On the ergodicity of perpendicular cosmic ray transport

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.