The role of nonlinear beating currents in the theory of parametric instabilities

It is shown that there are two contributions to the nonlinear beating current density arising from the interaction of a high‐frequency pump wave with a Langmuir wave. One of these has its origin in the product of the charge density of the Langmuir wave with the velocity vector of an electron due to the uniform high‐frequency pump field. The other one has not been given in explicit form before; its direction is that of the wave vector of the Langmuir wave for the case of an unmagnetized plasma and a dipole pump. If the wave vector of the Langmuir wave is parallel to the pump electric field and if the frequency ω2 of the Langmuir wave is only slightly smaller than the pump frequency ω1, then the two contributions almost cancel each other. However, in the more complicated case of collisional and magnetized plasmas the wave vector of the Langmuir wave is generally not parallel to the pump electric field. The current result makes it plausible that the two contributions to the nonlinear beating current may not cancel each other even for ω2 = ω1.