Kinetic theory of the stability of collisional plasma in curved magnetic field

1969 ◽  
Vol 3 (2) ◽  
pp. 155-160 ◽  
Author(s):  
K. Jungwirth
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Ion Temperature ◽  
Gravitation Field ◽  
Ion Collisions ◽  
Large Gradient ◽  
Field Lines ◽  
The Stability

The effect of curvature of magnetic field lines on plasma instabilities due to a large gradient of the ion temperature has been studied. It is shown that none of the discussed effects can be obtained so long as the curvature of magnetic field lines is simulated by a fictional gravitation field. In configurations with large enough minimum-B, the usual temperature-gradient instability is stabilized in collisionless plasma. However, a new dissipative instability arises due to ion–ion collisions with the maximum growth rate γmax ˜ Vii/40.

Longitudinal waves in a perpendicular collisionless plasma shock: I. Cold ions

1970 ◽  
Vol 4 (4) ◽  
pp. 739-751 ◽  
Author(s):  
S. Peter Gary ◽  
J. J. Sanderson
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Collisionless Plasma ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Wave Number ◽  
Zero Magnetic Field ◽  
Linear Dispersion ◽  
Electrostatic Waves ◽  
Cold Ions

This paper considers electrostatic waves in a Vlasov plasma of unmagnetized ions and magnetized, Maxwellian electrons. The linear dispersion relation is derived for waves in a perpendicular shock such that the most important sources of instability are the E × B and ∇B electron drifts. For the case of cold ions, propagation perpendicular to the applied magnetic field, and the E × B drift alone, a numerical analysis of frequency vs. wave-number is presented. The effects of the ∇B drift are also considered, and it is shown that the maximum growth rate can be larger than the maximum growth rate for the zero magnetic field ion acoustic instabifity under comparable conditions.

Plasma instabilities driven by pickup ions of ring-beam velocity distributions in the outer heliosheath 

2021 ◽  
Author(s):  
Ameneh Mousavi ◽  
Kaijun Liu ◽  
Sina Sadeghzadeh
Keyword(s):  
Magnetic Field ◽  
Maximum Growth ◽  
Dispersion Analysis ◽  
Maximum Growth Rate ◽  
Injection Velocity ◽  
Plasma Instabilities ◽  
Pickup Ions ◽  
Beam Velocity ◽  
Background Magnetic Field ◽  
Hybrid Simulations

<p><span>The stability of the pickup ions in the outer heliosheath has been studied by many researchers because of its relevance to the energetic neutral atom (ENA) ribbon observed by the Interstellar Boundary EXplorer. However, previous studies are primarily limited to pickup ions of near </span><span>90° </span><span>pickup angles, the angle between the pickup ion injection velocity and the background, local interstellar magnetic field. Investigations on pickup ions of smaller pickup angles are still lacking. In this paper, linear kinetic dispersion analysis and hybrid simulations are carried out to examine the plasma instabilities driven by pickup ions of ring-beam velocity distributions at various pickup angles between zero and </span><span>90°</span><span>. </span><span>Parallel propagating waves are studied in the parameter regime where the parallel thermal spread of the pickup ions falls into the Alfvén cyclotron stability gap. </span><span>The linear analysis results and hybrid simulations both show that the fastest growing modes are the right-hand helicity waves propagating in the direction of the background magnetic field, and the maximum growth rate occurs at the pickup angle of </span><span>82°</span><span>. The simulation results further reveal that the saturation level of the fluctuating magnetic fields for pickup angles below </span><span>45° </span><span>is higher than that for pickup angles above </span><span>45°</span><span>. So, the scattering of pickup ions at near zero pickup angles is likely more pronounced than that at near </span><span>90° </span><span>pickup angles</span> .</p>

Collisionless plasma transport mechanisms in stochastic open magnetic field lines in tokamaks

2021 ◽  
Author(s):  
Min-Gu Yoo ◽  
Weixing Wang ◽  
Edward A Startsev ◽  
Chenhao Ma ◽  
S Ethier ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Plasma Transport ◽  
Transport Mechanisms ◽  
Field Lines ◽  
Open Magnetic Field

