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. In this paper, we establish a connection between magnetic stochasticity S_{p}(t) and magnetic diffusion in magnetohydrodynamic (MHD) turbulence and use a homogeneous, incompressible MHD simulation to test this prediction. Our results agree with the well-known fact that magnetic diffusion in turbulent media follows the superlinear Richardson dispersion scheme. This is intimately related to stochastic magnetic reconnection in which superlinear Richardson diffusion broadens the matter outflow width and accelerates the reconnection process.