scholarly journals Three-wave interaction and Manley–Rowe relations in quantum hydrodynamics

2014 ◽  
Vol 80 (4) ◽  
pp. 643-652 ◽  
Author(s):  
Erik Wallin ◽  
Jens Zamanian ◽  
Gert Brodin
Keyword(s):  
Wave Interaction ◽  
Magnetized Plasmas ◽  
Coupling Coefficients ◽  
Quantum Hydrodynamics ◽  
Dispersive Term

The theory for nonlinear three-wave interaction in magnetized plasmas is reconsidered using quantum hydrodynamics. The general coupling coefficients are calculated for the generalized Bohm de Broglie term. It is found that the Manley–Rowe relations are fulfilled only if the form of the particle dispersive term coincides with the standard expression. The implications of our results are discussed.

Lagrangian approach to non-linear wave interactions in a warm plasma

1971 ◽  
Vol 6 (1) ◽  
pp. 53-72 ◽  
Author(s):  
J. J. Galloway ◽  
H. Kim
Keyword(s):  
Linear Equations ◽  
Wave Interaction ◽  
Lagrangian Approach ◽  
Linear Wave ◽  
Coupling Coefficients ◽  
Direct Expansion ◽  
Wave Interactions ◽  
Electrostatic Waves ◽  
Non Linear ◽  
Warm Plasma

In this paper, the coupled-mode equations and coupling coefficients for three-wave interaction are derived by a Lagrangian approach for a general medium. A derivation of the Low Lagrangian for a warm plasma is then given, which avoids certain problems associated with the original analysis. An application of the Lagrangian method is made to interaction between collinearly-propagating electrostatic waves, and a coupling coefficient is derived which agrees with a previous result obtained by direct expansion of the non-linear equations. The paper serves primarily to present and demonstrate a conceptually useful and efficient theoretical approach to non-linear wave interactions.

Kinetic theory for MHD-wave coupling coefficients

1992 ◽  
Vol 47 (3) ◽  
pp. 361-371 ◽  
Author(s):  
Ralf Elvsén
Keyword(s):  
Kinetic Theory ◽  
Wave Interaction ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Coupling Coefficients ◽  
Wave Coupling ◽  
Fluid Theory

The coupling coefficients for resonant three-wave interaction of magnetosonic and Alfvén waves, derived by means of kinetic theory, are presented. The calculations allow for anisotropic background temperatures. The results are compared with previous ones from fluid theory.

Three-wave interaction in a magnetized Vlasov plasma

1975 ◽  
Vol 14 (3) ◽  
pp. 467-473 ◽  
Author(s):  
J. Larsson
Keyword(s):  
Maxwell Equations ◽  
Wave Interaction ◽  
Resonant Interaction ◽  
Magnetized Plasma ◽  
Coupling Coefficients ◽  
Symmetric Form ◽  
Vlasov Plasma

The resonant interaction of three waves in a uniform hot magnetized plasma is examined. The coupling coefficients are obtained in a symmetric form from the Vlasov-Maxwell equations.

Nonlinear decay of dispersive Alfvén wave and solar coronal heating

2010 ◽  
Vol 77 (2) ◽  
pp. 237-244 ◽  
Author(s):  
SANJAY KUMAR ◽  
R. P. SHARMA
Keyword(s):  
Wave Interaction ◽  
Magnetized Plasma ◽  
Alfven Wave ◽  
Growth Time ◽  
Coupling Coefficients ◽  
Nonlinear Excitation ◽  
Simple Description ◽  
Wave Decay ◽  
Dispersive Alfvén Wave ◽  
Model Equations

AbstractThis paper presents a simple description of three-wave decay interactions involving a pump dispersive Alfvén wave (DAW), decay DAW and decay slow wave (SW) in a uniform magnetized plasma. When the ponderomotive nonlinearities are incorporated in DAW dynamics, the model equations governing the nonlinear excitation of the SWs by DAW in the low-β plasmas (β ≪ me/mi as applicable to solar corona) are given. The expressions for the coupling coefficients of the three-wave interaction have been derived. The growth rate of the instability is also calculated and found that the value of the decay growth time comes out to be of the order of milliseconds at the pump DAW amplitude B0y/B0 = 10−3.

A new Hamiltonian formulation for fluids and plasmas. Part 3. Multifluid electrodynamics

1996 ◽  
Vol 55 (2) ◽  
pp. 279-300 ◽  
Author(s):  
Jonas Larsson
Keyword(s):  
Nonlinear Theory ◽  
Hamiltonian Structure ◽  
Hamiltonian Formulation ◽  
Wave Interaction ◽  
Hermitian Structure ◽  
Coupling Coefficients ◽  
Symmetric Form ◽  
Hamiltonian Perturbation

The Hamiltonian structure underlying ideal multifluid electrodynamics is formulated in a way that simplifies Hamiltonian perturbation calculations. We consider linear and lowest-order nonlinear theory, and the results in Part 1 of this series of papers are generalized in a satisfactory way. Thus the Hermitian structure of linearized dynamics is derived, and we obtain the coupling coefficients for resonant three-wave interaction in symmetric form, giving the Manley–Rowe relations.

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.

Three-wave coupling coefficients for non-uniform plasmas

1981 ◽  
Vol 26 (3) ◽  
pp. 407-418 ◽  
Author(s):  
T. Lindgren ◽  
J. Larsson ◽  
L. Stenflo
Keyword(s):  
Wave Propagation ◽  
Wave Interaction ◽  
Density Gradients ◽  
Coupling Coefficients ◽  
Wave Coupling ◽  
Coupling Processes

Resonant three-wave interaction in a spatially non-uniform magnetized fluid plasma is considered. We calculate the coupling coefficientsVjfor wave propagation in arbitrary directions and demonstrate that new terms, which appear inVjowing to the presence of density gradients, can dominate actual wave coupling processes.

A new Hamiltonian formulation for fluids and plasmas. Part 1. The perfect fluid

1996 ◽  
Vol 55 (2) ◽  
pp. 235-259 ◽  
Author(s):  
Jonas Larsson
Keyword(s):  
Perfect Fluid ◽  
Generating Functions ◽  
Hamiltonian Formulation ◽  
Wave Interaction ◽  
Coupling Coefficients ◽  
Lagrange Equations ◽  
Time Dynamics ◽  
Promising Tool ◽  
Fluid Equations ◽  
New Formulation

A new formulation of the Hamiltonian structure underlying the perfect fluid equations is presented. Besides time, a parameter c is also used. Correspondingly, there are two interdependent systems of equations expressing time evolution and e evolution respectively. The accessibility equations define the e dynamics and give the variation in the usual Eulerian fluid variables as determined by the generating functions. The time evolutions of both the Eulerian fluid variables and the generating functions are obtained from an action principle. The consistency of the e and the time dynamics is crucial for this formulation, i.e. the accessibility equations must be propagated in time by the Euler–Lagrange equations. The reason for introducing this new formulation is its power in certain applications where the existing Hamiltonian alternatives seem less convenient to use. In particular, it is a promising tool for Hamiltonian perturbation theory. We consider the small-amplitude expansion, and find, very simply and naturally, the Hermitian structure of the linearized ideal fluid equations as well as coupling coefficients for resonant three-wave interaction exhibiting the Manley–Rowe relations.

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