Non-normal stability analysis of a shear current under surface gravity waves

2008 ◽  
Vol 609 ◽  
pp. 49-58
Author(s):  
D. AMBROSI ◽  
M. ONORATO
Keyword(s):  
Growth Rate ◽  
Modal Analysis ◽  
Gravity Waves ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Surface Gravity ◽  
Horizontal Shear ◽  
Surface Gravity Waves ◽  
Shear Current ◽  
The Stability

The stability of a horizontal shear current under surface gravity waves is investigated on the basis of the Rayleigh equation. As the differential operator is non-normal, a standard modal analysis is not effective in capturing the transient growth of a perturbation. The representation of the stream function by a suitable basis of bi-orthogonal eigenfunctions allows one to determine the maximum growth rate of a perturbation. It turns out that, in the considered range of parameters, such a growth rate can be two orders of magnitude larger than the maximum eigenvalue obtained by standard modal analysis.

Compositional convection in the presence of a magnetic field. II. Cartesian plume

2005 ◽  
Vol 461 (2060) ◽  
pp. 2605-2633 ◽  
Author(s):  
I.A Eltayeb ◽  
E.A Hamza ◽  
J.A Jervase ◽  
E.V Krishnan ◽  
D.E Loper
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Single Interface ◽  
Magnetic Prandtl Number ◽  
Infinite Extent ◽  
Chandrasekhar Number ◽  
The Magnetic Field ◽  
Field Inclination

The analysis of part I, dealing with the morphological instability of a single interface in a fluid of infinite extent, is extended to the case of a Cartesian plume of compositionally buoyant fluid, of thickness 2 x 0 , enclosed between two vertical interfaces. The problem depends on six dimensionless parameters: the Prandtl number, σ ; the magnetic Prandtl number, σ m ; the Chandrasekhar number, Q c ; the Reynolds number, Re ; the ratio, B v , of vertical to horizontal components of the ambient magnetic field and the dimensionless plume thickness. Attention is focused on the preferred mode of instability, which occurs in the limit Re ≪1 for all values of the parameters. This mode can be either sinuous or varicose with the wavenumber vector either vertical or oblique , comprising four types. The regions of preference of these four modes are represented in regime diagrams in the ( x 0 ,  σ ) plane for different values of σ m , Q c , B v . These regions are strongly dependent on the field inclination and field strength and, to a lesser extent, on magnetic diffusion. The overall maximum growth rate for any prescribed set of the parameters σ m , Q c , B v , occurs when 1.3< x 0 <1.7, and is sinuous for small σ and varicose for large σ . The magnetic field can enhance instability for a certain range of thickness of the plume. The enhancement of instability is due to the interaction of the field with viscous diffusion resulting in a reverse role for viscosity. The dependence of the helicity and α -effect on the parameters is also discussed.

On the stability of nonlinear magneto-sonic waves in a collisionless plasma

1975 ◽  
Vol 13 (1) ◽  
pp. 189-191 ◽  
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Nonlinear Function ◽  
Sonic Waves ◽  
The Stability ◽  
Space Dependence ◽  
The Magnetic Field

Demehenko & Hussein (1973) discussed some properties of nonlinear magneto-sonic waves in a collisionless plasma. The relevant equation describing the space dependence x of the magnetic field may be written in the form d2y/dx2+f(y) = 0, (1) where f(y) is a nonlinear function of y only.

Instabilities of a Baroclinic, Double Diffusive Frontal Zone

2008 ◽  
Vol 38 (4) ◽  
pp. 840-861 ◽  
Author(s):  
W. D. Smyth
Keyword(s):  
Growth Rate ◽  
Frontal Zone ◽  
Baroclinic Instability ◽  
Flux Ratio ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Variable Diffusivity ◽  
The Stability ◽  
Parameter Values ◽  
Double Diffusive

Abstract The linear theory of double diffusive interleaving is extended to take account of baroclinic effects. This study goes beyond previous studies by including the possibility of modes with nonzero tilt in the alongfront direction, which allows for advection by the baroclinic frontal flow. This requires that the stability equations be solved numerically. The main example is based on observations of interleaving on the lower flank of Meddy Sharon, but a range of parameter values is covered, leading to conclusions that are relevant in a variety of oceanic regimes. The frontal zone is treated as infinitely wide with uniform gradients of temperature, salinity, and alongfront velocity. The stationary, vertically symmetric interleaving mode is shown to have maximum growth rate when its alongfront wavenumber is zero, providing validation for previous studies in which this property was assumed. Besides this, there exist two additional modes of instability: the ageostrophic Eady mode of baroclinic instability and a mode not previously identified. The new mode is oblique (i.e., it tilts in the alongfront direction), vertically asymmetric, and propagating. It is strongly dependent on boundary conditions, and its relevance in the ocean interior is uncertain as a result. Effects of variable diffusivity and buoyancy flux ratio are also considered.

