Non-locality of the Turbulent Electromotive Force

TL;DR

This paper investigates the non-local relationship between the turbulent electromotive force and the mean magnetic field in astrophysical dynamos, using a novel data-fitting approach to determine the convolution kernel and assess the importance of non-local effects.

Contribution

It introduces a new method to directly fit the non-local kernel relating electromotive force and magnetic field from simulation data, highlighting the significance of non-locality in turbulent transport.

Findings

Non-locality over eddy scales is crucial for accurate transport coefficients.

Higher order corrections to standard coefficients are small.

The method effectively captures the convolution kernel from simulation data.

Abstract

The generation of large-scale magnetic fields ($\overline{\mathbf{B}}$) in astrophysical systems is driven by the mean turbulent electromotive force ($\overline{{\cal E}}$), the cross correlation between local fluctuations of velocity and magnetic fields. This can depend non-locally on $\overline{\mathbf{B}}$ through a convolution kernel $K_{ij}$. In a new approach to find $K_{ij}$, we directly fit the time series data of $\overline{{\cal E}}$ versus $\overline{\mathbf{B}}$ from a galactic dynamo simulation using singular value decomposition. We calculate the usual turbulent transport coefficients as moments of $K_{ij}$, show the importance of including non-locality over eddy length scales to fully capture their amplitudes and that higher order corrections to the standard transport coefficients are small in the present case.