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.

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.

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 Diffusion at the Earth magnetopause: enhancement by Kelvin-Helmholtz instability

2007 ◽  
Vol 25 (1) ◽  
pp. 271-282 ◽  
Author(s):  
R. Smets ◽  
G. Belmont ◽  
D. Delcourt ◽  
L. Rezeau
Keyword(s):  
Magnetic Field ◽  
Distribution Functions ◽  
Larmor Radius ◽  
Simple Analytical Model ◽  
Helmholtz Instability ◽  
Field Reversal ◽  
Finite Larmor Radius ◽  
The Earth ◽  
Specific Distribution ◽  
The Magnetic Field

Abstract. Using hybrid simulations, we examine how particles can diffuse across the Earth's magnetopause because of finite Larmor radius effects. We focus on tangential discontinuities and consider a reversal of the magnetic field that closely models the magnetopause under southward interplanetary magnetic field. When the Larmor radius is on the order of the field reversal thickness, we show that particles can cross the discontinuity. We also show that with a realistic initial shear flow, a Kelvin-Helmholtz instability develops that increases the efficiency of the crossing process. We investigate the distribution functions of the transmitted ions and demonstrate that they are structured according to a D-shape. It accordingly appears that magnetic reconnection at the magnetopause is not the only process that leads to such specific distribution functions. A simple analytical model that describes the built-up of these functions is proposed.

Rayleigh-Taylor Instability of a Stratified Plasma

1974 ◽  
Vol 29 (3) ◽  
pp. 518-523 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Boussinesq Approximation ◽  
Short Wave ◽  
Taylor Instability ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Wave Disturbances ◽  
Magnetic Field Gradients ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

We have investigated the effect of finite Larmor radius on the Rayleigh-Taylor instability of a semi-infinite, compressible, stratified and infinitely conducting plasma. The plasma is assumed to have a one dimensional density and magnetic field gradients. The eigenvalue problem has been solved under Boussinesq approximation for disturbances parallel to the magnetic field. It has been established that for perturbation parallel to the magnetic field, the system is stable for both stable and unstable stratification. For perturbation perpendicular to the magnetic field, the problem has been solved without Boussinesq approximation. The dispersion relation has been discussed in the two limiting cases, the short and long wave disturbances. It has been observed that the gyroviscosity has a destabilizing influence from k = 0 to k = 4.5 for ß* = 0.1 and for ß* = 0.1 up to k* = 2.85 and then onwards it acts as a stabilizing agent. It has a damping effect on the short wave disturbances. For some parameters, the largets imaginary part has been shown in Figs. 1 and 2

Stability of anisotropic plasmas to almost-perpendicular magnetosonic waves

1971 ◽  
Vol 6 (3) ◽  
pp. 495-512 ◽  
Author(s):  
R. W. Landau† ◽  
S. Cuperman
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Simple Form ◽  
Cyclotron Frequency ◽  
Plasma Frequency ◽  
Alfven Wave ◽  
Larmor Radius ◽  
Ion Plasma ◽  
The Stability ◽  
The Magnetic Field

The stability of anisotropic plasmas to the magnetosonic (or right-hand compressional Alfvén) wave, near the ion cyclotron frequency, propagating almost perpendicular to the magnetic field, is investigated. For this case, and for wavelengths larger than the ion Larmor radius and for large ion plasma frequency (w2p+ ≫ Ωp+) the dispersion relation is obtained in a simple form. It is shown that for T # T' (even T ≫ T) no instabifity occurs. The resonant ters are also included, and it is shown that there is no resonant instabifity, only damping.

Kelvin–Helmholtz instability of a plasma with anisotropic and polytropic pressure laws

1998 ◽  
Vol 60 (2) ◽  
pp. 229-241 ◽  
Author(s):  
P. K. SHARMA ◽  
R. K. CHHAJLANI
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Equations Of State ◽  
Anisotropic Pressure ◽  
Magnetohydrodynamic Equations ◽  
Helmholtz Instability ◽  
Instability Condition ◽  
Two Fluids ◽  
The Magnetic Field

The Kelvin–Helmholtz (K–H) instability of two fluids of plasma streaming in opposite directions with the same velocity and in the presence of an external magnetic field is investigated. The usual magnetohydrodynamic equations with anisotropic pressure are considered. In the present problem, the two pressures parallel and perpendicular to the direction of the magnetic field are defined by polytropic pressure laws. The generalized pressure relations are used, and two equations of state for two pressures are assumed. The equations are linearized, and initially two different flow velocities are taken for the system. The flow is assumed to be in the direction perpendicular to the magnetic field. The problem is solved and a dispersion relation is obtained. From the dispersion relation, the K–H instability condition is obtained. It is found that the instability condition depends upon the polytropic indices of the pressure relations. The condition of instability is further obtained for MHD and Chew–Goldberger–Low systems. It is also found that the growth rate of the instability depends upon various polytropic indices.

