A covariant formalism for wave propagation applied to stimulated Raman scattering

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 Mima et al. [Phys. Rev. Lett. 57, 1421 (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.