PHASE-SPACE DESCRIPTION OF PLASMA-WAVES .2. NONLINEAR-THEORY

A representation of the physical fields as functions on (k, omega, r, t) phase space can be based on Gaussian windows and Fourier transforms. Within this representation, we obtain a very general formula for the second-order nonlinear current J(k, omega, r, t) in terms of the vector potential A(k, omega, r, t). This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasmas, including the effects of inhomogeneous turbulence, wave convection and refraction.