scholarly journals Semi-hyperbolic patches of solutions to the two-dimensional compressible magnetohydrodynamic equations

2019 ◽  
Vol 18 (2) ◽  
pp. 943-958 ◽  
Author(s):  
Jianjun Chen ◽  
◽  
Geng Lai ◽  
Keyword(s):  
Two Dimensional ◽  
Magnetohydrodynamic Equations

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.

Excitation and damping of disturbances in cylindrical coronal loops

2005 ◽  
Vol 364 (1839) ◽  
pp. 547-550 ◽  
Author(s):  
Jaume Terradas ◽  
Ramón Oliver ◽  
José Luis Ballester
Keyword(s):  
Boundary Layer ◽  
Coronal Loop ◽  
Normal Mode Analysis ◽  
Resonant Absorption ◽  
Time Dependent ◽  
Mode Analysis ◽  
Coronal Loops ◽  
Two Dimensional ◽  
Magnetohydrodynamic Equations ◽  
Kink Mode

The excitation and damping of transversal coronal loop oscillations is studied using one-and two-dimensional models of line-tied cylindrical loops. By solving the time-dependent magnetohydrodynamic equations it is shown how an initial disturbance generated in the solar corona induces kink mode oscillations. We investigate the effect of the disturbance on a loop with a non-uniform boundary layer. In particular, a strong damping of transversal oscillations due to resonant absorption is found, such as predicted by previous works based on normal mode analysis.

Basis of the quasi-steady plasma accelerator theory in the presence of a longitudinal magnetic field

2008 ◽  
Vol 74 (2) ◽  
pp. 261-286 ◽  
Author(s):  
ANDREY N. KOZLOV
Keyword(s):  
Magnetic Field ◽  
Longitudinal Magnetic Field ◽  
Plasma Accelerator ◽  
Two Dimensional ◽  
Magnetohydrodynamic Equations ◽  
Plasma Flows ◽  
Azimuthal Magnetic Field ◽  
Transonic Flows ◽  
Accelerator Channel ◽  
Numerical Approaches

AbstractThe analytic and numerical approaches to the investigation of the two-dimensional steady-state plasma flows are analyzed and compared with reference to a plasma accelerator channel in the presence of a longitudinal magnetic field. The present study continues a cycle of research into the plasma flows in the coaxial channels with the traditional azimuthal magnetic field. The additional longitudinal field opens new possibilities for controlling the dynamic processes and achieving the transonic flows. The research is based on the magnetohydrodynamic equations.

scholarly journals Asymptotic Shallow Models Arising in Magnetohydrodynamics

Water Waves ◽  
2021 ◽  
Author(s):  
Diego Alonso-Orán
Keyword(s):  
Free Boundary ◽  
Water Waves ◽  
Large Scale ◽  
Three Dimensional ◽  
Magnetic Pressure ◽  
Two Dimensional ◽  
Magnetohydrodynamic Equations ◽  
Astrophysical Plasma ◽  
Asymptotic Models ◽  
Boundary Plasma

AbstractIn this paper, we derive new shallow asymptotic models for the free boundary plasma-vacuum problem governed by the magnetohydrodynamic equations which are vital when describing large-scale processes in flows of astrophysical plasma. More precisely, we present the magnetic analogue of the 2D Green–Naghdi equations for water waves under a weak magnetic pressure assumption in the presence of weakly sheared vorticity and magnetic currents. Our method is inspired by ideas for hydrodynamic flows developed in Castro and Lannes (2014) to reduce the three-dimensional dynamics of the vorticity and current to a finite cascade of two dimensional equations which can be closed at the precision of the model.

scholarly journals Weak-Strong Uniqueness for Compressible Magnetohydrodynamic Equations with Coulomb Force

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Lianhua He ◽  
Yonghui Zhou
Keyword(s):  
Relative Entropy ◽  
Coulomb Force ◽  
Two Dimensional ◽  
Strong Uniqueness ◽  
Magnetohydrodynamic Equations ◽  
Uniqueness Property ◽  
Magnetohydrodynamic System

In this paper, we consider the two-dimensional compressible magnetohydrodynamic system with Coulomb force. We apply the method of relative entropy to establish the weak-strong uniqueness property of this system.

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