Statistical analysis of stochastic magnetic fields.

Previous work has introduced scale-split energy density ψ_{l,L}(x,t)=1/2B_{l}·B_{L} for vector field B(x,t) coarse grained at scales l and L, in order to quantify the field stochasticity or spatial complexity. In this formalism, the L_{p} norms S_{p}(t)=1/2||1-B[over ̂]_{l}·B[over ̂]_{L}||_{p}, pth-order stochasticity level, and E_{p}(t)=1/2||B_{l}B_{L}||_{p}, pth order mean cross energy density, are used to analyze the evolution of the stochastic field B(x,t). Application to turbulent magnetic fields leads to the prediction that turbulence in general tends to tangle an initially smooth magnetic field increasing the magnetic stochasticity level, ∂_{t}S_{p}>0.

Magnetic stochasticity and diffusion.

We develop a quantitative relationship between magnetic diffusion and the level of randomness, or stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic stochasticity in turbulence has been developed in previous work in terms of the L_{p} norm S_{p}(t)=1/2∥1-B[over ̂]_{l}·B[over ̂]_{L}∥_{p}, pth-order magnetic stochasticity of the stochastic field B(x,t), based on the coarse-grained fields B_{l} and B_{L} at different scales l≠L. For laminar flows, the stochasticity level becomes the level of field self-entanglement or spatial complexity.

Topology and stochasticity of turbulent magnetic fields.

We present a mathematical formalism for the topology and stochasticity of vector fields based on renormalization group methodology. The concept of a scale-split energy density, ψ_{l,L}=B_{l}·B_{L}/2 for vector field B(x,t) renormalized at scales l and L, is introduced in order to quantify the notion of the field topological deformation, topology change, and stochasticity level. In particular, for magnetic fields, it is shown that the evolution of the field topology is directly related to the field-fluid slippage, which has already been linked to magnetic reconnection in previous work.

Inertial-Range Reconnection in Magnetohydrodynamic Turbulence and in the Solar Wind.

In situ spacecraft data on the solar wind show events identified as magnetic reconnection with wide outflows and extended "X lines," 10(3)-10(4) times ion scales. To understand the role of turbulence at these scales, we make a case study of an inertial-range reconnection event in a magnetohydrodynamic simulation. We observe stochastic wandering of field lines in space, breakdown of standard magnetic flux freezing due to Richardson dispersion, and a broadened reconnection zone containing many current sheets.

Turbulent reconnection and its implications.

Magnetic reconnection is a process of magnetic field topology change, which is one of the most fundamental processes happening in magnetized plasmas. In most astrophysical environments, the Reynolds numbers corresponding to plasma flows are large and therefore the transition to turbulence is inevitable. This turbulence, which can be pre-existing or driven by magnetic reconnection itself, must be taken into account for any theory of magnetic reconnection that attempts to describe the process in the aforementioned environments.