scholarly journals Hot Accretion Flow in Two-Dimensional Spherical Coordinates: Considering Pressure Anisotropy and Magnetic Field

Universe ◽  
2019 ◽  
Vol 5 (9) ◽  
pp. 197
Author(s):  
Hui-Hong Deng ◽  
De-Fu Bu
Keyword(s):  
Magnetic Field ◽  
Mhd Equations ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Strong Wind ◽  
Two Dimensional ◽  
Spherical Coordinates ◽  
Gas Temperature ◽  
Accretion Flow ◽  
Anisotropic Stress

For systems with extremely low accretion rate, such as Galactic Center Sgr A* and M87 galaxy, the ion collisional mean free path can be considerably larger than its Larmor radius. In this case, the gas pressure is anisotropic to magnetic field lines. In this paper, we pay attention to how the properties of outflow change with the strength of anisotropic pressure and the magnetic field. We use an anisotropic viscosity to model the anisotropic pressure. We solve the two-dimensional magnetohydrodynamic (MHD) equations in spherical coordinates and assume that the accretion flow is radially self-similar. We find that the work done by anisotropic pressure can heat the accretion flow. The gas temperature is heightened when anisotropic stress is included. The outflow velocity increases with the enhancement of strength of the anisotropic force. The Bernoulli parameter does not change much when anisotropic pressure is involved. However, we find that the energy flux of outflow can be increased by a factor of 20 in the presence of anisotropic stress. We find strong wind (the mass outflow is about 70% of the mass inflow rate) is formed when a relatively strong magnetic field is present. Outflows from an active galactic nucleus can interact with gas in its host galaxies. Our result predicts that outflow feedback effects can be enhanced significantly when anisotropic pressure and a relatively powerful magnetic field is considered.

A mechanism for Taylor relaxation in Z-pinches. Part 1. Dynamo mechanism

1986 ◽  
Vol 35 (2) ◽  
pp. 295-310 ◽  
Author(s):  
S. K. H. Auluck
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
Axial Magnetic Field ◽  
Positive Definite ◽  
Low Energy ◽  
Toroidal Field ◽  
Mhd Equations ◽  
Larmor Radius ◽  
Electron Mass ◽  
Dynamo Mechanism

The dynamo mechanism in an RFP is explained on the basis of new terms in the MHD equations which are proportional to the electron mass and are traditionally neglected. A new azimuthal dynamo current is obtained which is shown to be positive definite. Sustained, spontaneous self-reversal of the toroidal field naturally follows from this. The (F, Θ) curve calculated from this theory under certain assumptions agrees well with experimental data. The theory predicts the presence of large-Larmor-radius particles in the RFP. It also predicts a spontaneous axial magnetic field in linear Z-pinches. Preliminary experiments on low-energy Z-pinches corroborate this prediction.

scholarly journals Gravitational instability on propagation of MHD waves in astrophysical plasma

2013 ◽  
Vol 79 (5) ◽  
pp. 805-816 ◽  
Author(s):  
ALEMAYEHU MENGESHA CHERKOS ◽  
S. B. TESSEMA
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Gravitational Instability ◽  
Mhd Equations ◽  
Mhd Waves ◽  
Anisotropic Pressure ◽  
Heat Conducting ◽  
Magnetic Field Direction ◽  
Pressure Tensor ◽  
Astrophysical Plasma

AbstractWe determine the general dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in astrophysical plasma by considering the effect of gravitational instability and viscosity with anisotropic pressure tensor and heat-conducting plasma. Basic MHD equations have been derived and linearized by the method of perturbation to develop the general form of dispersion relation equation. Our result indicates that the transverse propagation of waves in such a plasma is affected by the inclusion of heat conduction. For wave propagation, parallel to the magnetic field direction, we find that the fairhose mode is unaffected, whereas the mode corresponding to the gravitational instability is modified in astrophysical plasma with anisotropic pressure tensor being stable in the presence of viscosity and strong magnetic field at considerable wavelength.

