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Extended guiding-center Vlasov–Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-timescale orderings. The guiding-center Vlasov–Maxwell equations are derived up to second order, which contains dipole and quadrupole contributions to the guiding-center polarization and magnetization that include finite-Larmor-radius corrections. Exact energy-momentum conservation laws are derived from the variational formulation of these higher-order guiding-center Vlasov–Maxwell equations.
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Action principles and conservation laws for Chew–Goldberger–Low anisotropic plasmas
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.
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- Award ID(s):
- 1655280
- PAR ID:
- 10355948
- Date Published:
- Journal Name:
- Journal of Plasma Physics
- Volume:
- 88
- Issue:
- 4
- ISSN:
- 0022-3778
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/S0022377822000642
