Resistive MHD stagnation-point flows at a current sheet

1975 ◽  
Vol 14 (2) ◽  
pp. 283-294 ◽  
Author(s):  
B. U. Ö. Sonnerup ◽  
E. R. Priest
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Viscous Effects ◽  
Three Dimensional Flow ◽  
Merging Process ◽  
The Magnetic Field ◽  
A Current

A family of exact solutions to the MHD equations is presented for steady incompressible two- and three-dimensional flow in the vicinity of the stagnation point, which forms in a current sheet separating two colliding plasma streams. The magnetic field in each plasma is strictly parallel to the current sheet, but can have different magnitudes and directions. Resistive and viscous effects are accounted for. These flows are of considerable interest in connexion with the magnetic field merging process. They represent the limit of resistive field annihilation with zero reconnexion.

MHD stagnation-point flows at a current sheet including viscous and resistive effects: general two-dimensional solutions

1990 ◽  
Vol 44 (3) ◽  
pp. 525-546 ◽  
Author(s):  
T. D. Phan ◽  
B. U. Ö. Sonnerup
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Current Sheet ◽  
Stagnation Point ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Special Cases ◽  
The Magnetic Field ◽  
A Current

Exact solutions are presented of two-dimensional steady-state incompressible stagnation point flows at a current sheet separating two colliding plasmas. They describe the process of resistive field annihilation (zero reconnection) where the magnetic field in each plasma is strictly parallel to the current sheet, but may have different magnitudes and direction on its two sides. The flow in the (x, y) plane toward the current sheet, located at x = 0, may have an arbitrary angle of incidence and an arbitrary amount of divergence from or convergence towards the stagnation point. We find the most general form of the solution for the plasma velocity and for the magnetic field. For the z compenents of the flow and field, solutions in the form of truncating power series in y are found. The cases obtained in this study contain the solutions obtained by Parker, Sonnerup & Priest, Gratton et al. and Besser, Biernat & Rijnbeek as special cases. The role of viscosity in determining the flow and field configurations is examined. When the two colliding plasmas have the same viscosity and density, it is shown that viscous effects usually are important only in strongly divergent or convergent viscous flows with viscous Reynolds number of the order of unity or smaller. For astrophysical applications the viscous Reynolds number is usually high and the effects of viscosity on the interaction of plasmas of similar properties are small. The formulation of the stagnation-point flow problem involving plasmas of different properties is also presented. Sample cases of such flows are shown. Finally, a possible application of the results from this study to the earth's magnetopause is discussed briefly.

scholarly journals MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 132 ◽  
Author(s):  
Muhammad Sadiq
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Stagnation Point Flow ◽  
Three Dimensional Flow ◽  
Moving Plate ◽  
Physical Quantities ◽  
The Magnetic Field ◽  
Momentum Boundary Layer

In this article, an axisymmetric three-dimensional stagnation point flow of a nanofluid on a moving plate with different slip constants in two orthogonal directions in the presence of uniform magnetic field has been considered. The magnetic field is considered along the axis of the stagnation point flow. The governing Naiver–Stokes equation, along with the equations of nanofluid for three-dimensional flow, are modified using similarity transform, and reduced nonlinear coupled ordinary differential equations are solved numerically. It is observed that magnetic field M and slip parameter λ 1 increase the velocity and decrease the boundary layer thickness near the stagnation point. Also, a thermal boundary layer is achieved earlier than the momentum boundary layer, with the increase in thermophoresis parameter N t and Brownian motion parameter N b . Important physical quantities, such as skin friction, and Nusselt and Sherwood numbers, are also computed and discussed through graphs and tables.

Kelvin-Helmholtz and Rayleigh-Taylor Instability of Two Superimposed Magnetized Fluids with Suspended Dust Particles

2009 ◽  
Vol 64 (7-8) ◽  
pp. 455-466 ◽  
Author(s):  
Ramprasad Prajapati ◽  
Raj Kamal Sanghvi ◽  
Rajendra Kumar Chhajlani ◽  
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Particle Density ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Mode Analysis ◽  
Dust Particles ◽  
Suspended Dust ◽  
The Magnetic Field

AbstractThe effect of a magnetic field and suspended dust particles on both the Kelvin-Helmholtz (K-H) and the Rayleigh-Taylor (R-T) instability of two superimposed streaming magnetized plasmas is investigated. The magnetized fluids are assumed to be incompressible and flowing on top of each other. The usual magnetohydrodynamic (MHD) equations are considered with suspended dust particles. The basic equations of the problem are linearized and the dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The general dispersion relation is found to be modified due to the presence of the suspended dust particles and of the magnetic field. The effect of the magnetic field appears in the dispersion relation if three-dimensional perturbations of the system are considered. The general conditions of the K-H instability as well as the R-T instability are derived for the considered medium. The stability of the system for both cases is discussed by applying the Routh-Hurwitz criterion. Numerical analysis is performed to show the effect of various parameters on the growth rates of the K-H and R-T instabilities. Three different cases of the present configurations are considered and the conditions of instability are obtained. It is found that the conditions for the K-H and R-T instabilities depend on the magnetic field, on the suspended dust particles and on the relaxation frequency of the particles. The magnetic field and particle density have stabilizing influence, while the density difference between the fluids has a destabilizing influence on the growth rate of the K-H and R-T configurations.

