We investigate test-particle diffusion in dynamical turbulence based on a numerical approach presented before. For the turbulence we employ the nonlinear anisotropic dynamical turbulence model which takes into account wave propagation effects as well as damping effects. We compute numerically diffusion coefficients of energetic particles along and across the mean magnetic field. We focus on turbulence and particle parameters which should be relevant for the solar system and compare our findings with different interplanetary observations.We vary different parameters such as the dissipation range spectral index, the ratio of the turbulence bendover scales, and the magnetic field strength in order to explore the relevance of the different parameters. We show that the bendover scales as well as the magnetic field ratio have a strong influence on diffusion coefficients whereas the influence of the dissipation range spectral index is weak.The best agreement with solar wind observations can be found for equal bendover scales and a magnetic field ratio of δB/B 0 = 0.75.
In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester & Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.
We explore analytically and numerically the motion of energetic particles such as electrons and protons through space. The electrically charged particles interact with a large scale or mean field B 0 and a turbulent component B d leading to a complicated stochastic motion. This type of physical scenario is important in plasma physics as well as particle astrophysics. Years ago a quasi-linear theory for particle transport was developed and applied in hundreds of research papers. Whereas it became clear that quasi-linear theory does not work for the transport of energetic particles across a large scale field, it is still unclear for which parameter regimes the theory works if diffusion along that field is explored. In the current paper, we therefore combine quasi-linear theory with dynamical isotropic turbulence and different turbulence spectra. The obtained results are then compared with test-particle simulations. We show that in the general case, quasi-linear theory does not provide an accurate description of parallel transport for isotropic turbulence even if dynamical turbulence effects are included.
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