  Non-linear wave-driven processes in plasmas are normally described by either
a monochromatic pump wave that couples to other monochromatic waves, or as a
random phase wave coupling to other random phase waves. An alternative approach
involves an incoherent, random or broadband pump coupling to monochromatic
and/or coherent structures in the plasma. This approach can be implemented
through the wave kinetic model. In this model, the incoming pump wave is
described by either a bunch (for coherent waves) or a sea (for random phase
waves) of quasi-particles. A particle-in-cell type code has been developed to
perform numerical simulations of such interactions using the quasi-particle
approach. This code allows for a comparatively easy description of both random
phase and coherent pump pulses coupling to slow electrostatic plasma waves,
while providing an extended range of powerful diagnostics leading to a deeper
physical insight into the dynamics of the fast waves. As an example, the
propagation of short, intense laser pulses through a plasma has been simulated.
A sample of the phenomena that can be studied for this case includes
modulational instabilities, photon wave breaking and turbulence, and pulse
compression, stretching, and chirping. The extensibility of the numerical
implementation to other types of fast wave-slow wave interactions is also
discussed.
