scholarly journals Parametric excitation of Alfvén and acoustic waves

1974 ◽  
Vol 12 (3) ◽  
pp. 445-453 ◽  
Author(s):  
Nguyen The Hung
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Sound Wave ◽  
Acoustic Waves ◽  
Pump Intensity ◽  
Alfven Wave ◽  
Frequency Matching ◽  
Coupled Equations ◽  
Parametric Instabilities ◽  
The Waves

The nonlinear interaction between two Alfvén waves and a sound wave is studied, using the normal-mode approach. This leads, in a simple way to a set of coupled equations, and consequently to a dispersion relation for the waves under consideration. It is shown that a large-amplitude Alfvén wave can give rise to two distinct types of parametric instabilities, namely the oscillating and the purely growing waves. In each case, the expressions for the threshold pump intensity, the frequency shift and the growth rate of the excited waves are obtained. In particular, the results for a propagating pump under perfect frequency matching conditions are compared with those of Sagdeev & Galeev.

Parametric excitation of magnetoacoustic waves by a pump magnetic field in a high-β plasma

1977 ◽  
Vol 17 (1) ◽  
pp. 93-103 ◽  
Author(s):  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Parametric Excitation ◽  
Acoustic Waves ◽  
Magnetic Pressure ◽  
Gas Pressure ◽  
Alfven Wave ◽  
Fast Wave ◽  
Magnetoacoustic Waves ◽  
Background Magnetic Field ◽  
The Waves

The parametric excitation of slow, intermediate (Alfvén) and fast magneto-acoustic waves by a modulated spatially non-uniform magnetic field in a plasma with a finite ratio of gas pressure to magnetic pressure is considered. The waves are excited in pairs, either pairs of the same mode, or a pair of different modes. The growth rates of the instabilities are calculated and compared with the known result for the Alfvén wave in a zero gas pressure plasma. The only waves that are found not to be excited are the slow plus fast wave pair, and the intermediate plus slow or fast wave pair (unless the waves have a component of propagation direction perpendicular to both the background magnetic field and the direction of non-uniformity of the field).

Kinetic Alfvén waves in an inhomogeneous anisotropic magnetoplasma in the presence of an inhomogeneous electric field: particle aspect analysis

2000 ◽  
Vol 63 (4) ◽  
pp. 311-328 ◽  
Author(s):  
A. BARONIA ◽  
M. S. TIWARI
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Electric Field ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Larmor Radius ◽  
Alfvén Waves ◽  
Temperature Anisotropy ◽  
Inhomogeneous Electric Field ◽  
Kinetic Alfvén Waves

Kinetic Alfvén waves in the presence of an inhomogeneous electric field applied perpendicular to the ambient magnetic field in an anisotropic, inhomogeneous magnetoplasma are investigated. The particle aspect approach is adopted to investigate the trajectories of charged particles in the electromagnetic field of a kinetic Alfvén wave. Expressions are found for the field-aligned current, the perpendicular current, the dispersion relation and the particle energies. The growth rate of the wave is obtained by an energy- conservation method. It is predicted that plasma density inhomogeneity is the main source of instability, and an enhancement of the growth rate by electric field inhomogeneity and temperature anisotropy is found. The dispersion relation and growth rate involve the finite-Larmor-radius effect, electron inertia and the temperature anisotropy of the magnetoplasma. The applicability of the investigation to the auroral acceleration region is discussed.

scholarly journals Two-fluid simulations of waves in the solar chromosphere

2019 ◽  
Vol 627 ◽  
pp. A25 ◽  
Author(s):  
B. Popescu Braileanu ◽  
V. S. Lukin ◽  
E. Khomenko ◽  
Á. de Vicente
Keyword(s):  
Acoustic Waves ◽  
Hydrogen Plasma ◽  
The Other ◽  
Alfven Wave ◽  
Numerical Code ◽  
Solar Chromosphere ◽  
Charged Fluid ◽  
Induction Equation ◽  
The Waves ◽  
Two Fluid

Solar chromosphere consists of a partially ionized plasma, which makes modeling the solar chromosphere a particularly challenging numerical task. Here we numerically model chromospheric waves using a two-fluid approach with a newly developed numerical code. The code solves two-fluid equations of conservation of mass, momentum, and energy, together with the induction equation for the case of the purely hydrogen plasma with collisional coupling between the charged and neutral fluid components. The implementation of a semi-implicit algorithm allows us to overcome the numerical stability constraints due to the stiff collisional terms. We test the code against analytical solutions of acoustic and Alfvén wave propagation in uniform medium in several regimes of collisional coupling. The results of our simulations are consistent with the analytical estimates, and with other results described in the literature. In the limit of a large collisional frequency, the waves propagate with a common speed of a single fluid. In the other limit of a vanishingly small collisional frequency, the Alfvén waves propagate with an Alfvén speed of the charged fluid only, while the perturbation in neutral fluid is very small. The acoustic waves in these limits propagate with the sound speed corresponding to either the charges or the neutrals, while the perturbation in the other fluid component is negligible. Otherwise, when the collision frequency is similar to the real part of the wave frequency, the interaction between charges and neutrals through momentum-transfer collisions cause alterations of the waves frequencies and damping of the wave amplitudes.

