Complexity and diffusion of magnetic flux surfaces in anisotropic turbulence

The complexity of magnetic flux surfaces is investigated analytically and numerically in static homogeneous magnetic turbulence. Magnetic surfaces are computed to large distances in magnetic fields derived from a reduced magnetohydrodynamic model. The question addressed is whether one can define magnetic surfaces over large distances when turbulence is present. Using a flux surface spectral analysis, we show that magnetic surfaces become complex at small scales, experiencing an exponential thinning that is quantified here. The computation of a flux surface is of either exponential or nondeterministic polynomial complexity, which has the conceptual implication that global identification of magnetic flux surfaces and flux exchange, e.g., in magnetic reconnection, can be intractable in three dimensions. The coarse-grained large-scale magnetic flux experiences diffusive behavior. The link between the diffusion of the coarse-grained flux and field-line random walk is established explicitly through multiple scale analysis. The Kubo number controls both large and small scale limits. These results have consequences for interpreting processes such as magnetic reconnection and field-line diffusion in astrophysical plasmas. © 2014. The American Astronomical Society. All rights reserved..