Action principles and conservation laws for Chew–Goldberger–Low anisotropic plasmas

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.

First Principles Description of Plasma Expansion Using the Expanding Box Model

“…Again, the first two terms of this equation are the same as in the non-expanding case. For a detailed derivation, see Hunana et al [43] or Webb et al [45] (we will follow the same definitions). The first term from the Vlasov's equation…”

Well-Posedness for Moving Interfaces with Surface Tension in Ideal Compressible MHD

“…The CGL model together with fluid models taking into account effects introduced by FLR corrections are discussed in full details in the nice survey [15]. As was noted in [15], in recent years there has been an increased emphasis on pressure/temperature anisotropy effects, in particular, on the CGL model (see, e.g., [7,31] and references therein) because the classical magnetohydrodynamic (MHD) fluid description does not satisfy all the needs of astrophysical applications requiring correct modelling of collisionless plasmas.…”