Space–time formulation of plasma turbulence theory

A formulation of plasma turbulence theory is developed which is based on the concept of the response function of the turbulent system to an infinitesimal, localized external perturbation. This infinitesimal response function describes the normal modes of the turbulent system. The theory is developed as an expansion in powers of the assumed small ratio of the incoherent wave energy to the particle kinetic energy. It is also assumed that while the wave fluctuations are weakly correlated, strong coherent fields may also be present which make the system arbitrarily nonstationary in time and inhomogenous in space. The equations of the system are therefore developed in physical space and time rather than in Fourier space. The first two orders of iteration are carried out to obtain the space–time analogs of all the familiar weak turbulence processes.