Relaxed magnetohydrodynamics with ideal Ohm's law constraint

Dewar, R. L.; Qu, Zhisong

doi:10.1017/s0022377821001355

Cited by 1 publication

(1 citation statement)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recent work by Dewar et al. (2020) and Dewar & Qu (2022) developed variational principles to describe time- dependent relaxed MHD using a global cross-helicity constraint with a phase space Lagrangian action principle (PSL) as opposed to a configuration space Lagrangian (CSL) action. The theory has been used to describe multi-region, extended MHD (RxMHD) in fusion plasma devices.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%