Pitch-angle diffusion coefficients in test particle simulations and the estimation of the particle parallel mean free path

The transport of energetic charged particles in turbulent magnetic fields is a topic of interest in various astrophysical contexts. In order to estimate the mean free path of a particle in the direction parallel to the mean magnetic field, one can use theoretical expressions that employ pitch-angle diffusion coefficients. In this work we review some of the methods used in estimating pitch-angle diffusion coefficients from test particle computer simulations. We examine if these methods and theoretical approaches are able to provide consistent estimates of the parallel mean free path, that can also be obtained directly from computer simulations. We perform test particle simulations for synthetic turbulence models over a range of turbulence parameters and particle energies. From the trajectories of test particles, pitch-angle distribution functions and statistics of pitch-angle displacements are obtained, which are then used to estimate the pitch-angle diffusion coefficients. We find that a method using the pitch-angle flux and derivative of the pitch-angle distribution is able to provide accurate values for the parallel mean free path over the range of parameters considered. Other methods considered are accurate only for a limited range of the turbulent fluctuation strength, or must be evaluated at a specific time to provide a reasonable estimate.