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

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.

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.

Stability of a stratified partially ionized plasma in a vertical magnetic field

1978 ◽  
Vol 19 (1) ◽  
pp. 183-191 ◽  
Author(s):  
S. L. Maheshwari ◽  
P. K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Growth Rate ◽  
The Other ◽  
Conducting System ◽  
Vertical Magnetic Field ◽  
One Dimensional ◽  
Finite Electrical Conductivity ◽  
Partially Ionized ◽  
The Stability

The dynamic stability of a stratified layer of partially ionized compressible plasma is discussed to investigate the effects of finite electrical conductivity and ion viscosity. The prevailing magnetic field is assumed to be uniform and vertical. For a semi-infinite plasma having a one-dimensional exponential density gradient along the vertical, the dispersion relation has been obtained by variational methods. It is found that the ion viscosity and ion–neutral collisions, whether included jointly or separately, do not change the stability criterion of the perfectly conducting system. Their inclusion, however, has a tendency to reduce the growth rate of the unstable perturbations showing that they have a stabilizing influence. On the other hand the inclusion of the effects of finite resistivity and compressibility of the medium is found to be destabilizing as the wavenumber range over which the plasma would otherwise be stable, becomes unstable.

scholarly journals Gravitational Instability of Rotating Viscoelastic Partially Ionized Plasma in the Presence of an Oblique Magnetic Field and Hall Current

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
M. F. El-Sayed ◽  
R. A. Mohamed
Keyword(s):  
Magnetic Field ◽  
Electrical Resistivity ◽  
Hall Current ◽  
Gravitational Instability ◽  
Angular Frequency ◽  
Physical Parameters ◽  
Physical Effects ◽  
Partially Ionized ◽  
The Magnetic Field ◽  
Oblique Magnetic Field

The gravitational instability of a rotating Walters B′ viscoelastic partially ionized plasma permeated by an oblique magnetic field has been investigated in the presence of the effects of Hall currents, electrical resistivity, and ion viscosity. The dispersion relation and numerical calculations have been performed to obtain the dependence of the growth rate of the gravitational unstable mode on the various physical effects. It is found that viscosity and collision frequency of plasma have stabilizing effects, while viscoelasticity and angular frequency of rotation have destabilizing effect; the electrical resistivity has a destabilizing effect only for small wavenumbers; the density of neutral particles and the magnetic field component in z-direction have stabilizing effects for wavenumbers ranges k<5 and k<10, respectively; the Hall current has a slightly destabilizing effect. Finally, the inclination angle to z-direction has a destabilizing effect to all physical parameters.

Growth and Performance of Agriculture Sector in India

2015 ◽  
Vol 3 (2) ◽  
Author(s):  
Naresh Singla ◽  
Mamandeep Kaur
Keyword(s):  
Growth Rate ◽  
Capital Formation ◽  
The Other ◽  
Agricultural Credit ◽  
Agricultural Growth ◽  
Indian Economy ◽  
Agriculture Sector ◽  
Food Grain ◽  
And Performance ◽  
Agricultural Labourers

The growth of agriculture and allied sectors is critical for the Indian economy as about 49 percent of the population is directly or indirectly dependent on agriculture. During the last decade and so, the agriculture sector has undergone profound changes resulting in sharp deceleration in its growth. The study has attempted to analyze growth and performance of the agriculture sector in India since 1980-81 and tries to comprehend some of the factors responsible for the deceleration in growth. The study has shown that agriculture sector has been able to show tremendous improvement in expansion of area and production of food grain and non-food grain crops. However, there are so many underlying factors responsible for slowdown of the agricultural growth. Some of the factors identified include: Increase in area under non-agriculture uses, excessive dependence on rain fed farming, increase in number of agricultural labourers, reducing size of the operation holdings, over use of agri-inputs, inequity in the distribution of agriculture credit along with sharp deceleration in public gross capital formation in agriculture etc. The study pointed in order to achieve higher growth rate, there is a need to enhance the gross capital formation in agriculture sector particularly on irrigation so that more area can be brought under assured irrigation. Bringing equity in distribution of agricultural credit coupled with judicious and need-based agricultural inputs are some of the other recommendations drawn based upon the study.

A polycentric growth model of gallium arsenide epitaxial layers from the gas phase with simultaneous diffusion, adsorption and chemical reaction

1988 ◽  
Vol 53 (12) ◽  
pp. 2995-3013
Author(s):  
Emerich Erdös ◽  
Jindřich Leitner ◽  
Petr Voňka ◽  
Josef Stejskal ◽  
Přemysl Klíma
Keyword(s):  
Growth Rate ◽  
Gallium Arsenide ◽  
Epitaxial Growth ◽  
Gas Phase ◽  
Surface Reaction ◽  
Quantitative Description ◽  
The Other ◽  
Rate Equations ◽  
Impact Interaction ◽  
Partial Pressures

For a quantitative description of the epitaxial growth rate of gallium arsenide, two models are proposed including two rate controlling steps, namely the diffusion of components in the gas phase and the surface reaction. In the models considered, the surface reaction involves a reaction triple - or quadruple centre. In both models three mechanisms are considered which differ one from the other by different adsorption - and impact interaction of reacting particles. In every of the six cases, the pertinent rate equations were derived, and the models have been confronted with the experimentally found dependences of the growth rate on partial pressures of components in the feed. The results are discussed with regard to the plausibility of individual mechanisms and of both models, and also with respect to their applicability and the direction of further investigations.

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