Magneto-Fluid Dynamics Seminar
3D flows in nonsymmetric magnetic geometries : from stellarators to astrophysics.
Speaker: Wrick Sengupta, Courant Institute of Mathematical Sciences, NYU
Location: Warren Weaver Hall 905
Date: Wednesday, May 12, 2021, 10 a.m.
While two-dimensional magnetohydrodynamic (MHD) flows can be described by the modified Grad-Shafranov equation, our understanding of three-dimensional flows remains incomplete. Large flows are intimately connected to symmetries. In the world of stellarators, it can be shown that large flows can exist only in pure axisymmetric or quasi-symmetric devices. In astrophysics, there is an increasing need to understand non-symmetric three-dimensional flows in the presence of magnetic fields near accretion discs and compact objects that typically require very high resolution to simulate. In this talk, we shall explore a class of perturbative MHD equilibrium in a doubly-periodic domain with nearly parallel flows by systematically eliminating magnetic resonances order by order, utilizing a method pioneered by H. Weitzner. With an additional relabelling symmetry (first discussed by E. Hameiri in 1981), a reduction of the 3D system to a generalized Grad-Shafranov equation is possible. For this class of flows, non-symmetric generalizations of integrals of motion, such as Bernoulli’s function and angular momentum will be discussed. Finally, the close connection of E.Hameiri's symmetry and quasi-symmetry will be discussed.