Non-locality of the turbulent electromotive force

Abstract

ABSTRACT The generation of large-scale magnetic fields ($\overline{\boldsymbol {B}}$) in astrophysical systems is driven by the mean turbulent electromotive force ($\overline{\rm{\boldsymbol {\cal E}} {}}$), the cross-correlation between local fluctuations of velocity and magnetic fields. This can depend non-locally on $\overline{\boldsymbol {B}}$ through a convolution kernel Kij. In a new approach to find Kij, we directly fit the time-series data of $\overline{\rm{\boldsymbol {\cal E}} {}}$ versus $\overline{\boldsymbol {B}}$ from a galactic dynamo simulation using singular value decomposition. We calculate the usual turbulent transport coefficients as moments of Kij, and 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 this case.