Magnetic stochasticity and diffusion

Abstract

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 ${\mathcal{L}}_p$-norm $S_p(t)=\frac{1}{2}||1-{\hat{\mathbf{B}}}_l.{\hat{\mathbf{B}}}_L|{|}_p$, $p$th order magnetic stochasticity of the stochastic field $\mathbf{B}(\mathbf{x},t)$, based on the coarse-grained fields, ${\mathbf{B}}_l$ and ${\mathbf{B}}_L$, at different scales, $l\ne L$. For laminar flows, 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 super-linear Richardson dispersion scheme. This is intimately related to stochastic magnetic reconnection in which super-linear Richardson diffusion broadens the matter outflow width and accelerates the reconnection process.

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• 3D Turbulent Reconnection: Theory, Tests and Astrophysical Implications
• Nanoflare Theory Revisited
• Statistical Analysis of Stochastic Magnetic Fields
• Turbulent drag reduction in magnetohydrodynamic and quasi-static magnetohydrodynamic turbulence
• Power and spatial complexity in stochastic reconnection
• Fast nuclear spin relaxation rates in tilted cone Weyl semimetals: Redshift factors from Korringa relation