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Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

Part of: PLA 17th European Fusion Theory Conference

Published online by Cambridge University Press:  24 May 2018

D. A. Kaltsas Open the ORCID record for D. A. Kaltsas [Opens in a new window] ,
G. N. Throumoulopoulos Open the ORCID record for G. N. Throumoulopoulos [Opens in a new window]  and
P. J. Morrison Open the ORCID record for P. J. Morrison [Opens in a new window]
D. A. Kaltsas
Affiliation:
Department of Physics, University of Ioannina, GR 451 10 Ioannina, Greece
G. N. Throumoulopoulos*
Affiliation:
Department of Physics, University of Ioannina, GR 451 10 Ioannina, Greece
P. J. Morrison
Affiliation:
Department of Physics and Institute for Fusion Studies, University of Texas, Austin, TX 78712, USA
*
†Email address for correspondence: [email protected]
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Abstract

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 (Kaltsas et 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.

Keywords

plasma confinementplasma dynamicsplasma flows
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 3 , June 2018 , 745840301
Copyright
© Cambridge University Press 2018 

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