Three-wave coupling coefficients for magnetized plasmas with pressure anisotropy

1989 ◽  
Vol 41 (1) ◽  
pp. 199-208 ◽  
Author(s):  
G. Brodin ◽  
L. Stenflo
Keyword(s):  
Energy Exchange ◽  
Low Frequency ◽  
Mhd Equations ◽  
Alfven Wave ◽  
Magnetized Plasmas ◽  
System Of Equations ◽  
Coupling Coefficients ◽  
Pressure Anisotropy ◽  
Nonlinear Energy ◽  
Low Frequency Waves

In order to find the equations for the nonlinear energy exchange between low-frequency waves in magnetized plasmas in the presence of pressure anisotropy, we start from the Chew–Goldberger–Low equations, the isothermal MHD equations, as well as a new hybrid system of equations. The coupling coefficients describing the interaction between two Alfvén waves and one magnetosonic wave as well as the interaction between two magnetosonic waves and one Alfvén wave are deduced.

scholarly journals Transformation of Infragravity Waves during Hurricane Overwash

2020 ◽  
Vol 8 (8) ◽  
pp. 545
Author(s):  
Katherine Anarde ◽  
Jens Figlus ◽  
Damien Sous ◽  
Marion Tissier
Keyword(s):  
Energy Exchange ◽  
Low Frequency ◽  
Barrier Island ◽  
Coastal Flooding ◽  
Bispectral Analysis ◽  
Infragravity Waves ◽  
Sea Level Anomalies ◽  
Hurricane Impact ◽  
Nonlinear Energy ◽  
Low Frequency Waves

Infragravity (IG) waves are expected to contribute significantly to coastal flooding and sediment transport during hurricane overwash, yet the dynamics of these low-frequency waves during hurricane impact remain poorly documented and understood. This paper utilizes hydrodynamic measurements collected during Hurricane Harvey (2017) across a low-lying barrier-island cut (Texas, U.S.A.) during sea-to-bay directed flow (i.e., overwash). IG waves were observed to propagate across the island for a period of five hours, superimposed on and depth modulated by very-low frequency storm-driven variability in water level (5.6 min to 2.8 h periods). These sea-level anomalies are hypothesized to be meteotsunami initiated by tropical cyclone rainbands. Estimates of IG energy flux show that IG energy was largely reduced across the island (79–86%) and the magnitude of energy loss was greatest for the lowest-frequency IG waves (<0.01 Hz). Using multitaper bispectral analysis, it is shown that, during overwash, nonlinear triad interactions on the sea-side of the barrier island result in energy transfer from the low-frequency IG peak to bound harmonics at high IG frequencies (>0.01 Hz). Assuming this pattern of nonlinear energy exchange persists across the wide and downward sloping barrier-island cut, it likely contributes to the observed frequency-dependence of cross-barrier IG energy losses during this relatively low surge event (<1 m).

scholarly journals Nonlinear evolution of the parametric instability: numerical predictions versus observations in the heliosphere

2001 ◽  
Vol 8 (3) ◽  
pp. 159-166 ◽  
Author(s):  
F. Malara ◽  
L. Primavera ◽  
P. Veltri
Keyword(s):  
Large Scale ◽  
Parametric Instability ◽  
Low Frequency ◽  
Heliospheric Current Sheet ◽  
Mhd Equations ◽  
Alfven Wave ◽  
The Sun ◽  
High Latitudes ◽  
Initial Correlation ◽  
Numerical Predictions

Abstract. Low-frequency turbulence in the solar wind is characterized by a high degree of Alfvénicity close to the Sun. Cross-helicity, which is a measure of Alfvénic correlation, tends to decrease with increasing distance from the Sun at high latitudes as well as in slow-speed streams at low latitudes. In the latter case, large scale inhomogeneities (velocity shears, the heliospheric current sheet) are present, which are sources of decorrelation; yet at high latitudes, the wind is much more homogeneous, and a possible evolution mechanism is represented by the parametric instability. The parametric decay of an circularly polarized broadband Alfvén wave is then investigated, as a source of decorrelation. The time evolution is followed by numerically integrating the full set of nonlinear MHD equations, up to instability saturation. We find that, for <beta>  ~ 1, the final cross-helicity is ~ 0.5, corresponding to a partial depletion of the initial correlation. Compressive fluctuations at a moderate level are also present. Most of the spectrum is dominated by forward propagating Alfvénic fluctuations, while backscattered fluctuations dominate large scales. With increasing time, the spectra of Elsässer variables tend to approach each other. Some results concerning quantities measured in the high-latitude wind are reviewed, and a qualitative agreement with the results of the numerical model is found.

scholarly journals Energy exchange and wave action conservation for magnetohydrodynamic (MHD) waves in a general, slowly varying medium

2014 ◽  
Vol 32 (12) ◽  
pp. 1495-1510 ◽  
Author(s):  
A. D. M. Walker
Keyword(s):  
Ray Tracing ◽  
Wave Energy ◽  
Energy Exchange ◽  
Energy Transport ◽  
Wave Action ◽  
Mhd Equations ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Sound Waves ◽  
Uniform Compression