Stability of static current sheets connecting plane magnetic null points

1999 ◽  
Vol 61 (4) ◽  
pp. 623-631
Author(s):  
MANUEL NÚÑEZ
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Lorentz Force ◽  
Critical Points ◽  
Null Point ◽  
The Other ◽  
Magnetic Null ◽  
Local Topology ◽  
The Magnetic Field ◽  
A Current

The configuration created in the plane by the separation of a magnetic hyperbolic null point into two critical points connected by a current sheet is considered. The main parameters are the orders of the zeros of these new null points, which determine the local topology of the magnetic field. It is shown that when the magnetic field is static, the fluid tends to flow orthogonally to the field in the vicinity of the sheet endpoints. Moreover, the Lorentz force pushes one of them towards the other, so the configuration tends to collapse again into a single null point except when the order of both is precisely ½.

The formation of magnetic singularities by time-dependent collapse of an X -type magnetic field

1995 ◽  
Vol 351 (1695) ◽  
pp. 1-37 ◽  
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Strong Magnetic Field ◽  
Field Approximation ◽  
Magnetic Potential ◽  
Time Dependent ◽  
Basic Solution ◽  
Variable Theory ◽  
The Magnetic Field ◽  
A Current

A self-consistent solution is presented for nonlinear time-dependent collapse of a two-dimensional X-type magnetic field to form a current sheet. A so-called ‘strong magnetic field approximation’ is adopted for highly sub-Alfvenic flow of an ideal low-beta plasma. To lowest order in the Alfven Mach number, the magnetic field evolves through a series of topologically accessible piece-wise potential states with the constraint that the acceleration be perpendicular to the magnetic field. A wide class of solutions is obtained using complex variable theory by assuming the magnetic potential is frozen to the plasma. The current sheet in the basic solution stretches along the x-axis from —/ t to +/ t , and regions of reversed current are found near the ends of the sheet. A current conservation theorem is proved, which states that the total current in the sheet is zero if it forms by collapse of an initially current-free X-point under the strong magnetic field approximation and with the magnetic potential frozen to the plasma. The basic solution is generalized to include other initial states and initial flows. A general numerical method for the evolution of magnetic fields under the strong magnetic field approximation is set up when the magnetic potential is not necessarily frozen to the plasma. This method is applied to an example of the formation of a current sheet with Y-type neutral points at its ends.

scholarly journals Meniscus of a Magnetic Fluid in the Field of a Current-Carrying Wire: Three-Dimensional Numerical Simulations

Materials ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 775
Author(s):  
Paul-Benjamin Eißman ◽  
Stefan Odenbach ◽  
Adrian Lange
Keyword(s):  
Magnetic Field ◽  
Magnetic Fluid ◽  
Material Properties ◽  
Three Dimensional ◽  
Applied Current ◽  
Great Strength ◽  
Magnetisation Curve ◽  
The Wire ◽  
The Magnetic Field ◽  
A Current

Three-dimensional calculations of the meniscus of a magnetic fluid placed around a current carrying vertical and cylindrical wire are presented. Based on the material properties of experimentally used magnetic fluids, the numerically determined menisci are compared with the experimentally measured ones reported by May. The comparison is made for a linear law of magnetisation as well as for the experimentally measured nonlinear magnetisation curve. Up to moderate strengths of the applied current ( I < = 45 A), i.e., up to moderate strengths of the magnetic field close to the wire, the calculated profiles agree satisfyingly with the experimentally measured ones for a linear as well as for a nonlinear law of magnetisation. At a great strength of the applied current ( I = 70 A), i.e., at a large strength of the magnetic field close to the wire, the agreement is less good than in the range up to moderate strengths. Our analysis revealed that the numerically assumed isothermal conditions are not present in the experiment, particularly at the great strength of the applied current. A control of the temperature in the experiment and the implementation of a coupled thermal model in the numerics are considered the most relevant future steps for an improved agreement.