Parametric instabifity of transverse and Langmuir waves in a plasma

1975 ◽  
Vol 13 (2) ◽  
pp. 317-326 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Growth Rate ◽  
Electromagnetic Field ◽  
Kinetic Model ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Threshold Intensity ◽  
Langmuir Waves ◽  
Scale Perturbation ◽  
The Subject ◽  
Parametric Instabilities

The parametric excitation of transverse and Langmuir waves by an externally-driven electromagnetic field of frequency (ω0 > 2ωp) in a warm and collisional plasma is studied, using the fluid equations. By an application of the multiple- time-scale perturbation method, the threshold intensity and the growth rate above threshold are obtained. The results are compared with those of Goldman (1969) and Prasad (1968), both of whom worked with a kinetic model.The theory of parametric instabilities in plasmas has been the subject of numerous investigations in recent years. Broadly speaking, the instabilities can be grouped into two categories: those for which the excited waves are purely electrostatic (see e.g. DuBois & Goldman 1965, 1967; Silin 1965; Lee & Su 1966; Jackson 1967; Nishikawa 1968; Kaw & Dawson 1969; Tzoar 1969; Sanmartin 1970; McBride 1970; Perkins & Flick 1971; Fejer & Leer 1972a, b; Bezzerides & Weinstock 1972; DuBois & Goldman 1972), and those for which one of the excited waves is electromagnetic (see e.g. Goldman & Dubois 1965; Montgomery & Alexeff 1966; Chen & Lewak 1970; Bodner & Eddleman 1972; Fejer & Leer 1972b; Lee & Kaw 1972; Forslund et al. 1972).

Attenuation of longitudinal electro-acoustic waves in a plasma

1974 ◽  
Vol 11 (1) ◽  
pp. 37-49
Author(s):  
R. J. Papa ◽  
P. Lindstrom
Keyword(s):  
Dispersion Relation ◽  
Electric Field ◽  
Acoustic Waves ◽  
Collision Frequency ◽  
Wave Dispersion ◽  
Signal Frequency ◽  
Variable Theory ◽  
Longitudinal Waves ◽  
Confluent Hypergeometric Functions ◽  
Linearized Boltzmann Equation

There are several practical situations in partially ionized plasmas when both collisionless (Landau) damping and electron-neutral collisions contribute to the attenuation of longitudinal waves. The longitudinal-wave dispersion relation is derived from Maxwell's equations and the linearized Boltzmann equation, in which electron-neutral collisions are represented by a Bhatnagar–Gross–Krook model that conserves particles locally. (The dispersion relation predicts that, for a given signal frequency ώ), an infinite number of complex wavenumbers kn can exist. Using Fourier–Laplace transform techniques, an integral representation for the electric field of the longitudinal waves is readily derived. Then, using theorems from complex variable theory, a modal expansion of the electric field can be made in terms of an infinite sum of confluent hypergeometric functions, whose arguments are proportional to the complex wavenumbers kn. It is demonstrated numerically that the spatial integral of the square of the electric field amplitude decreases as the electron-neutral collision frequency increases. Also, the amount of energy contained in the first few (lowest) modes, and the coupling between the modes, is examined as a function of plasma frequency, signal frequency and collision frequency.

Dispersion relations of dust lattice waves in two-dimensional honeycomb configuration

2013 ◽  
Vol 79 (5) ◽  
pp. 629-633
Author(s):  
B. FAROKHI
Keyword(s):  
Dispersion Relation ◽  
Group Velocity ◽  
Hexagonal Lattice ◽  
Dispersion Relations ◽  
Two Dimensional ◽  
The Third ◽  
Lattice Waves ◽  
The Waves

AbstractThe linear dust lattice waves propagating in a two-dimensional honeycomb configuration is investigated. The interaction between particles is considered up to distance 2a, i.e. the third-neighbor interactions. Longitudinal and transverse (in-plane) dispersion relations are derived for waves in arbitrary directions. The study of dispersion relations with more neighbor interactions shows that in some cases the results change physically. Also, the dispersion relation in the different direction displays anisotropy of the group velocity in the lattice. The results are compared with dispersion relations of the waves in the hexagonal lattice.

