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.

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.

Effect of finite ion Larmor radius on the Kelvin–Helmholtz instability

1978 ◽  
Vol 20 (2) ◽  
pp. 149-160 ◽  
Author(s):  
Hirosh Nagano
Keyword(s):  
Magnetic Field ◽  
Flow Velocity ◽  
Wave Vector ◽  
Uniform Magnetic Field ◽  
Critical Value ◽  
Larmor Radius ◽  
Helmholtz Instability ◽  
Finite Larmor Radius ◽  
Compressible Plasma ◽  
The Difference

The effect of finite ion Larmor radius on the Kelvin–Helmholtz instability is investigated in the cases of an incompressible and a compressible plasma. When a wave vector is perpendicular to a uniform magnetic field, the effect of finite Larmor radius (FLR) stabilizes perturbations with a wavenumber exceeding a critical value, while there exists another case that the FLR effect destabilizes still more than the usual MHD approximation. The difference between these cases is decided from the configuration of flow velocity and magnetic field. When a wave vector is parallel to a magnetic field, the FLR effect tends to stabilize perturbations with a larger wavenumber.

Hydromagnetic Kelvin-Heimholtz Instability in the Presence of Suspended Particles and Finite Larmor Radius Effect

1994 ◽  
Vol 49 (12) ◽  
pp. 1102-1110 ◽  
Author(s):  
R. K. Sanghvi ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Suspended Particles ◽  
Linear Analysis ◽  
Wave Number ◽  
Larmor Radius ◽  
Helmholtz Instability ◽  
Finite Larmor Radius ◽  
Simplifying Assumptions ◽  
The Magnetic Field

Abstract A linear analysis of the combined influence of a finite ion Larmor radius and suspended particles on Kelvin-Helmholtz instability in the presence of a uniform magnetic field is carried out. The magnetic field is assumed to be uniform and transverse to the direction of streaming. The medium is assumed to be incompressible. Certain simplifying assumptions are made for the motion of the suspended particles. A dispersion relation for such a medium has been obtained using appropriate boundary conditions. The stabilizing effect of a finite Larmor radius has been reasserted in the absence of the suspended particles. A stability criterion for the medium is derived, which is found to be independent of the presence of the suspended particles. Similarly a condition of instability of the system is also derived. Numerical analysis is presented in a few limiting cases of interest. Furthermore, growth rates of unstable modes of the configuration with increasing relaxation fre­quency of the particles and finite Larmor radius have been evaluated analytically. It is shown that the finite Larmor radius in the presence of the suspended particles destabilizes a certain wave number band which is stable otherwise. Implications of the suspended particles on the growth rate of unstable modes are discussed in the limit of vanishing ion Larmor radius.

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.

scholarly journals Magnetic field generation in a jet-sheath plasma via the kinetic Kelvin-Helmholtz instability

2013 ◽  
Vol 31 (9) ◽  
pp. 1535-1541 ◽  
Author(s):  
K.-I. Nishikawa ◽  
P. Hardee ◽  
B. Zhang ◽  
I. Duţan ◽  
M. Medvedev ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Magnetic Fields ◽  
Electric Field ◽  
Flow Direction ◽  
Transverse Magnetic ◽  
Velocity Shear ◽  
Helmholtz Instability ◽  
Magnetic Field Generation ◽  
Relativistic Jet

Abstract. We have investigated the generation of magnetic fields associated with velocity shear between an unmagnetized relativistic jet and an unmagnetized sheath plasma. We have examined the strong magnetic fields generated by kinetic shear (Kelvin–Helmholtz) instabilities. Compared to the previous studies using counter-streaming performed by Alves et al. (2012), the structure of the kinetic Kelvin–Helmholtz instability (KKHI) of our jet-sheath configuration is slightly different, even for the global evolution of the strong transverse magnetic field. In our simulations the major components of growing modes are the electric field Ez, perpendicular to the flow boundary, and the magnetic field By, transverse to the flow direction. After the By component is excited, an induced electric field Ex, parallel to the flow direction, becomes significant. However, other field components remain small. We find that the structure and growth rate of KKHI with mass ratios mi/me = 1836 and mi/me = 20 are similar. In our simulations saturation in the nonlinear stage is not as clear as in counter-streaming cases. The growth rate for a mildly-relativistic jet case (γj = 1.5) is larger than for a relativistic jet case (γj = 15).

