Particle diffusion in random fields: Time-nonlocal description and numerical simulations

The theory of time-nonlocal random processes formulated in terms of the non-Markovian Fokker–Planck equation is used to describe the results of numerical simulations of particle diffusion in the random longitudinal field with given statistical properties. The simulations of particle motion were performed for the wide range of particle velocity and random field parameters. It is confirmed that conventional quasilinear theory in the approximation disregarding the time and velocity dependence of the diffusion coefficient in the velocity space can be used only in the case of small intensity and large width of turbulent field spectrum. The increase of the intensity as well as the decrease of the spectral width lead to considerable deviation of the results of simulations (such as saturation and frequent oscillation of the mean-square velocity displacement) from the predictions of the quasilinear theory. It is shown that in the case of small intensities these deviations can be successfully described in terms of non-Markovian generalization of the quasilinear approximation. In the case of high field intensity the description of these features would require more consistent account for the diffusion coefficient velocity dependence and time-nonlocal effects.