# Three-dimensional nonlinear ideal MHD equilibria with field-aligned incompressible and compressible flows

## Abstract

The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.

- Authors:

- Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef (Egypt)

- Publication Date:

- OSTI Identifier:
- 22599977

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AXIAL SYMMETRY; COMPRESSIBLE FLOW; CONFINEMENT; DENSITY; EQUATIONS; EQUILIBRIUM; EXACT SOLUTIONS; INCOMPRESSIBLE FLOW; LIMITING VALUES; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; PLASMA; STEADY-STATE CONDITIONS; THREE-DIMENSIONAL CALCULATIONS; VELOCITY

### Citation Formats

```
Moawad, S. M., E-mail: smmoawad@hotmail.com, and Ibrahim, D. A..
```*Three-dimensional nonlinear ideal MHD equilibria with field-aligned incompressible and compressible flows*. United States: N. p., 2016.
Web. doi:10.1063/1.4960043.

```
Moawad, S. M., E-mail: smmoawad@hotmail.com, & Ibrahim, D. A..
```*Three-dimensional nonlinear ideal MHD equilibria with field-aligned incompressible and compressible flows*. United States. doi:10.1063/1.4960043.

```
Moawad, S. M., E-mail: smmoawad@hotmail.com, and Ibrahim, D. A.. Mon .
"Three-dimensional nonlinear ideal MHD equilibria with field-aligned incompressible and compressible flows". United States.
doi:10.1063/1.4960043.
```

```
@article{osti_22599977,
```

title = {Three-dimensional nonlinear ideal MHD equilibria with field-aligned incompressible and compressible flows},

author = {Moawad, S. M., E-mail: smmoawad@hotmail.com and Ibrahim, D. A.},

abstractNote = {The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.},

doi = {10.1063/1.4960043},

journal = {Physics of Plasmas},

number = 8,

volume = 23,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}