Electromagnetic wave propagation in turbulent and nonlinear plasmas

The propagation of an electromagnetic wave in a time stationary turbulent and nonlinear plasma is studied with a view to ascertaining the statistical moments of the wavefield. The authors find that the functional method which was used by Hopf in his study of ordinary turbulence is a powerful one also for turbulent and nonlinear media. A functional differential equation is derived for the moments of electromagnetic waves propagating in an isotropic plasma in which the dielectric constant undergoes statistical fluctuations. Using the Markov and small-angle forward-scattering approximations, they find a hierarchy of coupled partial differential equations for the moments containing different wave numbers. An approximate perturbation method is devised for decoupling and solving the hierarchy to any desired order. They draw attention to the similarity of the closure problem of the moment equations to that in turbulence generally and in statistical mechanics. Possible applications are discussed.