POYNTING FLUX DOMINATED ACCRETION FLOW: A TWO-DIMENSIONAL MODEL

2006 ◽  
Vol 21 (03) ◽  
pp. 181-196
Author(s):  
HYUN KYU LEE
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Accretion Disk ◽  
Magnetic Surface ◽  
Energy Tensor ◽  
Two Dimensional ◽  
Accretion Flow ◽  
Poynting Flux ◽  
Stress Energy ◽  
The Magnetic Field

The dynamics of the accretion flow onto a black hole driven by Poynting flux is discussed in a simplified model of a two-dimensional accretion disk on equatorial plane. In an axisymmetric, stationary and force-free magnetosphere, the accretion flow is described by the three accretion equations obtained from the conservation of stress–energy tensor and one stream equation for a force-free magnetosphere. It is found that the angular velocity of the magnetic surface can be obtained by the dynamics of the accreting matter, [Formula: see text]. The effect of the magnetic field on the accretion flow is discussed in detail using the paraboloidal type configuration suggested by Blandford in 1976. In numerical analysis, it is demonstrated that the angular velocity of the disk, ΩD, deviates from the Keplerian angular velocity and the dynamics of the accretion disk is found to depend strongly on the ratio of the accretion rate to the magnetic field strength.

On the stability of the screw pinch in the CGL model

1976 ◽  
Vol 16 (3) ◽  
pp. 261-283 ◽  
Author(s):  
Krishna M. Srivastava ◽  
F. Waelbroeck
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Finite Larmor Radius ◽  
Main Column ◽  
First Order Correction ◽  
The Stability ◽  
The Magnetic Field ◽  
Ideal Plasma

We have investigated the stability of the screw pinch with the help of the double adiabatic (CGL) equations including the finite Larmor radius effects through the anisotropic pressure tensor. The calculations are approximate, with FLR treated as a first-order correction to the ideal plasma equations. The dispersion relation has been solved for various values of R2 = p∥/p⊥ and α for the rale and imaginary part of the frequency (ω = ωR ± iωI) in three particular cases: (a) μ = 0, the θ-pinch, (b) μ = ∞, the Z-pinch, (c) μ = -α/m, field distubances parallel to the equilibrium field. Here μ is the pitch of the magnetic field in the pressureless plasma surrounding the main column, α is the wave number, m is the azimuthal number, p∥ and p⊥ are plasma pressures along and perpendicular to the magnetic field.

scholarly journals Effect of viscosity on propagation of MHD waves in astrophysical plasma

2013 ◽  
Vol 79 (5) ◽  
pp. 535-544 ◽  
Author(s):  
ALEMAYEHU MENGESHA ◽  
S. B. TESSEMA
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Strong Magnetic Field ◽  
Mhd Equations ◽  
Mhd Waves ◽  
Anisotropic Pressure ◽  
Pressure Tensor ◽  
Astrophysical Plasma ◽  
General Dispersion

AbstractWe determine the general dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in an astrophysical plasma by considering the effect of viscosity with an anisotropic pressure tensor. Basic MHD equations have been derived and linearized by the method of perturbation to develop the general form of the dispersion relation equation. Our result indicates that an astrophysical plasma with an anisotropic pressure tensor is stable in the presence of viscosity and a strong magnetic field at considerable wavelength.

scholarly journals On Liouville-type theorems for the 2D stationary MHD equations

Nonlinearity ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 870-888
Author(s):  
Nicola De Nitti ◽  
Francis Hounkpe ◽  
Simon Schulz
Keyword(s):  
Magnetic Field ◽  
Maximum Principle ◽  
Diffusion Equation ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Drift Diffusion ◽  
Liouville Type ◽  
Dirichlet Integral ◽  
Liouville Type Theorems ◽  
The Magnetic Field

Abstract We establish new Liouville-type theorems for the two-dimensional stationary magneto-hydrodynamic incompressible system assuming that the velocity and magnetic field have bounded Dirichlet integral. The key tool in our proof is observing that the stream function associated to the magnetic field satisfies a simple drift–diffusion equation for which a maximum principle is available.

Magnetogravitational instability of a rotating anisotropic plasma with finite-ion-Larmor-radius corrections and generalized polytropic laws

1998 ◽  
Vol 60 (4) ◽  
pp. 673-694 ◽  
Author(s):  
G. D. SONI ◽  
R. K. CHHAJLANI
Keyword(s):  
Magnetic Field ◽  
Electrical Resistivity ◽  
Dispersion Relation ◽  
Normal Mode Analysis ◽  
Transverse Mode ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Axis Of Rotation ◽  
The Magnetic Field

