Exact solutions of magnetohydrodynamic equations for fluids in a circular magnetic field

1988 ◽  
Vol 31 (4) ◽  
pp. 887 ◽  
Author(s):  
Tomikazu Namikawa ◽  
Hiromitsu Hamabata
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Magnetohydrodynamic Equations ◽  
Circular Magnetic Field

A New Derivation of Exact Solutions for Incompressible Magnetohydrodynamic Plasma Turbulence

2021 ◽  
Vol 10 (1) ◽  
pp. 98-105
Author(s):  
Adel M. Morad ◽  
S. M. A. Maize ◽  
A. A. Nowaya ◽  
Y. S. Rammah
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Exact Solutions ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equation ◽  
Reductive Perturbation Method ◽  
Constant Density ◽  
Magnetohydrodynamic Equations ◽  
Nls Equation ◽  
Ansatz Method

The objective of this paper is to study the propagation of nonlinear, quasi-parallel, magnetohydrodynamic waves of small-amplitude in a cold Hall plasma of constant density. Magnetohydrodynamic equations, along with the cold plasma were expanded using the reductive perturbation method, which leads to a nonlinear partial differential equation that complies with a modified form of the derivative nonlinear evolution Schrödinger equation. Exact solutions of the turbulent magnetohydrodynamic model in plasma were formulated for the physical quantities that describe the problem completely by using the complex ansatz method. In addition, the complete set of equations was used taking into account the magnetic field, which can be considered to be constant in the x-direction to create stable vortex waves. Vortex solutions of the modified nonlinear Schrödinger equation (MNLS) were compared with the solutions of incompressible magnetohydrodynamic equations. The obtained equations differ from the standard NLS equation by one additional term that describes the interaction of the nonlinear waves with the constant density. The behavior of both the velocity profile and the waveform of pressure were studied. The results showed that there are clear disturbances in the identity of the velocity and thus pressure. The identity of both velocity and pressure results from that a magnetic field is formed.

Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a non-uniform magnetic field

1989 ◽  
Vol 42 (2) ◽  
pp. 247-256 ◽  
Author(s):  
Hiromitsu Hamabata ◽  
Tomikazu Namikawa
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Uniform Magnetic Field ◽  
Magnetohydrodynamic Equations ◽  
Wave Solutions ◽  
Laboratory Plasmas ◽  
Special Cases ◽  
Circular Magnetic Field ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Nonlinear Wave Solutions

Exact wave solutions of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within an axisymmetric container are obtained. It is shown that there are four types of exact wave solutions with large amplitude in a non-uniform magnetic field. These solutions are very useful because they can be expressed in terms of arbitrary scalar functions and they are applicable to astrophysical and laboratory plasmas as well as the earth's core. The solutions also include as special cases the nonlinear Alfvén waves in a uniform magnetic field and in a circular magnetic field found respectively by Walén (1944) and by Namikawa & Hamabata (1987, 1988).

Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a sheared magnetic field

1990 ◽  
Vol 44 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Hiromitsu Hamabata
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Large Amplitude ◽  
Uniform Magnetic Field ◽  
Magnetohydrodynamic Equations ◽  
Wave Solutions ◽  
Field Lines ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Physical Quantities ◽  
Nonlinear Wave Solutions

Exact wave solutions of the nonlinear jnagnetohydrodynamic equations for a highly conducting incompressible fluid are obtained for the cases where the physical quantities are independent of one Cartesian co-ordina.te and for where they vary three-dimensionally but both the streamlines and magnetic field lines lie in parallel planes. It is shown that there is a class of exact wave solutions with large amplitude propagating in a straight but non-uniform magnetic field with constant or non-uniform velocity.

Solving Magnetohydrodynamic Equations Without Special Treatment for Divergence-Free Magnetic Field

AIAA Journal ◽  
2004 ◽  
Vol 42 (12) ◽  
pp. 2605-2608 ◽  
Author(s):  
Moujin Zhang ◽  
S.-T. John Yu ◽  
Shang-Chuen Lin ◽  
Sin-Chung Chang ◽  
Isaiah Blankson
Keyword(s):  
Magnetic Field ◽  
Special Treatment ◽  
Magnetohydrodynamic Equations ◽  
Divergence Free

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

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