Sydney Dynamics Group: Bob Dewar -- Time-dependent relaxed magnetohydrodynamics -- inclusion of cross helicity constraint using phase-space action

Dear all, 

This week, Friday June 5, Bob Dewar (ANU) will give a talk at 4pm (Sydney time) via
Zoom.  
Zoom link: https://uni-sydney.zoom.us/j/96418715544 
Meeting ID: 964 1871 5544 

Title: Time-dependent relaxed magnetohydrodynamics -- inclusion of cross helicity
constraint using phase-space action 

Abstract: A phase-space version of the ideal MHD Lagrangian is derived from first
principles and shown to give a relabeling transformation when a cross-helicity
constraint is added in Hamilton’s Action Principle.  A new formulation of time-dependent
\emph{Relaxed} Magnetohydrodynamics (RxMHD) is derived using microscopic conservation of
mass, and macroscopic constraints on total magnetic helicity, cross helicity and entropy
under variations of density, pressure, fluid velocity, and magnetic vector potential.
This gives Euler--Lagrange equations consistent with previous work on both ideal and
relaxed MHD equilibria with flow, but generalizes the relaxation concept from statics to
dynamics.  The application of the new dynamical formalism is illustrated for
short-wavelength linear waves, and the interface connection conditions for Multiregion
Relaxed MHD (MRxMHD) are derived.  The issue of whether $\vec{E} + \vec{u}\cross\vec{B}
= 0$ should be a constraint is discussed.  

Past talks can be found on the YouTube channel:
https://www.youtube.com/channel/UCZqgDJ21wbdzMbeIdealpUg/ 

I hope to see you all online.  

Lachlan