Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.

doi:10.1017/s0022377818000338

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

Journal Article · Thu May 24 04:00:00 EDT 2018 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s0022377818000338· OSTI ID:1538937

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DOE/OSTI

Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for the three-dimensional dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric XMHD (Kaltsaset al.,Phys. Plasmas, vol. 24, 2017, 092504). Four families of Casimir invariants are obtained directly from the symmetric Poisson bracket and they are used to construct Energy–Casimir variational principles for deriving generalized XMHD equilibrium equations with arbitrary macroscopic flows. The system is then cast into the form of Grad–Shafranov–Bernoulli equilibrium equations. The axisymmetric and the translationally symmetric formulations can be retrieved as geometric reductions of the helically symmetric one. As special cases, the derivation of the corresponding equilibrium equations for incompressible plasmas is discussed and the helically symmetric equilibrium equations for the Hall MHD system are obtained upon neglecting electron inertia. An example of an incompressible double-Beltrami equilibrium is presented in connection with a magnetic configuration having non-planar helical magnetic axis.

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE

DOE Contract Number:: FG05-80ET53088

OSTI ID:: 1538937

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 3 Vol. 84; ISSN 0022-3778

Publisher:: Cambridge University Press

Country of Publication:: United States

Language:: English

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