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A covariant formalism for wave propagation applied to stimulated Raman scattering. (English) Zbl 0661.76122

The governing equations for stimulated Raman scattering are derived in a Lorentz frame moving with arbitrary velocity relative to the background plasma. These equations are fundamental to the study of relativistic beat-wave solitary waves, which have recently been proposed for particle acceleration by K. Mima, T. Ohsuga, H. Takabe, K. Nishihara, E. Zaidman and W. Horton [Phys. Rev. Lett. 57, 1421-1424 (1986)]. An averaged Lagrangian density is constructed for this three-wave interaction. This results in a natural definition for the action flux density four-vector of each wave and the combined stress- energy tensor. It also follows from the Lagrangian structure of the system that the Manley-Rowe relations are satisfied. The covariant formalism presented here can also be used to study wave propagation in a multicomponent plasma, in which each plasma species moves with arbitrary velocity relative to the frame of observation. As a specific example, the dispersion relation for Langmuir-wave propagation in two warm relativistic electron beams is derived for the first time.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76M99 Basic methods in fluid mechanics
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