[1] We employ a turbulence transport model to compute distributions of turbulence throughout the heliosphere. The model determines the radial dependence of three (coupled) quantities that characterize interplanetary turbulence, the energy per unit mass, the cross helicity or Alfvénicity, and a similarity length scale. A fourth integrated quantity, the plasma temperature, is modified by heat deposition due to turbulent dissipation. The model includes advection, expansion, and reflection effects as well as the tendency toward dynamic alignment, and a von Kármán type dissipation function that represents decay of turbulence due to cascade to small scales. Two types of forcing are also featured, one a simple model of stream shear, and the other a driving in the outer heliosphere associated with wave energy injection due to pickup protons of interstellar origin. Parameters for the model have been tuned using observation data from Voyager and Ulysses. We analyze the constraining observations to provide boundary conditions and parameters that vary with heliocentric latitude, with some extrapolations. The fully assembled model permits the computation of the distribution of turbulence throughout the entire heliosphere, and we present solutions for several appropriate parameter sets.

Two-dimensional (2D) models of magnetic field fluctuations and turbulence are widely used in space, astrophysical, and laboratory contexts. Here we discuss some general properties of such models and their observable power spectra. While the field line random walk in a one-dimensional (slab) model is determined by the correlation scale, for 2D models, it is characterized by a different length scale, the ultrascale. We discuss properties of correlation scales and ultrascales for 2D models and present a technique for determining an ultrascale from observations at a single spacecraft, demonstrating its accuracy for synthetic data. We also categorize how the form of the low-wavenumber spectrum affects the correlation scales and ultrascales, thus controlling the diffusion of magnetic field lines and charged test particle motion.

We present results from direct numerical simulations showing the suppression of the large-scale drift motion of an ensemble of charged particles in a nonuniform turbulent magnetic field. We find that when scattering is negligible, the ensemble average drift velocity is in the direction predicted by the usual guiding center theory. When scattering is very strong, we find that all large-scale drift motions vanish. For an intermediate amount of scattering we find that the antisymmetric drift velocity is typically suppressed by a larger amount than the antisymmetric drift coefficient. We show that the total drift motion of the ensemble is not necessarily completely contained in the antisymmetric part of the diffusion tensor. Because of the occurrence of scattering, knowledge of the spatial variation of the symmetric part of the diffusion tensor is also needed to fully describe the total drift motion of the ensemble.

[1] A transport theory including cross helicity, magnetohydrodynamic (MHD) turbulence, and driving by shear and pickup ions, is applied to the radial evolution of the solar wind. The radial decrease of cross helicity observed in the solar wind can be accounted for when sufficient driving is included to overcome the inherent tendency for MHD turbulence to produce Alfvénic states.

[1] We employ a turbulence transport theory to explain the high-latitude radial evolution of cross helicity, or Alfvénicity, observed by the Ulysses spacecraft. Evolution is slower than at low latitudes due to weakened shear driving.

Q1,Q2 We examine energetic charged particle diffusion perpendicular to a mean magnetic field B 0 due to turbulent fluctuations in a plasma, relaxing the common assumption of axisymmetry around B 0 and varying the ratio of two fluctuation components, a slab component with parallel wavenumbers and a two-dimensional (2D) component with perpendicular wavenumbers. We perform computer simulations mostly for 80% 2D and 20% slab energy and a fluctuation amplitude on the order of B 0. The nonlinear guiding center (NLGC) theory provides a reasonable description of asymptotic perpendicular diffusion as a function of the nonaxisymmetry and particle energy. These values are roughly proportional to the particle speed times the field line diffusion coefficient, with a prefactor that is much lower than in the classical field line random walk model of particle diffusion. NLGC predicts a prefactor in closer agreement with simulations. Next we consider extreme fluctuation anisotropy and the approach to reduced dimensionality. For 99% slab fluctuation energy, field line trajectories are diffusive, but the particle motion is subdiffusive. For 99% 2D fluctuation energy, both field lines and particle motions are initially subdiffusive and then diffusive, but NLGC gives unreliable results. The time dependence of the running particle diffusion coefficient shows that in all cases asymptotic diffusion is preceded by free streaming and subdiffusion, but the latter differs from standard compound subdiffusion. We can model the time profiles in terms of a decaying negative correlation of the perpendicular velocity due to the possibility of backtracking along magnetic field lines.

We present direct numerical simulations of charged-particle transport in a turbulent magnetic field. The magnetic field model used in the simulations consists of a composite of statistically homogeneous slab and two-dimensional turbulence representative of solar wind conditions at Earth. This turbulent magnetic field is then added to a uniform background magnetic field. We find that the parallel and perpendicular mean free paths are well described by power laws as a function of rigidity at different turbulence levels. At a low level of turbulence we find that quasi-linear theory and the field line random walk theory for the parallel and perpendicular mean free paths, respectively, provide predictions that are in good agreement with the simulated mean free paths. At intermediate turbulence levels the simulated parallel and perpendicular mean free paths are best accounted for by recently proposed nonlinear theories, while quasi-linear theory and the field line random walk theory overestimate the simulated mean free paths. At high turbulence levels neither quasi-linear theory and the field line random walk theory nor the nonlinear theories provide predictions that are in good agreement with the simulated parallel and perpendicular mean free paths.

[1] We examine charged particle transport perpendicular to the large scale magnetic field. We find that the limit of an infinite parallel mean free path of particles diffusing along the large scale magnetic field is a necessary condition for which the diffusive spread of the magnetic field lines leads to a proportional spread of the particles. When it occurs this requires that parallel mean free path is well in excess of the smaller of the system size and the turbulence ultrascale. However, there are alternative situations in which particles may diffuse, but field lines do not. In the latter cases the asymptotic behavior is that which persists after the parallel mean free path exceeds some multiple of the correlation scales. This phenomenon of diffusing particles/non-diffusing field lines is typically determined by the 2D turbulence spectrum, where the diffusion coefficient of the magnetic field due to 2D turbulence can diverge if the spectrum of the 2D fluctuations is not well behaved at small wave numbers. We also show that the classical relation between parallel and perpendicular diffusion for high energy particles is consistent with the field line random walk description of particle diffusion.