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Anisotropic cosmic-ray diffusion in isotropic Kolmogorov turbulence

Understanding the time scales for diffusive processes and their degree of anisotropy is essential for modelling cosmic-ray transport in turbulent magnetic fields. We show that the diffusion time scales are isotropic over a large range of energy and turbulence levels, notwithstanding the high degree of anisotropy exhibited by the components of the diffusion tensor for cases with an ordered magnetic field component. The predictive power of the classical scattering relation as a description for the relation between the parallel and perpendicular diffusion coefficients is discussed and compared to numerical simulations. Very good agreement for a large parameter space is found, transforming classical scattering relation predictions into a computational prescription for the perpendicular component. We discuss and compare these findings and in particular the time scales to become diffusive with the time scales that particles reside in astronomical environments, the so-called escape time scales. The results show that, especially at high energies, the escape times obtained from diffusion coefficients may exceed the time scales required for diffusion. In these cases, the escape time cannot be determined by the diffusion coefficients.