Non-locality of the Turbulent Electromotive Force

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.