The microinstabilities of a high-β plasma flow with a non-uniform velocity profile

1980 ◽  
Vol 24 (3) ◽  
pp. 385-407 ◽  
Author(s):  
A. B. Mikhailovskii ◽  
V. A. Klimenko
Keyword(s):  
Magnetic Field ◽  
High Pressure ◽  
Velocity Profile ◽  
Kinetic Analysis ◽  
Plasma Flow ◽  
Large Family ◽  
Larmor Radius ◽  
Helmholtz Instability ◽  
Uniform Velocity ◽  
Pressure Plasma

The microinstabilities of a high-pressure plasma moving along a magnetic field with a non-uniform velocity profile are investigated. A similar problem was studied earlier by Dobrowolny on the basis of hydromagnetic equations with an oblique viscosity tensor. The present paper, unlike Dobrowolny's work, gives a kinetic analysis. Perturbations with transverse wavelength both larger and smaller than the ion Larmor radius are considered. The analysis indicates that there is a large family of microinstabilities of the ‘drift’ type whose mechanism differs from the classical Kelvin–Helmholtz instability.

Electron whistler mode instability in an inhomogeneous thermal plasma in the presence of an inhomogeneous beam of suprathermal electrons

1983 ◽  
Vol 29 (3) ◽  
pp. 439-448 ◽  
Author(s):  
H.A. Shah ◽  
V.K. Jain
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Thermal Plasma ◽  
Uniform Magnetic Field ◽  
Inhomogeneous Plasma ◽  
Mode Instability ◽  
Whistler Mode ◽  
Suprathermal Electrons ◽  
Whistler Mode Waves

The excitation of the whistler mode waves propagating obliquely to the constant and uniform magnetic field in a warm and inhomogeneous plasma in the presence of an inhomogeneous beam of suprathermal electrons is studied. The full dispersion relation including electromagnetic effects is derived. In the electrostatic limit the expression for the growth rate is given. It is found that the inhomogeneities in both beam and plasma number densities affect the growth rates of the instabilities.

Effect of Finite Larmor Radius on the Rayleigh-Taylor Instability of Two Component Magnetized Rotating Plasma

1998 ◽  
Vol 53 (12) ◽  
pp. 937-944 ◽  
Author(s):  
P. K. Sharma ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Horizontal Magnetic Field ◽  
Finite Larmor Radius ◽  
Neutral Particles ◽  
Rayleigh Taylor Instability ◽  
Superposed Fluids

Abstract The Rayleigh-Taylor (R-T) instability of two superposed plasmas, consisting of interacting ions and neutrals, in a horizontal magnetic field is investigated. The usual magnetohydrodynamic equations, including the permeability of the medium, are modified for finite Larmor radius (FLR) corrections. From the relevant linearized perturbation equations, using normal mode analysis, the dispersion relation for the two superposed fluids of different densities is derived. This relation shows that the growth rate unstability is reduced due to FLR corrections, rotation and the presence of neutrals. The horizontal magnetic field plays no role in the R-T instability. The R-T instability is discussed for various simplified configurations. It remains unaffected by the permeability of the porous medium, presence of neutral particles and rotation. The effect of different factors on the growth rate of R-T instability is investigated using numerical analysis. Corresponding graphs are plotted for showing the effect of these factors on the growth of the R-T instability.

Stability of a plasma stream in a magnetic field

1971 ◽  
Vol 6 (1) ◽  
pp. 169-186
Author(s):  
A. Lamont ◽  
J. C. Taylor ◽  
E. W. Laing
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Uniform Magnetic Field ◽  
Transverse Direction ◽  
Equilibrium Distribution ◽  
Larmor Radius ◽  
Equilibrium Distribution Function ◽  
Plasma Stream ◽  
Vlasov Equations ◽  
The Fourier Transform

The system studied is a plasma streaming parallel to a uniform magnetic field with a velocity which varies in a transverse direction. The flow is bounded at y =± a by perfectly conducting planes.The Poisson-Vlasov equations are used to derive an integro-differential equation for ø the Fourier transform of the electrostatic potential. The kernel of this equation is expanded using a small Larmor radius expansion for ø and for the equilibrium distribution function f0.

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