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The computation of charged particle orbits in model turbulent magnetic fields is used to investigate the properties of particle transport in the directions perpendicular to the large-scale magnetic field. Recent results by Qin, Matthaeus, & Bieber demonstrate that parallel scattering suppresses perpendicular diffusion to a subdiffusive level when the turbulence lacks transverse structure. Here numerical computations are used to show that in turbulence in which there is substantial transverse structure, a second regime of diffusive transport can be established. In both the subdiffusion regime and this "second diffusion" regime, perpendicular transport is intrinsically nonlinear. The regime of second diffusion persists for long times and may therefore be of interest in astrophysical transport problems such as the scattering and solar modulation of cosmic rays.

This paper presents a model calculation of solar energetic particle propagation in a three-dimensional interplanetary magnetic field. The model includes essentially all the particle transport mechanisms: streaming along magnetic field lines, convection with the solar wind, pitch-angle diffusion, focusing by the inhomogeneous interplanetary magnetic field, perpendicular diffusion, and pitch-angle dependent adiabatic cooling by the expanding solar wind. We solve the Fokker-Planck transport equation with simulation of backward stochastic processes in a fixed reference frame in which any spacecraft is roughly stationary. As an example we model the propagation of those high-energy (E 10 MeV) solar energetic particles in gradual events that are accelerated by large coronal mass ejection shocks in the corona and released near the Sun into interplanetary space of a Parker spiral magnetic field. Modeled with different scenarios, the source of solar energetic particles can have a full or various limited coverages of latitude and longitude on the solar surface. We compute the long-term time profiles of particle flux and anisotropy at various locations in the heliosphere up to 3 AU, from the ecliptic to high latitudes. Features from particle perpendicular diffusion are revealed. Our simulation reproduces the observed reservoir phenomenon of solar energetic particles with constraints on either solar particle source or the magnitude of perpendicular diffusion.

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[1] A nonlinear guiding center (NLGC) theory for diffusion of charged particles perpendicular to the mean magnetic field was recently proposed. Here, we draw attention to a number of attractive features of this theory:(1) The theory provides a natural mechanism to connect the perpendicular mean free path with the parallel mean free path. In fact, the parallel mean free path is the only particle property required to determine uniquely the perpendicular mean free path. (2) Under a broad range of conditions, the theory predicts that the perpendicular mean free path will be of order one percent or a few percent of the parallel mean free path, in agreement with numerical simulations of particle transport. (3) For conditions representative of the inner heliosphere, the theory predicts values of the perpendicular mean free path in agreement with observational determinations from Jovian electrons and from modeling Ulysses observations of Galactic protons.

[1] Transport of charged particles across the mean magnetic field due to broad band, powerlaw-distributed magnetic fluctuations is examined by direct computation of a large number of charged test particle trajectories. Fluctuations consist of a one dimensional slab spectrum with an additional 0.01 percent level of two dimensional fluctuations; the net field has no ignorable directions. We find that, at long times (t), the mean square displacements subdiffusively scale as $t 1/2 . This confirms that perpendicular diffusion is suppressed when turbulence lacks strong three dimensional structure, in agreement with theories of Urch and of Kóta and Jokipii.

Computation of charged-particle orbits shows that large-amplitude two-dimensional magnetic turbulence supports diffusive transport of charged test particles parallel to the mean magnetic field. This stands in sharp contrast to scattering in the quasi-linear approximation, for which we show quite generally that the two-dimensional scattering rate vanishes. We also demonstrate that at large amplitude, two-dimensional turbulence makes important contributions to the parallel mean free path of particles in mixtures of two-dimensional and slab turbulence. This raises important questions regarding cosmic-ray mean free paths that had been thought to be settled based on quasi-linear theory.