Structure and computation of two-dimensional incompressible extended MHD

  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},
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… 

Figures from this paper

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


Hamiltonian formulation and analysis of a collisionless fluid reconnection model
The Hamiltonian formulation of a plasma four-field fluid model that describes collisionless reconnection is presented. The formulation is noncanonical with a corresponding Lie–Poisson bracket. The
Derivation of the Hall and Extended Magnetohydrodynamics Brackets
There are several plasma models intermediate in complexity between ideal magnetohydrodynamics (MHD) and two-fluid theory, with Hall and Extended MHD being two important examples. In this paper we
Hamiltonian four-field model for magnetic reconnection: nonlinear dynamics and extension to three dimensions with externally applied fields
The nonlinear dynamics of a two-dimensional (2D) model for collisionless magnetic reconnection is investigated both numerically and analytically. For very low values of the plasma β, parallel
Electron parallel compressibility in the nonlinear development of two-dimensional collisionless magnetohydrodynamic reconnection
Some topological aspects of the magnetic reconnection phenomenon are summarized and recent numerical results, derived within a two-fluid model, of two-dimensional collisionless magnetic reconnection
Generalized two-fluid theory of nonlinear magnetic structures
A system of equations is introduced and discussed that describe the nonlinear dynamics of magnetic perturbations in a magnetized, high‐temperature plasma. Diamagnetism, ion gyroradii effects, and
A Hamiltonian five-field gyrofluid model
A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the
Nonlinear, three‐dimensional magnetohydrodynamics of noncircular tokamaks
Rosenbluth’s nonlinear, approximate tokamak equations of motion are generalized to three dimensions. The equations describe magnetohydrodynamics in the low β, incompressible, large aspect ratio
A four‐field model for tokamak plasma dynamics
A generalization of reduced magnetohydrodynamics is constructed from moments of the Fokker–Planck equation. The new model uses familiar aspect‐ratio approximations but allows for (i) evolution as
On the structure and statistical theory of turbulence of extended magnetohydrodynamics
Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the