Action principles and conservation laws for Chew–Goldberger–Low anisotropic plasmas. (10th August 2022) - Webb, G.M.; Anco, S.C.; Meleshko, S.V.; Zank, G.P.
Abstract : The ideal Chew–Goldberger–Low (CGL) plasma equations, including the double adiabatic conservation laws for the parallel (p_ ) and perpendicular pressure (p_ ), 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 M, the density ρ, the entropy variable σ =ρ S and the magnetic induction 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 B or otherwise. The point Lie symmetries of the CGL system are shown to comprise the Galilean transformations and scalings.