Action principles and conservation laws for Chew–Goldberger–Low anisotropic plasmas. (10th August 2022)

• Record Type: Journal Article
• Authors: Webb, G.M.; Anco, S.C.; Meleshko, S.V.; Zank, G.P.
• Is Part Of: Journal of plasma physics. Volume 88:Number 4(2022)
• Publication Date: 2022-08-10
• Subjects: fusion plasma -- plasma nonlinear phenomena -- space plasma physics; Plasma (Ionized gases) -- Periodicals; 530.4405
• DOI: 10.1017/S0022377822000642
• Languages: English
• ISSNs: 0022-3778

Abstract

Abstract : The ideal Chew–Goldberger–Low (CGL) plasma equations, including the double adiabatic conservation laws for the parallel ($p_\parallel$ ) and perpendicular pressure ($p_\perp$ ), are investigated using a Lagrangian variational principle. An Euler–Poincaré variational principle is developed and the non-canonical Poisson bracket is obtained, in which the non-canonical variables consist of the mass flux ${\boldsymbol {M}}$, the density $\rho$, the entropy variable $\sigma =\rho S$ and the magnetic induction ${\boldsymbol {B}}$ . Conservation laws of the CGL plasma equations are derived via Noether's theorem. The Galilean group leads to conservation of energy, momentum, centre of mass and angular momentum. Cross-helicity conservation arises from a fluid relabelling symmetry, and is local or non-local depending on whether the gradient of $S$ is perpendicular to ${\boldsymbol {B}}$ or otherwise. The point Lie symmetries of the CGL system are shown to comprise the Galilean transformations and scalings.