scholarly journals Rayleigh-Taylor instability of two superposed magnetized viscous fluids with suspended dust particles

2010 ◽  
Vol 14 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Praveen Sharma ◽  
Ram Prajapati ◽  
Rajendra Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Dust Particles ◽  
Stable Configuration ◽  
Rayleigh Taylor Instability ◽  
Suspended Dust ◽  
The Stability

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

scholarly journals ANALYSIS OF DISPERSION ERRORS IN ACOUSTIC WAVE SIMULATIONS

2006 ◽  
Vol 5 (1) ◽  
pp. 62
Author(s):  
R. A. C. Germanos ◽  
L. F. De Souza
Keyword(s):  
Acoustic Wave ◽  
Fourth Order ◽  
Finite Differences ◽  
Acoustic Waves ◽  
Time Integration ◽  
Compact Scheme ◽  
High Order Accuracy ◽  
Discretization Schemes ◽  
Analysis Of Dispersion ◽  
The Waves

The governing equations of the acoustic problem are the compressible Euler equations. The discretization of these equations has to ensure that the acoustic waves are transported with non-dispersive and non-dissipative characteristics. In the present study numerical simulations of a standing acoustic wave are performed. Four different space discretization schemes are tested, namely, a second order finite-differences, a fourth order finitedifferences, a fourth order finite-differences compact scheme and a sixth order finite-differences compact scheme. The time integration is done with a fourth order Runge-Kutta scheme. The results obtained are compared with linearized analytical solutions. The influence of the dispersion on the simulation of a standing wave is analyzed. The results confirm that high order accuracy schemes can be more efficient for simulation of acoustic waves, especially the waves with high frequency.

scholarly journals Partitioning Waves and Eddies in Stably Stratified Turbulence

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 420 ◽  
Author(s):  
Henri Lam ◽  
Alexandre Delache ◽  
Fabien S Godeferd
Keyword(s):  
Dispersion Relation ◽  
Kinetic Energy ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Energy Concentration ◽  
Kinetic Energy Density ◽  
Stratified Turbulence ◽  
The Waves

We consider the separation of motion related to internal gravity waves and eddy dynamics in stably stratified flows obtained by direct numerical simulations. The waves’ dispersion relation links their angle of propagation to the vertical θ , to their frequency ω , so that two methods are used for characterizing wave-related motion: (a) the concentration of kinetic energy density in the ( θ , ω ) map along the dispersion relation curve; and (b) a direct computation of two-point two-time velocity correlations via a four-dimensional Fourier transform, permitting to extract wave-related space-time coherence. The second method is more computationally demanding than the first. In canonical flows with linear kinematics produced by space-localized harmonic forcing, we observe the pattern of the waves in physical space and the corresponding concentration curve of energy in the ( θ , ω ) plane. We show from a simple laminar flow that the curve characterizing the presence of waves is distorted differently in the presence of a background convective mean velocity, either uniform or varying in space, and also when the forcing source is moving. By generalizing the observation from laminar flow to turbulent flow, this permits categorizing the energy concentration pattern of the waves in complex flows, thus enabling the identification of wave-related motion in a general turbulent flow with stable stratification. The advanced method (b) is finally used to compute the wave-eddy partition in the velocity–buoyancy fields of direct numerical simulations of stably stratified turbulence. In particular, we use this splitting in statistics as varied as horizontal and vertical kinetic energy, as well as two-point velocity and buoyancy spectra.

scholarly journals Magnetic Rayleigh–Taylor instability at a contact discontinuity with an oblique magnetic field

2020 ◽  
Vol 634 ◽  
pp. A96
Author(s):  
E. Vickers ◽  
I. Ballai ◽  
R. Erdélyi
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Contact Discontinuity ◽  
Homogeneous Magnetic Field ◽  
Taylor Instability ◽  
Wide Range ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field ◽  
Theoretical Results

Aims. We investigate the nature of the magnetic Rayleigh–Taylor instability at a density interface that is permeated by an oblique homogeneous magnetic field in an incompressible limit. Methods. Using the system of linearised ideal incompressible magnetohydrodynamics equations, we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by numerically solving the dispersion relation. Results. The critical wavenumber at which waves become unstable, which is present for a parallel magnetic field, disappears because the magnetic field is inclined. Instead, waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When we apply our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angles, from 0.5° up to 30°. These results highlight the diagnostic possibilities that our study offers.

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