Abstract. Magnetohydrodynamic (MHD) waves in the solar wind and magnetosphere are propagated in a medium whose velocity is comparable to or greater than the wave velocity and which varies in both space and time. In the approximation where the scales of the time and space variation are long compared with the period and wavelength, the ray-tracing equations can be generalized and then include an additional first-order differential equation that determines the variation of frequency. In such circumstances the wave can exchange energy with the background: wave energy is not conserved. In such processes the wave action theorem shows that the wave action, defined as the ratio of the wave energy to the frequency in the local rest frame, is conserved. In this paper we discuss ray-tracing techniques and the energy exchange relation for MHD waves. We then provide a unified account of how to deal with energy transport by MHD waves in non-uniform media. The wave action theorem is derived directly from the basic MHD equations for sound waves, transverse Alfvén waves, and the fast and slow magnetosonic waves. The techniques described are applied to a number of illustrative cases. These include a sound wave in a medium undergoing a uniform compression, an isotropic Alfvén wave in a steady-state shear layer, and a transverse Alfvén wave in a simple model of the magnetotail undergoing compression. In each case the nature and magnitude of the energy exchange between wave and background is found.

scholarly journals Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
J. L. Verniero ◽  
G. G. Howes ◽  
K. G. Klein
Keyword(s):  
Turbulent Energy ◽  
Mhd Equations ◽  
Alfven Wave ◽  
Initial State ◽  
Astrophysical Plasmas ◽  
Current Sheets ◽  
Nonlinear Energy Transfer ◽  
Kinetic Effects ◽  
Gyrokinetic Simulations ◽  
Nonlinear Energy

In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. The nonlinear interaction between counterpropagating Alfvén waves, denoted Alfvén wave collisions, drives this turbulent energy cascade, as recognized by early work with incompressible magnetohydrodynamic (MHD) equations. Recent work employing analytical calculations and nonlinear gyrokinetic simulations of Alfvén wave collisions in an idealized periodic initial state have demonstrated the key properties that strong Alfvén wave collisions mediate effectively the transfer of energy to smaller perpendicular scales and self-consistently generate current sheets. For the more realistic case of the collision between two initially separated Alfvén wavepackets, we use a nonlinear gyrokinetic simulation to show here that these key properties persist: strong Alfvén wavepacket collisions indeed facilitate the perpendicular cascade of energy and give rise to current sheets. Furthermore, the evolution shows that nonlinear interactions occur only while the wavepackets overlap, followed by a clean separation of the wavepackets with straight uniform magnetic fields and the cessation of nonlinear evolution in between collisions, even in the gyrokinetic simulation presented here which resolves dispersive and kinetic effects beyond the reach of the MHD theory.

The parametric excitation of kinetic Alfvén waves by a magnetic pump

1981 ◽  
Vol 26 (2) ◽  
pp. 253-266 ◽  
Author(s):  
N. F. Cramer ◽  
I. J. Donnelly
Keyword(s):  
Finite Temperature ◽  
Acoustic Waves ◽  
Temperature Effects ◽  
Mode Conversion ◽  
Low Frequency ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Ion Acoustic Wave ◽  
Low Frequency Waves

The parametric decay of a magneto-acoustic pump wave into low-frequency waves modified by finite temperature effects is considered. The excited waves are the kinetic Alfvén wave and the ion-acoustic wave. The former wave plays an important role in linear heating schemes employing the mode conversion of magneto-acoustic waves at the Alfvén resonance. Here we calculate the parametric growth rates and pump thresholds for excitation of these waves. The main result is that finite temperature effects tend to reduce the growth rate of Alfvén waves.

scholarly journals On the propagation of MHD eigenmodes in a 2-D-magnetotail

2011 ◽  
Vol 29 (1) ◽  
pp. 19-30 ◽  
Author(s):  
G. Fruit ◽  
P. Louarn
Keyword(s):  
Plasma Sheet ◽  
Initial Perturbation ◽  
Low Frequency ◽  
Mhd Equations ◽  
General Idea ◽  
Gradient Term ◽  
Energy Flows ◽  
Set Up ◽  
Low Frequency Waves

Abstract. The propagation of MHD kink/sausage low frequency waves in the magnetotail with a finite normal Bz component is addressed. The general idea is to investigate how a finite Bz may affect the propagation of MHD eigenmodes in the plasma sheet. The standard MHD equations are linearized and solved numerically in a modified Harris sheet. Boundary conditions are chosen such that energy flows outward of the frame box (free propagating system). An initial perturbation is set up in the pressure gradient term and the wave energy is then traced in the system. While a pure 1-D-Harris sheet constitutes an efficient wave guide for MHD eigenmodes, the introduction of a finite Bz in the zero-order geometry changes significantly the propagation of MHD fluctuations: the eigenmodes propagate much more slowly and carry little energy whereas a pure sound wave is excited and propagates isotropically in the system. The presence of a finite Bz thus tends to inhibit the MHD propagation of energy along the plasma sheet. It tends rather to spread the energy throughout the magnetotail. As an application of the above study, the role of a permanent X-point structure on MHD propagation in the plasma sheet is also explored.

The interaction of high-frequency and low-frequency waves in magnetized plasmas

1988 ◽  
Vol 39 (3) ◽  
pp. 369-384 ◽  
Author(s):  
I. V. Relke ◽  
A. M. Rubenchik
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Magnetized Plasmas ◽  
Magnetic Field Fluctuation ◽  
Hamiltonian Description ◽  
Frequency Wave ◽  
Magnetohydrodynamic Waves ◽  
Self Focusing ◽  
Low Frequency Waves

The interaction of high-frequency and low-frequency waves in magnetized plasmas is considered. The narrowness of high-frequency wave packets makes possible a concise Hamiltonian description of the problem. Some concrete problems are studied with the help of the derived equations. The competitive role of scattering in self-consistent density and magnetic-field fluctuation are considered. The self-focusing and solitons of potential plasma waves and magnetohydrodynamic waves are studied.

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