Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas

Hameiri, Eliezer

doi:10.1063/1.4820769

Cited by 9 publications

(19 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So the HMHD Bernoulli equation is simply Also from (4.35) and (4.39) we have For , equations (5.8)–(5.10) reduce to the axisymmetric Grad–Shafranov–Bernoulli system of Throumoulopoulos & Tasso (2006). For the baroclinic version of the axisymmetric HMHD equilibrium equations the reader is referred to Hameiri (2013), Guazzotto & Betti (2015).…”

Section: Special Equilibriamentioning

confidence: 99%

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

2018

View full text Add to dashboard Cite

Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for 3D dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric XMHD (D.A. Kaltsas et al, Phys. Plasmas 24, 092504 (2017)). 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 helical 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. †

show abstract

Section: Special Equilibriamentioning

confidence: 99%

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

2018

View full text Add to dashboard Cite

show abstract

“…This follows from the fact that the magnetic helicity is a common Casimir invariant for both models. The MHD limit of the HMHD model is also discussed in [24,25], although it is not shown how to limit the HMHD Casmirs into their MHD values.…”

Section: Mhd Limitmentioning

confidence: 99%

Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria

2017

View full text Add to dashboard Cite

The Hamiltonian structure of ideal translationally symmetric extended MHD (XMHD) is obtained by employing a method of Hamiltonian reduction on the three-dimensional noncanonical Poisson bracket of XMHD. The existence of the continuous spatial translation symmetry allows the introduction of Clebsch-like forms for the magnetic and velocity fields. Upon employing the chain rule for functional derivatives, the 3D Poisson bracket is reduced to its symmetric counterpart. The sets of symmetric Hall, Inertial, and extended MHD Casimir invariants are identified, and used to obtain energy-Casimir variational principles for generalized XMHD equilibrium equations with arbitrary macroscopic flows. The obtained set of generalized equations is cast into Grad-Shafranov-Bernoulli (GSB) type, and special cases are investigated: static plasmas, equilibria with longitudinal flows only, and Hall MHD equilibria, where the electron inertia is neglected. The barotropic Hall MHD equilibrium equations are derived as a limiting case of the XMHD GSB system, and a numerically computed equilibrium configuration is presented that shows the separation of ion-flow from electromagnetic surfaces.

show abstract

“…As it has been highlighted in [48][49][50], the MHD limit of the Casimirs and variational functionals (e.g. the Lagrangian) of XMHD and HMHD, presents certain peculiarities because the Hall term gives rise to singular perturbations, making the derivation of their MHD counterparts rather not straightforward, a difficulty that, as regards to the Casimirs, was treated in [48] and [50]. Hence, it is natural that this complication is inherited by the variational principles involving the Casimirs, e.g., the energy-Casimir method.…”

Section: Dynamically Accessible Variationsmentioning

confidence: 99%

Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

2020

View full text Add to dashboard Cite

The formal stability analysis of Eulerian extended MHD (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flows under constrained perturbations. A Lyapunov functional that can potentially provide explicit stability criteria for generic equilibria under dynamically accessible variations is also obtained. Moreover, we examine the Lagrangian stability of the general quasi-neutral twofluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass we derive a HMHD energy principle and in addition the perturbed induction equation arises from Hamilton's equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.

show abstract

Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas

Cited by 9 publications

References 33 publications

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria

Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

Contact Info

Product

Resources

About