Gravitational instability with Hall effect in a plasma

1968 ◽  
Vol 46 (22) ◽  
pp. 2553-2556 ◽  
Author(s):  
Amiya K. Sen ◽  
Chih Kang Chou
Keyword(s):  
Growth Rate ◽  
Hall Effect ◽  
Stability Problem ◽  
Hall Current ◽  
Gravitational Instability ◽  
Jeans Criterion ◽  
Gravitational Stability

It is shown that the new modes introduced by the inclusion of the Hall effect in the gravitational stability problem of a plasma are stable. However, an old mode (which is stable in the absence of a Hall current) becomes unstable. We conclude that the Hall current has a destabilizing effect and that the Jeans criterion for stability is adversely affected by its presence. However, the growth rate of the Hall instability is found to be negligible for any astrophysical system.

The Hall effect and Kelvin–Helmholtz instability in a plasma

1968 ◽  
Vol 46 (22) ◽  
pp. 2557-2561 ◽  
Author(s):  
Amiya K. Sen ◽  
Chih Kang Chou
Keyword(s):  
Growth Rate ◽  
Hall Effect ◽  
Upper Bound ◽  
Cyclotron Frequency ◽  
Hall Current ◽  
Unstable Mode ◽  
Helmholtz Instability ◽  
Helmholtz Problem ◽  
Ion Cyclotron ◽  
Ideal Plasma

It is shown that a new unstable mode due to the Hall effect appears in the Kelvin–Helmholtz problem in an ideal plasma. The instability appears whether or not the Kelvin–Helmholtz discontinuity is stable or unstable in the absence of a Hall current. An upper bound on the growth rate of the Hall instability is found to be of the order of the ion cyclotron frequency.

Jeans’ Gravitational Instability of a Thermally Conducting, Unbounded, Partially Ionized Plasma

2006 ◽  
Vol 61 (5-6) ◽  
pp. 275-280 ◽  
Author(s):  
Shaista Shaikh ◽  
Aiyub Khan ◽  
Prem Kumar Bhatia
Keyword(s):  
Growth Rate ◽  
Gravitational Instability ◽  
The Other ◽  
Wave Number ◽  
Finite Conductivity ◽  
Jeans Criterion ◽  
Partially Ionized ◽  
Thermally Conducting ◽  
Limiting Case ◽  
Oblique Magnetic Field

The gravitational instability of an infinitely extending homogenous, partially ionized plasma, permeated by an oblique magnetic field, has been studied to investigate the effects of Hall currents, finite conductivity, viscosity, collision with neutrals and thermal conductivity on the growth rate of the disturbance. The dispersion relation obtained has been solved numerically, and it has been found that Hall currents and collision with neutrals have a destabilizing influence on the growth rate while the other mechanisms reinforce the gravitational instability. Jeans’ criterion, derived within a purely hydrodynamic framework, has been rediscussed along a nonextensive kinetic theory. A new Jeans’ criterion was deduced, which depends on the nonextensive parameter q and the standard Jeans’ wave number is recovered in the limiting case q = 1

Combined Taylor and Helmholtz instability in hydromagnetics including Hall effect

1967 ◽  
Vol 1 (1) ◽  
pp. 145-155 ◽  
Author(s):  
S. P. Talwar ◽  
G. L. Kalra
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Hall Effect ◽  
Uniform Magnetic Field ◽  
Hall Current ◽  
Larmor Frequency ◽  
Larmor Radius ◽  
Helmholtz Instability ◽  
Unstable Configuration

The problem of combined Rayleigh—Taylor and Kelvin—Helmholtz instability for incompressible plasmas carrying a uniform magnetic field is investigated taking account of the Hall current. The resistivity and the finite ion Larmor radius effects are left out. It is found that the finite Larmor frequency is destabilizing in nature. The growth rate of an otherwise (without the Hall current) unstable configuration is increased, and unstable modes may be produced in otherwise stable situations for reasonably large values of the Hall current. The Hall effect also results in overstable modes.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

Effect of electron inertia on radiative instability of rotating two-component gaseous plasma

2012 ◽  
Vol 90 (12) ◽  
pp. 1209-1221 ◽  
Author(s):  
A.K. Patidar ◽  
R.K. Pensia ◽  
V. Shrivastava
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Growth Rate ◽  
Electrical Resistivity ◽  
Heat Loss ◽  
Loss Function ◽  
Mode Analysis ◽  
Electron Inertia ◽  
Radiative Instability ◽  
Jeans Criterion

The problem of radiative instability of homogeneous rotating partially ionized plasma incorporating viscosity, porosity, and electron inertia in the presence of a magnetic field is investigated. A general dispersion relation is obtained using normal mode analysis with the help of relevant linearized perturbation equations of the problem. The modified Jeans criterion of instability is obtained. The conditions of Jeans instabilities are discussed in the different cases of interest. It is found that the simultaneous effect of viscosity, rotation, finite conductivity, and porosity of the medium does not essentially change the Jeans criterion of instability. It is also found that the presence of arbitrary radiative heat-loss function and thermal conductivity modified the conditions of Jeans instability for longitudinal propagation. It is found that, for longitudinal propagation, the conditions of radiative instability are independent of magnetic field, viscosity, rotation, finite electrical resistivity, and electron inertia, but for the transverse mode of propagation it depends upon finite electrical resistivity and strength of magnetic field and is independent of viscosity, electron inertia, and rotation. From the curves we find that viscosity has a stabilizing effect on the growth rate of instability but the thermal conductivity and density-dependent heat-loss function has a destabilizing effect on the instability growth rate.

scholarly journals Current Percolation in Medium with Boundaries under Quantum Hall Effect Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
M. U. Malakeeva ◽  
V. E. Arkhincheev
Keyword(s):  
Finite Number ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Hall Current ◽  
Quantum Hall ◽  
Singular Points ◽  
Hall Conductivity

The current percolation has been considered in the medium with boundaries under quantum Hall effect conditions. It has been shown that in that case the effective Hall conductivity has a nonzero value due to percolation of the Hall current through the finite number of singular points (in our model these are corners at the phase joints).

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