Perpendicular transport in isotropic magnetic turbulence. The role of stochastic drifts

In the context of cosmic ray propagation in a turbulent magnetic field, transport perpendicular to the mean field plays an important role in a variety of situations of physical interest. Numerical simulations of test particles in isotropic turbulence with a guide field show that, for r_L<L_c, the parallel and perpendicular diffusion coefficients scale differently with energy, so that the corresponding ratio D_⊥/D_∥ increases with energy. Several attempts have been made to address this phenomenon, but no consensus theoretical understanding has yet been reached. We used test-particle numerical simulations of particle transport in synthetic turbulence over a broad energy range to establish a general trend of the perpendicular diffusion coefficient. We also provide a theoretical description of our findings based on an extension of the nonlinear guiding-center theory that includes stochastic drifts. The numerical simulations of isotropic turbulence are based on a wavelet method that allows us to reproduce turbulence over ∼ 6-7 orders of magnitude in wavenumber. This wide wavenumber range is reflected in a correspondingly wide energy range for test particles. The theoretical part presents a novel description of perpendicular transport based on autocorrelation functions of turbulent magnetic fields. It describes how particles diffuse perpendicular to the field lines through a combination of field-line random walk and random drift motion of the guiding center. We demonstrate that, for diverse levels of turbulence, the perpendicular diffusion coefficient has the same energy dependence as the parallel diffusion coefficient only at energies corresponding to r_Lłesssim 10^ -2 L_c, where r_L is the particle Larmor radius and L_c is the coherence length of the turbulence. At higher energies, the perpendicular diffusion coefficient acquires a stronger energy dependence. Our theoretical approach suggests that this phenomenon is likely attributable to stochastic drifts that particles experience perpendicular to the guide field when a component of the turbulent field is parallel to it.