Resonant Four-Wave Interaction of Electron-Plasma Oscillations

The time evolution of a uniformly turbulent ensemble of electron fluids is studied in the electrostatic approximation. A kinetic equation for the action density is obtained in the longwavelength limit, in which resonant four-wave processes cause the nonlinear transfer of energy in the oscillation spectrum. It is shown that the entire region of $\overrightarrow{\mathrm{k}}$ space (within the limits of the simple-fluid model) is accessible to resonant four-wave interactions. Such fourwave mode coupling serves as a mechanism for the transfer of wave energy into shorter wavelengths.