The gravitational instability of an infinite homogeneous, finitely conducting, rotating, collisionless, anisotropic-pressure plasma in the presence of a uniform magnetic field with finite-ion-Larmor-radius (FLR) corrections and generalized polytropic laws is investigated. The polytropic laws are considered for the pressure components in directions parallel and perpendicular to the magnetic field. The method of normal-mode analysis is applied to derive the dispersion relation. Wave propagation is considered for both parallel and perpendicular axes of rotation. Longitudinal and transverse modes of propagation are discussed separately. The effects of rotation, finite electrical resistivity, FLR corrections and polytropic indices on the gravitational, firehose and mirror instabilities are discussed. The stability of the system is discussed by applying the Routh–Hurwitz criterion. Extensive numerical treatment of the dispersion relation leads to several interesting results. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, it is observed that rotation stabilizes the system by decreasing the critical Jeans wavenumber. It is also seen that the region of instability and the value of the critical Jeans wavenumber are larger for the Chew–Goldberger–Low (CGL) set of equations in comparison with the magnetohydrodynamic (MHD) set of equations. It is found that the effect of FLR corrections is significant only in the low-wavelength range, and produces a stabilizing influence. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, the finite electrical resistivity removes the polytropic index [nu] from the condition for instability. The inclusion of rotation alone or FLR corrections alone or both together does not affect the condition for mirror instability. The growth rate of the mirror instability is modified owing to uniform rotation or FLR corrections or both together. We note that the condition of mirror instability depends upon the polytropic indices. We also note that neither the mirror instability nor the firehose instability can be observed for the isotropic MHD set of equations.

scholarly journals The Spontaneous Reconnection of Force Free Magnetic Field

1993 ◽  
Vol 141 ◽  
pp. 450-453
Author(s):  
Li Xing ◽  
Y.Q. Hu
Keyword(s):  
Magnetic Field ◽  
Solar Atmosphere ◽  
Potential Field ◽  
Solar Physics ◽  
Free Field ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Compressible Mhd Equations ◽  
Scientific Significance ◽  
Force Free Field

AbstractTwo dimensional, three components compressible MHD equations are solved with multistep implicit scheme. The spontaneous reconnection of current sheets with force free field background is simulated. In comparison with the case where the background is potential field, a great difference is found. Our conclusion is that the force free magnetic field can accelerate reconnection. It may have important scientific significance to solar physics, for force free field is widely present in solar atmosphere.

Self-gravitational instability of dense degenerate viscous anisotropic plasma with rotation

2017 ◽  
Vol 83 (6) ◽  
Author(s):  
Prerana Sharma ◽  
Archana Patidar
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Instability Criterion ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Degenerate Plasma ◽  
Finite Larmor Radius ◽  
Quantum Parameter ◽  
Longitudinal Modes ◽  
The Magnetic Field

The influence of finite Larmor radius correction, tensor viscosity and uniform rotation on self-gravitational and firehose instabilities is discussed in the framework of the quantum magnetohydrodynamic and Chew–Goldberger–Low (CGL) fluid models. The general dispersion relation is obtained for transverse and longitudinal modes of propagation. In both the modes of propagation the dispersion relation is further analysed with respect to the direction of the rotational axis. In the analytical discussion the axis of rotation is considered in parallel and in the perpendicular direction to the magnetic field. (i) In the transverse mode of propagation, when rotation is parallel to the direction of the magnetic field, the Jeans instability criterion is affected by the rotation, finite Larmor radius (FLR) and quantum parameter but remains unaffected due to the presence of tensor viscosity. The calculated critical Jeans masses for rotating and non-rotating dense degenerate plasma systems are$3.5M_{\odot }$and$2.1M_{\odot }$respectively. It is clear that the presence of rotation enhances the threshold mass of the considered system. (ii) In the case of longitudinal mode of propagation when rotation is parallel to the direction of the magnetic field, Alfvén and viscous self-gravitating modes are obtained. The Alfvén mode is modified by FLR corrections and rotation. The analytical as well as graphical results show that the presence of FLR and rotation play significant roles in stabilizing the growth rate of the firehose instability by suppressing the parallel anisotropic pressure. The viscous self-gravitating mode is significantly affected by tensor viscosity, anisotropic pressure and the quantum parameter while it remains free from rotation and FLR corrections. When the direction of rotation is perpendicular to the magnetic field, the rotation of the considered system coupled the Alfvén and viscous self-gravitating modes to each other. The finding of the present work is applicable to strongly magnetized dense degenerate plasma.

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