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Electrodynamics of turbulent fluids with fluctuating electric conductivity

The influence of fluctuating conductivity on the coefficients known from the mean-field electrodynamics is considered. If the conductivity fluctuations are assumed as uncorrelated with the turbulent velocity field then only the effective magnetic diffusivity of the fluid is reduced and the decay time of a large-scale magnetic field is increased. If the fluctuations of conductivity and flow are correlated in a certain direction then an additional diamagnetic pumping effect results transporting magnetic field in opposite direction to the resistivity flux vector $\langle η'\vec{u}'\rangle$. Even for homogeneous turbulence fields in the presence of rotation an alpha effect appears. With the characteristic values of the outer core of the Earth or the solar convection zone, however, the dynamo number of the alpha effect never reaches supercritical values to operate as an $α^2$-dynamo.