scholarly journals Finite-Larmor-radius equilibrium and currents of the Earth’s flank magnetopause

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
S. S. Cerri
Keyword(s):  
Fluid Model ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Current Layer ◽  
Ion Dynamics ◽  
Finite Larmor Radius ◽  
Analytic Expressions ◽  
The One ◽  
Flr Effects ◽  
The Magnetic Field

We consider the one-dimensional equilibrium problem of a shear-flow boundary layer within an ‘extended-fluid model’ of a plasma that includes the Hall and the electron pressure terms in Ohm’s law, as well as dynamic equations for anisotropic pressure for each species and first-order finite-Larmor-radius (FLR) corrections to the ion dynamics. We provide a generalized version of the analytic expressions for the equilibrium configuration given in Cerri et al., (Phys. Plasmas, vol. 20 (11), 2013, 112112), highlighting their intrinsic asymmetry due to the relative orientation of the magnetic field $\boldsymbol{B}$, $\boldsymbol{b}=\boldsymbol{B}/|\boldsymbol{B}|$, and the fluid vorticity $\unicode[STIX]{x1D74E}=\unicode[STIX]{x1D735}\times \boldsymbol{u}$ (‘$\unicode[STIX]{x1D74E}\boldsymbol{b}$ asymmetry’). Finally, we show that FLR effects can modify the Chapman–Ferraro current layer at the flank magnetopause in a way that is consistent with the observed structure reported by Haaland et al., (J. Geophys. Res. (Space Phys.), vol. 119, 2014, pp. 9019–9037). In particular, we are able to qualitatively reproduce the following key features: (i) the dusk–dawn asymmetry of the current layer, (ii) a double-peak feature in the current profiles and (iii) adjacent current sheets having thicknesses of several ion Larmor radii and with different current directions.

Effect of finite Larmor radius on Rayleigh–Taylor instability of a plasma

1969 ◽  
Vol 47 (22) ◽  
pp. 2435-2437 ◽  
Author(s):  
P. D. Ariel ◽  
P. K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Density Gradient ◽  
Taylor Instability ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Unstable Configuration ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

The effects of a finite Larmor radius of the ions are investigated on the Rayleigh–Taylor instability of a plasma in which there is a density gradient in a direction perpendicular to that of the magnetic field. It is found that the unstable configuration is completely stabilized by the finite Larmor radius effect.

Evolution of nonlinear Alfvén waves propagating along the magnetic field in a collisionless plasma

1982 ◽  
Vol 28 (3) ◽  
pp. 459-468 ◽  
Author(s):  
M. Khanna ◽  
R. Rajaram
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Momentum Equation ◽  
Finite Amplitude ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Flr Effects ◽  
The Magnetic Field

It is shown that the asymptotic evolution of a finite-amplitude Alfvén wave propagating parallel to the uniform magnetic field in a warm homogeneous collisionless plasma is governed by the modified nonlinear Schrödinger equation. The dispersion is provided by the ion finite Larmor radius (FLR) effects in the momentum equation and the Hall current and electron pressure corrections to the generalized Ohm's law. In the cold plasma limit the equations reduce to those available in the literature. It is suggested that these calculations can have a bearing on the investigation of the structure of MHD waves in the solar wind.

scholarly journals Beat wave cyclotron heating of rippled density plasma

2018 ◽  
Vol 36 (4) ◽  
pp. 465-469 ◽  
Author(s):  
Pushplata ◽  
A. Vijay
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Ponderomotive Force ◽  
Beat Frequency ◽  
Magnetized Plasma ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Wave Heating ◽  
The Magnetic Field ◽  
Density Plasma

AbstractLaser beat wave heating of magnetized plasma via electron cyclotron damping is proposed and analyzed. A plasma density ripple is presumed to exist across the magnetic field. Two collinear lasers propagating along the magnetic field exert a beat frequency ponderomotive force on electrons, driving a large amplitude Bernstein quasi-mode which suffers cyclotron damping on electrons. Finite Larmor radius effects play an important role in the heating. Electron temperature initially rises linearly with time. As the temperature rises cyclotron damping becomes stronger and temperature rises rapidly. The process, however, requires ripple wavelength shorter than the wavelength of the beat wave.

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