Parallel solitary Alfvén waves in warm multi-species beam-plasma systems. Part 1

1992 ◽  
Vol 47 (1) ◽  
pp. 15-24 ◽  
Author(s):  
Frank Verheest ◽  
B. Buti
Keyword(s):  
Magnetic Field ◽  
Perturbation Analysis ◽  
Cold Plasma ◽  
Soliton Solutions ◽  
Magnetohydrodynamic Waves ◽  
Beam Plasma ◽  
Self Consistent ◽  
Reductive Perturbation ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Ion Species

A self-consistent reductive perturbation analysis for parallel-propagating magnetohydrodynamic waves in warm multi-species plasmas, in which different constituents can have differing equilibrium drifts, leads to a derivative nonlinear Schrödinger equation for the wave magnetic field. Soliton solutions are discussed, including applications to plasmas with two ion species. Such solitons are larger (in amplitude) and wider than in the non-streaming and/or cold-plasma case, other parameters being equal.

Parallel solitary Alfvén waves in warm multi-species beam-plasma systems. Part 2. Anisotropic pressures

1992 ◽  
Vol 47 (1) ◽  
pp. 25-37 ◽  
Author(s):  
Frank Verheest
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Soliton Solutions ◽  
Mhd Waves ◽  
Beam Plasma ◽  
Electric And Magnetic Fields ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Ion Species ◽  
Anisotropic Pressures

A nonlinear treatment is given for MHD waves that propagate parallel to the external magnetic field in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts. Both the wave electric and magnetic fields obey a derivative nonlinear Schrödinger equation. Soliton solutions are discussed, in particular for plasmas with two ion species.

Resistively induced plasma diffusion due to the trivial marginal modes of ideal MHD

1988 ◽  
Vol 39 (1) ◽  
pp. 157-168
Author(s):  
W. Liebert ◽  
E. Rebhan
Keyword(s):  
Magnetic Field ◽  
Heat Conduction ◽  
Perturbation Analysis ◽  
Cross Diffusion ◽  
Magnetic Surfaces ◽  
Ideal Mhd ◽  
Reductive Perturbation ◽  
Plasma Diffusion ◽  
Field Lines ◽  
The Magnetic Field

The influence of nonlinearities and plasma resistivity on the so-called trivial marginal modes of ideal MHD is investigated. It turns out that to lowest significant order of a reductive perturbation analysis nonlinearities have no influence, while in toroidal confinement configurations resistivity induces a local plasma diffusion across the magnetic surfaces. This is demonstrated for tokamaks with zero poloidal current density. In addition, the appearance of singularities in the plasma motion parallel to the magnetic field lines suggests a profile condition at the edge of the plasma. Heat conduction would directly tend to keep these effects at lower level, while indirectly it creates a reinforcement mechanism through the coupling to usual cross diffusion.

On the stability of self-consistent large-amplitude waves in a cold plasma. Part 3. Transverse circularly polarized waves in the presence of a large-scale magnetic field

1979 ◽  
Vol 21 (1) ◽  
pp. 43-50 ◽  
Author(s):  
M. A. Lee ◽  
I. Lerche
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Cold Plasma ◽  
Large Scale ◽  
Circularly Polarized ◽  
Polarized Waves ◽  
Large Scale Magnetic Field ◽  
Self Consistent ◽  
Instability Rate ◽  
The Stability

We demonstrate that a self-consistent large-amplitude circularly polarized wave, propagating in a cold plasma in the presence of a large-scale magnetic field, is unstable if the constant bulk streaming speed of the plasma is zero in the frame in which the wave depends oniy on time. The growth rate is of the order of the plasma frequency or the gyrofrequency at short perturbation wavelengths, and is proportional to the perturbation wave vector at long wavelengths. For nonzero but small streaming the instability rate increases for one streaming direction and decreases for the other. We conclude that instability is the rule rather than the exception for large-amplitude waves in a cold plasma.

scholarly journals Higher Frequency Spectrum of a Diffuse Linear Pinch with Multiple Ion Species

1985 ◽  
Vol 38 (2) ◽  
pp. 143 ◽  
Author(s):  
WN-C Sy
Keyword(s):  
Magnetic Field ◽  
Cold Plasma ◽  
Cyclotron Frequency ◽  
Cutoff Frequency ◽  
Plasma Model ◽  
Frequency Effects ◽  
Soluble Model ◽  
Ion Cyclotron ◽  
Arbitrary Magnetic Field ◽  
Ion Species

A cold plasma model which takes into account finite ion cyclotron frequency effects and multiple ion species has been developed for wave propagation in arbitrary magnetic field geometries. This model has been used to derive an elegant system of normal mode equations for a 10w-fJ diffuse linear pinch. From a soluble model, general features of the spectrum are discussed up to and including the ion cyclotron range of frequencies. It is indicated that in the vicinity of the ion-ion hybrid cutoff frequency, there could exist global eigenmodes which might be useful for supplementary heating of diffuse linear pinches.

On the stability of self-consistent large-amplitude waves in a cold plasma. Part 2. Longitudinal waves in the absence of large-scale magnetic field

1979 ◽  
Vol 21 (1) ◽  
pp. 27-42 ◽  
Author(s):  
M. A. Lee ◽  
I. Lerche
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Cold Plasma ◽  
Large Scale ◽  
Plasma Frequency ◽  
Longitudinal Waves ◽  
Large Scale Magnetic Field ◽  
Self Consistent ◽  
Instability Growth ◽  
The Stability

We demonstrate that self-consistent large-amplitude longitudinal waves in a cold plasma are unstable to at least transverse perturbations, with an instability growth rate which is roughly of the order of the plasma frequency of the system. The instability statements derived here are conservative, since modes not discussed may be more unstable.

scholarly journals Two typical collective behaviors of the heavy ions expanding in cold plasma with ambient magnetic field

2021 ◽  
Vol 33 (7) ◽  
pp. 076602
Author(s):  
Guo-Liang Peng ◽  
Jun-Jie Zhang ◽  
Jian-Nan Chen ◽  
Tai-Jiao Du ◽  
Hai-Yan Xie
Keyword(s):  
Magnetic Field ◽  
Heavy Ions ◽  
Cold Plasma ◽  
Collective Behaviors ◽  
Ambient Magnetic Field

On the existence of compressional MHD oscillations in an inhomogeneous magnetoplasma

1990 ◽  
Vol 44 (2) ◽  
pp. 361-375 ◽  
Author(s):  
Andrew N. Wright
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
Density Distribution ◽  
Cold Plasma ◽  
Wave Equations ◽  
Perturbation Field ◽  
Plasma Density Distribution ◽  
Background Magnetic Field ◽  
Transverse Fields ◽  
The Magnetic Field

In a cold plasma the wave equation for solely compressional magnetic field perturbations appears to decouple in any surface orthogonal to the background magnetic field. However, the compressional fields in any two of these surfaces are related to each other by the condition that the perturbation field b be divergence-free. Hence the wave equations in these surfaces are not truly decoupled from one another. If the two solutions happen to be ‘matched’ (i.e. V.b = 0) then the medium may execute a solely compressional oscillation. If the two solutions are unmatched then transverse fields must evolve. We consider two classes of compressional solutions and derive a set of criteria for when the medium will be able to support pure compressional field oscillations. These criteria relate to the geometry of the magnetic field and the plasma density distribution. We present the conditions in such a manner that it is easy to see if a given magnetoplasma is able to executive either of the compressional solutions we investigate.

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