We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein’s equations for the gravitational field, and the equations of relativistic MHD for a perfectly conducting ideal gas. The adopted form of the equations is suitable for evolving numerically a relativistic M...

It is proved that irrespective of compressibility tokamak steady states with purely poloidal mass flow can not exist in the framework of either magnetohydrodynamics (MHD) or Hall MHD models. Non-existence persists within single fluid plasma models with pressure anisotropy and incompressible flows.

An optimal control problem for the equations governing the stationary problem of magnetohydrodynamics (MHD) is considered. Control mechanisms by external and injected currents and magnetic fields are treated. An optimal control problem is formulated. First order necessary and second order sufficient conditions are developed. An operator splitting scheme for the numerical solution of the MHD sta...

The preceding chapter discussed the microscopic, kinetic and two-fluid decsriptions of a plasma. But we would actually like a simpler model — one that would include most of the macroscopic properties of a plasma in a “one-fluid” model. The simplest such model is magnetohydrodynamics (MHD), which is a combination of a one-fluid (hydrodynamic-type plus Lorentz force effects) model for the plasma ...

In this article, a laminar magnetohydrodynamics (MHD) developing flow of an incompressible electrically conducting fluid subjected to an external magnetic field is considered. The aim of the study is to propose a correlation for computing the development length of the laminar MHD developing flow in a pipe. A numerical approach is considered to solve the problem. In the first step, the numerical...

We study the three-dimensional (3D) regularized magnetohydrodynamics (MHD) equations. Using the method of splitting of the asymptotic approximate solutions into higher and lower Fourier components, we prove that the global attractor of the 3D regularized MHD equations consists of real analytic functions, whenever the forcing terms are analytic.

The lowest-order description of a magnetized plasma is given by magnetohydrodynamics (MHD). However, many astrophysical plasmas (as well as some laboratory plasmas) are relativistic, in that either the thermal speed or the fluid flow speed approaches the speed of light, and conventional MHD is not consistent with special relativity. Beginning with exact laws of motion, this work derives a gener...

Lagrangian symmetries and concomitant generalized Bianchi identities associated with the relabeling of fluid elements are found for hydrodynamics and magnetohydrodynamics (MHD). In hydrodynamics, relabeling results in Ertel's theorem of conservation of potential vorticity, while in MHD it yields the conservation of cross helicity. The symmetries of the reduction from Lagrangian (material) to Eu...

An optimal control problem for the equations governing the stationary problem of magnetohydrodynamics (MHD) is considered. Control mechanisms by external and injected currents and magnetic fields are treated. Motivated by practical applications, an optimal control problem is formulated. First order necessary and second order sufficient conditions are developed. An operator splitting scheme for ...

Article history: Received 2 November 2014 Accepted 5 December 2014 Available online 9 December 2014 Communicated by F. Porcelli A version of extended magnetohydrodynamics (MHD) that incorporates electron inertia is obtained by constructing an action principle. Unlike MHD which freezes in magnetic flux, the present theory freezes in an alternative flux related to the electron canonical momentum....