# Structure and computation of two-dimensional incompressible extended MHD

@article{DGrasso2016StructureAC, title={Structure and computation of two-dimensional incompressible extended MHD}, author={D.Grasso and Emanuele Tassi and Hamdi M. Abdelhamid and Philip J. Morrison}, journal={Physics of Plasmas}, year={2016}, volume={24}, pages={012110} }

A comprehensive study of the extended magnetohydrodynamic model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way, the energy conservation along with four families of Casimir invariants is naturally obtained. The construction facilitates various limits leading to the…

## 9 Citations

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

- Physics
- 2017

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…

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

- PhysicsJournal of Plasma Physics
- 2018

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…

Helically symmetric extended MHD: Hamiltonian formulation and equilibrium variational principles

- Physics
- 2018

Hamiltonian extended MHD (XMHD) dynamics 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…

Hamiltonian closures in fluid models for plasmas

- Physics
- 2017

Abstract
This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures…

Hamiltonian kinetic-Hall magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes

- PhysicsJournal of Plasma Physics
- 2021

We present two generalized hybrid kinetic-Hall magnetohydrodynamics (MHD) models describing the interaction of a two-fluid bulk plasma, which consists of thermal ions and electrons, with energetic,…

Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales

- PhysicsPhysics of Plasmas
- 2018

The direction of cascades in a two-dimensional model that takes electron inertia and ion sound Larmor radius into account is studied, resulting in analytical expressions for the absolute equilibrium…

A class of three-dimensional gyroviscous magnetohydrodynamic models

- EngineeringJournal of Plasma Physics
- 2020

A Hamiltonian and action principle formalism for deriving three-dimensional gyroviscous magnetohydrodynamic models is presented. The uniqueness of the approach in constructing the gyroviscous tensor…

Nonlinear helicons bearing multi-scale structures

- Physics
- 2017

The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here, we elucidate an intrinsic multi-scale property embodied by the combination of the…

Yet another modification of relativistic magnetohydrodynamic waves: Electron thermal inertia

- PhysicsPhysics Letters A
- 2022

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