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.

Electromagnetic waves in a relativistic plasma stream: fusion instability

1982 ◽  
Vol 27 (2) ◽  
pp. 205-213 ◽  
Author(s):  
J. N. Mohanty ◽  
P. Misra
Keyword(s):  
Distribution Function ◽  
Electromagnetic Waves ◽  
Equilibrium Distribution ◽  
Relativistic Plasma ◽  
Equilibrium Distribution Function ◽  
Plasma Stream ◽  
Thermal Velocity ◽  
Relativistic Kinematics ◽  
Streaming Velocity

We derive the dispersion formulae for electromagnetic waves including relativistic kinematics and a corresponding Maxwellian equilibrium distribution function without any approximations and having anisotropy in the streaming velocity. For non-relativistic temperatures, waves propagate when the streaming velocity is much smaller than the thermal velocity of the species, with varying thermal modes.

scholarly journals On the Role of Magnetic Field Fluctuations in Diffusive Shock Acceleration

2011 ◽  
Vol 21 (3) ◽  
pp. 199
Author(s):  
Doan Kim The ◽  
Pham Tuan Anh ◽  
Pham Ngoc Diep ◽  
Pham Ngoc Dong ◽  
Nguyen Van Hiep ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Field Component ◽  
Larmor Radius ◽  
Shock Acceleration ◽  
Simultaneous Presence ◽  
Diffusive Shock Acceleration ◽  
Cosmic Particle ◽  
Field Fluctuations

A simple numerical simulation of the mechanism of diffusive shock acceleration, responsible for the acceleration of cosmic rays in the environment of young Super Nova Remnants, is presented. The relative roles of a uniform magnetic field component, inherited from the parent collapsed star, and of magnetic turbulences, known to be present in the vicinity of the shock, are investigated. It is shown that a uniform magnetic field allows for only doubling the energy of the cosmic particle. Important accelerations require the simultaneous presence of magnetic field turbulences at a scale commensurable with its Larmor radius.

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.

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.

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