasov-Maxwell-Landau model used in plasma physics. In this talk, we review the basic principles of metriplectic dynamics and discuss some prominent methods for time discretization. We focus on the Vlasov-Maxwell-Landau model and, especially, on the Landau collision operator for which a genuine metriplectic integrator is demonstrated. The gyrokinetic version of the Vlasov-Maxwell-Landau system is briefly visited.