scholarly journals New data-driven method of simulating coronal mass ejections

2019 ◽  
Vol 626 ◽  
pp. A91 ◽  
Author(s):  
Cheng’ao Liu ◽  
Tao Chen ◽  
Xinhua Zhao
Keyword(s):  
Magnetic Field ◽  
Coronal Mass Ejections ◽  
Three Dimensional ◽  
Flux Rope ◽  
Mhd Equations ◽  
Data Driven ◽  
Flux Emergence ◽  
Polarity Inversion ◽  
Polarity Inversion Line ◽  
The Magnetic Field

Context. Coronal mass ejections (CMEs) are large eruptions of plasma and magnetic field from the Sun’s corona. Understanding the evolution of the CME is important to evaluate its impact on space weather. Using numerical simulation, we are able to reproduce the occurrence and evolution process of the CME. Aims. The aim of this paper is to provide a new data-driven method to mimic the coronal mass ejections. By using this method, we can investigate the phsical mechanisms of the flux rope formation and the cause of the CME eruption near the real background. Methods. Starting from a potential magnetic field extrapolation, we have solved a full set of magnetohydrodynamic (MHD) equations by using the conservation element and solution element (CESE) numerical method. The bottom boundary is driven by the vector magnetograms obtained from SDO/HMI and vector velocity maps derived from DAVE4VM method. Results. We present a three-dimensional numerical MHD data-driven model for the simulation of the CME that occurred on 2015 June 22 in the active region NOAA 12371. The numerical results show two elbow-shaped loops formed above the polarity inversion line (PIL), which is similar to the tether-cutting picture previously proposed. The temporal evolutions of magnetic flux show that the sunspots underwent cancellation and flux emergence. The signature of velocity field derived from the tracked magnetograms indicates the persistent shear and converging motions along the PIL. The simulation shows that two elbow-shaped loops were reconnected and formed an inverse S-shaped sigmoid, suggesting the occurrence of the tether-cutting reconnection, which was supported by observations of the Atmospheric Imaging Assembly (AIA) telescope. Analysis of the decline rate of the magnetic field indicates that the flux rope reached a region where the torus instability was triggered. Conclusions. We conclude that the eruption of this CME was caused by multiple factors, such as photosphere motions, reconnection, and torus instability. Moreover, our simulation successfully reproduced the three-component structures of typical CMEs.

scholarly journals Analysis of Injected Electron Beam Propagation in a Planar Crossed-Field Gap

2021 ◽  
Vol 11 (6) ◽  
pp. 2540
Author(s):  
Ranajoy Bhattacharya ◽  
Adam M. Darr ◽  
Allen L. Garner ◽  
Jim Browning
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Critical Current Density ◽  
Critical Current ◽  
Current Density ◽  
Three Dimensional ◽  
One Dimensional ◽  
Field Device ◽  
The Magnetic Field ◽  
A Current

This paper examines basic crossed-field device physics in a planar configuration, specifically electron beam perturbation and instability as a function of variation in magnetic field, and angle between magnetic and electric field. We perform a three-dimensional (3-D) simulation of electron perturbation in a planar crossed-field system using the full 3-D particle trajectory solver in CST Particle Studio (CST-PS). The structure has a length, height, width and anode-sole gap of 15 cm, 2 cm, 10 cm, and 2 cm, respectively. The anode to sole voltage is fixed at 3 kV, and the magnetic field and injected current varied from 0.01 T to 0.05 T and 1.5 mA to 1 A, respectively. The simulations show that applying a magnetic field of 0.05 T makes the beam stable for a critical current density of 94 mA/cm2 for an anode-sole gap of 20 mm. Above this current density, the beam was unstable, as predicted. Introducing a 1° tilt in the magnetic field destabilizes the beam at a current density of 23 mA/cm2, which is lower than the critical current density for no tilt, as predicted by our theory. The simulation results also agree well with prior one-dimensional (1-D) theory and simulations that predict stable bands of current density for a 5° tilt where the beam is stable at low current density (<13.3 mA/cm2), unstable above this threshold, and then stable again at higher current density, (>33 mA/cm2).

Reduced MHD in nearly potential magnetic fields

1997 ◽  
Vol 57 (1) ◽  
pp. 83-87 ◽  
Author(s):  
H. R. STRAUSS
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Potential Field ◽  
Three Dimensional ◽  
Pressure Effects ◽  
Mhd Equations ◽  
Dimensional Structure ◽  
Three Dimensional Structure ◽  
The Magnetic Field

Reduced, approximate MHD equations are derived for the case where the magnetic field is close to a potential field. The potential field can have an arbitrary three-dimensional structure, as long as it is non-vanishing. Finite current and pressure effects are included.

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