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

1996 ◽  
Vol 55 (2) ◽  
pp. 279-300 ◽  
Author(s):  
Jonas Larsson

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.

1975 ◽  
Vol 14 (3) ◽  
pp. 467-473 ◽  
Author(s):  
J. Larsson

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.


1996 ◽  
Vol 55 (2) ◽  
pp. 235-259 ◽  
Author(s):  
Jonas Larsson

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.


1996 ◽  
Vol 14 (3) ◽  
pp. 304-308 ◽  
Author(s):  
P. Axelsson ◽  
J. Larsson ◽  
L. Stenflo

Abstract. The resonant interaction between three acoustic gravity waves is considered. We improve on the results of previous authors and write the new coupling coefficients in a symmetric form. Particular attention is paid to the low-frequency limit.


2014 ◽  
Vol 80 (4) ◽  
pp. 643-652 ◽  
Author(s):  
Erik Wallin ◽  
Jens Zamanian ◽  
Gert Brodin

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.


1971 ◽  
Vol 6 (1) ◽  
pp. 53-72 ◽  
Author(s):  
J. J. Galloway ◽  
H. Kim

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.


1996 ◽  
Vol 55 (2) ◽  
pp. 261-278 ◽  
Author(s):  
Jonas Larsson

The new Hamiltonian formulation of the perfect fluid equations presented in part 1 of this series of papers is generalized to a class of IVIHD models, including for example ideal MHD and the Chew–Goldberger–Low equations. The mathematical structure is to a great extent unchanged by this generalization, and most results about the small-amplitude expansion of the perfect fluid equations remain obviously valid. For example, we now have a rigorous proof of the Manley-Rowe relations in resonant three-wave interaction, valid for this class of MHD models and for quite general inhomogeneous but stationary background states, including equilibrium flows.


1992 ◽  
Vol 47 (3) ◽  
pp. 361-371 ◽  
Author(s):  
Ralf Elvsén

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.


1998 ◽  
Vol 5 (1) ◽  
pp. 3-12 ◽  
Author(s):  
R. Grimshaw ◽  
S. R. Pudjaprasetya

Abstract. We consider solitary waves propagating on the interface between two fluids, each of constant density, for the case when the upper fluid is bounded above by a rigid horizontal plane, but the lower fluid has a variable depth. It is well-known that in this situation, the solitary waves can be described by a variable-coefficient Korteweg-de Vries equation. Here we reconsider the derivation of this equation and present a formulation which preserves the Hamiltonian structure of the underlying system. The result is a new variable-coefficient Korteweg-de Vries equation, which conserves energy to a higher order than the more conventional well-known equation. The new equation is used to describe the transformation of an interfacial solitary wave which propagates into a region of decreasing depth.


2012 ◽  
Vol 24 (7) ◽  
pp. 1513-1514
Author(s):  
薛智浩 Xue Zhihao ◽  
刘濮鲲 Liu Pukun ◽  
杜朝海 Du Chaohai

2010 ◽  
Vol 77 (2) ◽  
pp. 237-244 ◽  
Author(s):  
SANJAY KUMAR ◽  
R. P. SHARMA

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.


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