Test-particle transport: higher-order correlations and time-dependent diffusion

In recent years progress has been achieved in the theory of propagating particles that experience scattering due to interactions with magnetic turbulence. Modern theories for transport are nonlinear as opposed to the traditional quasilinear approach. However, nonlinear theories are based on certain assumptions such as approximations of higher-order correlations. Recently it has been demonstrated that very simple approaches, such as the replacement of fourth-order correlations by a product of two second-order correlations, are often not appropriate. In this paper fourth-order correlations are studied analytically by solving the Fokker-Planck equation of particle transport. Special cases are considered for which an exact analytical treatment is possible. Thereafter, the general case is explored using approximations. A unified theory is derived for compound diffusion, the field line random walk limit, and Markovian diffusion of energetic particles.