  Aims. The random walk of energetic charged particles in turbulent magnetic
fields is investigated. Special focus is placed on transport across the mean
magnetic field, which had been found to be subdiffusive on many occasions.
Therefore, a characterization using the concept of ergodicity is attempted by
noting the connection to the time evolution of the mean-square displacement.
Methods. Based on the test-particle approach, a numerical Monte-Carlo
simulation code is used to integrate the equation of motion for particles that
are scattered by magnetic turbulence. The turbulent fields are generated by
superposing plane waves with a Kolmogorov-type power spectrum. The individual
particle trajectories are then used to calculate a variety of statistical
quantities. Results. The simulation results clearly demonstrate how the
heterogeneity of the particle ensemble causes the system to be weakly
non-ergodic. In addition, it is shown how the step length distribution varies
with the particle energy. In conclusion, cross-field transport is non-Gaussian
but still almost diffusive.
