Coherent four-wave scattering in plasmas—application to plasma diagnostics

An explicit solution for the third-order nonlinear transverse susceptibility and for the scattered power in a collisionless unmagnetized plasma is presented. We show that a consistent second-order approximation of the Vlasov equation that treats on equal footing the electric and the magnetic fields of the electromagnetic waves produces a ponderomotive force term that drives various plasma excitations. In analogy with Thomson scattering from thermal fluctuations, the wavevector and frequency dependence of the scattered power is dominated by the first-order longitudinal susceptibilities of the plasma. Even though the Landau damping may be considerable and the plasma resonances may not be well defined, the coherent nature of this four-photon process produces a considerably enhanced scattered power within a narrow scattering cone. These features make this technique well suited for plasma diagnostics. These techniques are a close counterpart of the coherent anti-Stokes Raman spectroscopy and the Raman-induced Kerr effect spectroscopy used with Raman active transitions in gas, liquid, and solid spectroscopy.