Abstract
In this article we address the problem of magnetic field generation and front propagation in turbulent electrically conducting fluids, involving the velocity with finite correlations times and small magnetic diffusivity. We suggest an integro-differential dynamo equation which involves the non-local terms for both the dynamo source α-term and turbulent transport of the mean magnetic field. We derive a set of formulas which allows us to determine the rate of magnetic front propagation in galaxies valid for arbitrary memory kernels. We illustrate the general results through the use of the exponential correlation functions for memory kernels and 'no-z' approximation. We find that the memory effects have strong influence on for both the growth rate and propagation speed. We perform numerical simulations of exterior front speed, and find that the transport memory essentially decreases the propagation rate.
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