Electrohydrodynamic stability of a slightly viscous jet

1994 ◽  
Vol 274 ◽  
pp. 93-113 ◽  
Author(s):  
A. J. Mestel
Keyword(s):  
Surface Charge ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Small Fields ◽  
Weakly Conducting ◽  
Tangential Field ◽  
Tangential Surface ◽  
The Stability ◽  
Electric Effects ◽  
Phase Differences

Many electro-spraying devices raise to a high electric potential a pendant drop of weakly conducting fluid, which may adopt a conical shape from whose apex a thin, charged jet is emitted. Such a jet eventually breaks up into fine droplets, but often displays surprising longevity. This paper examines the stability of an incompressible cylindrical jet carrying surface charge in a tangential electric field, allowing for the finite rate of charge relaxation. The viscosity is assumed to be small so that the shear resulting from the tangential surface stress can be large, even for relatively small fields. This shear can suppress surface tension instabilities, but if too large, it excites electrical ones. For imperfect conductors, surface charge is redistributed by the rapid fluid reaction to variations in tangential stress as well as by conduction. Phase differences between the effects due to the tangential field and the surface charge lead to charge ‘over-relaxation’ instabilities, but the maximum growth rate can still be lower than in the absence of electric effects.

Stability of relativistic transverse cold plasma waves. Part 2. Linearly polarized waves

1979 ◽  
Vol 22 (2) ◽  
pp. 201-222 ◽  
Author(s):  
F. J. Romeiras
Keyword(s):  
Nonlinear Wave ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Transverse Modes ◽  
Electron Positron ◽  
Polarized Waves ◽  
Linearly Polarized ◽  
Linear Differential ◽  
Unmagnetized Plasma ◽  
The Stability

This is part 2 of a paper concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized plasma. It refers to transverse linearly polarized waves in an electron-positron plasma. A numerical method, based on Floquet's theory of linear differential equations with periodic coefficients, is used to solve the perturbation equations and obtain the instability growth rates. All the three possible types of perturbations are discussed for a typical value of the (large) amplitude of the nonlinear wave: electrically longitudinal slightly unstable modes (with maximum growth rate γ approximately equal to 0·07ω0, where ω0is the frequency of the nonlinear wave); purely transverse moderately unstable modes (with γ ≃ 0·26ω0); and highly unstable electrically transverse modes (with γ ≃ l·5ω0).

scholarly journals Stability of an electrified liquid jet approaching to critical point

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402093637
Author(s):  
Zixuan Fang ◽  
Ping Wang
Keyword(s):  
Surface Tension ◽  
Critical Point ◽  
Weber Number ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Wave Number ◽  
Electrical Field ◽  
Electric Stress ◽  
Electrical Field Intensity ◽  
The Stability

This article reports the linear stability analysis of a thermodynamic-transcritical jet sprayed to a radial electrical field. An asymptotic approach was used to obtain the stability solution of a supercritical jet subjected to electrical field. In order to obtain the solutions for the electrified supercritical jet, the surface tension was decreased and consequently led the increase in Weber number in the linear governing equation of subcritical charged jet. To investigate the role of surface tension and electric stress playing in the destabilizing process when approaching the critical point, the energy budget is performed by tracing the energy sources. It was found that, when the Weber number is increased to a sufficiently large value, the solution will become an asymptotic value, which can be considered as a solution under the supercritical conditions. The electric stress can increase both the maximum growth rate and the dominant wave number of electrified supercritical jet, that is, higher electrical field intensity would enhance the instability of the electrified supercritical jet and decrease the wavelength of the disturbances.

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