Random walk of magnetic field lines for different values of the energy-range spectral index

TL;DR

This paper investigates how the energy-range spectral index affects magnetic field line wandering, demonstrating superdiffusive behavior generally, with free-streaming when the spectral index exceeds one, suggesting superdiffusion as the typical pattern.

Contribution

It applies a recent analytical nonlinear model to study the impact of the energy-range spectral index on field line random walk, revealing superdiffusive behavior as the norm.

Findings

Superdiffusive behavior observed in all cases.

Free-streaming occurs when the spectral index exceeds one.

Superdiffusion appears to be the normal behavior of field line wandering.

Abstract

An analytical nonlinear description of field-line wandering in partially statistically magnetic systems was proposed recently [A. Shalchi, I. Kourakis, Astronomy and Astrophysics, 470, 405 (2007)]. In this article we investigate the influence of the wave-spectrum in the energy-range onto field line random walk by applying this formulation. It is demonstrated that in all considered cases we clearly obtain a superdiffusive behaviour of the field-lines. If the energy-range spectral index exceeds unity a free-streaming behaviour of the field-lines can be found for all relevant length-scales of turbulence. Since the superdiffusive results obtained for the slab model are exact, it seems that superdiffusion is the normal behavior of field line wandering.