Nonlinear coupling of small-amplitude waves in a plasma

A DP device is used to study the nonlinear coupling between a small-amplitude ion wave and a small-amplitude electron wave propagated on a weak electron beam with a directed energy of about 30 volts. The two waves are excited externally, so that both the frequencies and the amplitudes are controllable. Typically, the electron wave is driven at about 300 MHz and has a wave potential which is three to four orders of magnitude below the electron temperature. The ion wave frequency is variable over a wide range of several hundred kilohertz, and its wave potential is two orders of magnitude below the electron temperature. Interaction products of the two driven waves are observed as both upper and lower sidebands of the electron wave. Absolute values of all wave amplitudes are measured using electrostatic probes. The wavelengths are determined by a highly selective two-probe heterodyne interferometer. The interaction products propagate with phase velocities which are quite different from those of the driven waves. The experimental results are analyzed in terms of a one-dimensional steady-state three-wave interaction model based on a second-order perturbation of the Vlasov-Poisson equations. The resonance conditions on frequency and wave number are verified exactly. The matrix element which couples the waves is both measured experimentally and derived theoretically; its dimensionless value is much larger than unity. The agreement between the experimental results and the theory is good