Numerical study of Cosmic Ray Diffusion in MHD turbulence

We study diffusion of Cosmic Rays (CRs) in turbulent magnetic fields using test particle simulations. Electromagnetic fields are produced in direct numerical MHD simulations of turbulence and used as an input for particle tracing, particle feedback on turbulence being ignored. Statistical transport coefficients from the test particle runs are compared with earlier analytical predictions. We find qualitative correspondence between them in various aspects of CR diffusion. In the incompressible case, that we consider in this paper, the dominant scattering mechanism occurs to be the non-resonant mirror interactions with the slow-mode perturbations. Perpendicular transport roughly agrees with being produced by magnetic field wandering.Comment: 8 pages, 8 figures, ApJ sub

Non-locality of Hydrodynamic and Magnetohydrodynamic Turbulence

We compare non-locality of interactions between different scales in hydrodynamic (HD) turbulence and magnetohydrodynamic (MHD) turbulence in a strongly magnetized medium. We use 3-dimensional incompressible direct numerical simulations to evaluate non-locality of interactions. Our results show that non-locality in MHD turbulence is much more pronounced than that in HD turbulence. Roughly speaking, non-local interactions count for more than 10\% of total interactions in our MHD simulation on a grid of $512^3$ points. However, there is no evidence that non-local interactions are important in our HD simulation with the same numerical resolution. We briefly discuss how non-locality affects energy spectrum.Comment: 6 pages, 5 figure

Comparison of spectral slopes of magnetohydrodynamic and hydrodynamic turbulence and measurements of alignment effects

We performed a series of high-resolution (up to 1024^3) direct numerical simulations of hydro and MHD strong turbulence. We found that for simulations with normal viscosity the slopes for spectra of MHD are similar, although slightly more shallower than for hydro simulations. However, for simulations with hyperviscosity the slopes were very different, for instance, the slopes for hydro simulations showed pronounced and well-defined bottleneck effect, while the MHD slopes were relatively much less affected. We believe that this is indicative of MHD strong turbulence being less local than Kolmogorov turbulence. This calls for revision of MHD strong turbulence models that assume local "as-in-hydro case" cascading. Nonlocality of MHD turbulence casts doubt on numerical determination of the slopes with currently available (512^3--1024^3) numerical resolutions, including simulations with normal viscosity. We also measure various so-called alignment effects and discuss their influence on the turbulent cascade.Comment: 10 pages, 6 figures, extended version, ApJ accepte