Models of random magnetic fields and some implications for turbulence structure and particle transport in the heliosphere

Abstract

We consider the magnetic field line random walk in the two-component model of magnetic turbulence (2D+slab), which is a reasonable model for magnetic fields in interplanetary space. We develop the theory for the diffusion of field lines in non-asixymmetric 2D+slab turbulence. The solution is in the form of non-perturbative coupled bi-quadratic equations. The separation of two adjacent field lines in 2D+slab axisymmetric turbulence has also been analytically examined in this research. We found two diffusive regimes, with slow diffusion at short distances and fast diffusion in the long distance limit. The theories have been verified by the numerical simulations. Furthermore, we also explain the dropout phenomena of solar energetic particle transport by representing the field line trajectories in 2D+slab turbulence as a guiding center motion of the particles. Here, the idea of conditional statistics is introduced, in which we propose that the field linetrajectories depend on the topology of the potential function of 2D turbulence at the starting point. We perform numerical simulations, which support our idea. The results show that field lines starting near O-points are temporarily trapped within 2D islands while the field lines initially located near X-points rapidly diffuse away from 2D islands. When we simply set the 2D potential function as a Gaussian, we found that the strong 2D field can suppress the random walk of field lines inside in 2D islands and derive a quasilinear theory to explain this. This research provides a better understanding of the transport of particles in the heliosphere and can be applied to other similar systems.