  It is shown that partial incoherence, in the form of stochastic phase noise,
of a Langmuir wave in an unmagnetized plasma gives rise to a Landau-type
damping. Starting from the Zakharov equations, which describe the nonlinear
interaction between Langmuir and ion-acoustic waves, a kinetic equation is
derived for the plasmons by introducing the Wigner-Moyal transform of the
complex Langmuir wave field. This equation is then used to analyze the
stability properties of small perturbations on a stationary solution consisting
of a constant amplitude wave with stochastic phase noise. The concomitant
dispersion relation exhibits the phenomenon of Landau-like damping. However,
this damping differs from the classical Landau damping in which a Langmuir
wave, interacting with the plasma electrons, loses energy. In the present
process, the damping is non-dissipative and is caused by the resonant
interaction between an instantaneously-produced disturbance, due to the
parametric interactions, and a partially incoherent Langmuir wave, which can be
considered as a quasi-particle composed of an ensemble of partially incoherent
plasmons.
