## 1. Introduction

[2] Populations of energetic particles observed in the heliosphere are described frequently using transport equations that incorporate diffusion in an essential way. The standard view is that spatial transport of an ensemble of charged particles involves two types of diffusion – parallel diffusion along and perpendicular diffusion across the mean local magnetic field [*Jokipii*, 1966]. To these additional effects such as convection, adiabatic expansion and local acceleration may be added to formulate a complete transport theory [*Parker*, 1965]. This type of transport theory has been successful to the degree that it is tempting to regard the approach as fundamental. There are however problems, especially for perpendicular transport, the most serious of which are observational. As an example, heliospheric energetic particle observations seem to require rapid cross field transport over large expanses of latitude in Ulysses observations [*McKibben et al.*, 2001]. On the other hand the persistence of sharp gradients in the observed flux of solar energetic particles, known as dropouts, seems to set an upper limit on cross field diffusion that is much lower than what is needed to account for latitudinal transport [*Mazur et al.*, 2000]. Evidently, to account for these observed features, one must take in to account factors not ordinarily included in standard diffusive transport theory. These include time dependence of the heliospheric field lines at their base [*Fisk*, 1996; *Giacalone et al.*, 2000] and topological trapping associated with turbulent flux tube structure transverse to the large scale heliospheric magnetic field [*Ruffolo et al.*, 2003; *Chuychai et al.*, 2005, 2007]. Here we further explore the second of these ideas, examining whether charged particles as well as magnetic field lines might experience effects associated with the magnetic field topology of the homogeneous turbulence in which their transport is initiated.

[3] The usual sequence of events in transport is that particles (or field lines) initially stream freely, and then begin to be affected by a random force. Once the random force is sampled over its correlation length (or time) the process of random walk, or diffusion, becomes evident. A well known difficulty arises when the magnetic irregularities responsible for diffusion have reduced dimensionality [*Jokipii et al.*, 1993; *Jones et al.*, 1998], so that diffusion might not occur at all, or perhaps it can only be recovered by defining a suitably designed ensemble. A further difficulty in arriving at a time-asymptotic transport limit (diffusive or not) is that certain subsets of particles with special initial or boundary conditions might require different times to relax to the statistical state, meanwhile retaining memory of the initial state. In this way the pre-diffusive epoch of single particle transport (ordinarily associated with free streaming) might persist for widely varying times, for specially prepared subensembles of particles. Therefore, for example, diffusion might be a good approximation when averaged over all energetic particles in the heliosphere, but might not apply to particles from a particular solar flare as observed at Earth orbit.

[4] The basic idea explored here originates in a careful examination of magnetic flux surfaces in so-called two-component turbulence models. These are a composite of two ingredients – slab (1D) fluctuations that vary only along the (uniform) mean magnetic field direction, and two-dimensional (2D) fluctuations that vary only in the two perpendicular directions [e.g., *Bieber et al.*, 1994]. The superposition of the two types of fluctuations is fully three dimensional (3D) even though the separate components are of reduced dimensionality. Field line trajectories in large amplitude fluctuations of this type [*Matthaeus et al.*, 1995] are well described by diffusion theory, for displacements greater than a few correlation lengths along the mean field, provided that averages are taken over an unbiased random sampling of field lines. However a closer inspection [*Ruffolo et al.*, 2003] reveals that diffusive transport can be greatly delayed for a subset of field lines that begins in the vicinity of O-type neutral points of the 2D fluctuations. This delay is due to the confining topology of the flux tube along with suppressed diffusive escape where the 2D field is strong [*Chuychai et al.*, 2005]. A single 2D flux tube provides a useful model of both contributions to the field line trapping near O-type structures that naturally occur at random locations in 2D turbulence [*Chuychai et al.*, 2007]. If particles injected near O-points experience delays similar to those of the field lines, that may explain the dropouts in solar energetic particles.

[5] We propose that charged particles can experience delays in perpendicular transport associated with the initial magnetic topology into which they are injected. To examine this conjecture, we will examine test particle experiments in which the O-type structure of the transverse fluctuating magnetic field is represented by a single two-dimensional magnetic flux tube with a Gaussian profile, sufficiently small that it does not affect other plasma properties. The rest of the system is the very simple case of a uniform DC magnetic field, on which is superposed a statistically uniform field of magnetostatic 1D slab turbulence that also permeates the flux tube. The results confirm our basic conjecture that temporary trapping leads to a delay in perpendicular transport and the formation of steep perpendicular gradients in an initially localized particle distribution. Trapping is more effective for stronger flux tubes and lower energy test particles.