One of the challenges in astrophysics is describing the motion of cosmic rays in chaotic magnetic fields. I present a qualitative analysis of results from simulations of the motion of cosmic rays in axisymmetric turbulent magnetic fields. A test-particle code was employed using a modified sympletic integration method to calculate the particle trajectories. From the trajectories we calculate the diffusion coefficients along and across the mean field, the particle densities, as well as the particle’s characteristic function and the exact and approximate fourth order velocity correlations which are important in analytical theories describing particle transport across the mean field. We show that having several definitions for the diffusion coefficient can provide insight into the behaviour of those diffusion coefficients as t → ∞. We also show that for early times the parallel characteristic function does not take the form of a Gaussian distribution as assumed in several theories.