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tokens: linearly by the axial mean magnetic field vector , then only the formulationis possible if pseudoscalars, such as or , are not available. Without global rotation, an effect in the formulation does not occur in the linear relation ( 16 ). The parameter describes the turbulence-induced eddy diffusivity in the fluid, while the vector gives a velocity which transports (“pumps”) the large-scale magnetic field downward for positive . If, however, terms that are nonlinear in are included in the heuristic expression ( 16 ), then the extra termsoccur within the second-order-correlation approximation (Kitchatinov et al. 1994 ). The first term of the right hand side represents the known magnetic influence on the eddy diffusivity, while the second one forms a magnetic-induced pumping effect. There is no term representing an effect with the large-scale current helicity of the background field as (pseudoscalar) coefficient. For nonrotating and nonhelically driven turbulence, the large-scale current helicity does not create an effect in this approximation. Indeed, we do not find an effect in the numerical simulations below. There is instead the – sometimes ignored – magnetic-induced new pumping term, which for positive advects the magnetic field towards the maximum magnetic field. This effect should appear in all numerical models with helical large-scale field and nonhelically driven flow (Yousef et al. 2003 ; Bhat et al. 2014 ). Equations ( 16 ) and ( 17 ) yieldThe nonlinear terms magnetically affect both the eddy diffusivity and the advection velocity, which are basically reduced if the factor is positive. The possesses the dimension of a time and can be estimated as in the high-conductivity limit. One easily finds for important cases. For , the coefficient is always positive for all spectral functions that do not grow with growing frequency. Moreover, for all the full expression ( 19 ) is positive for which represents long correlation times as well as for , i.e.very short correlation times (so-called white noise). If compared with the magnetic-diffusion time , the delta-like spectral line represents the low-conductivity limit, while the white-noise spectrum represents the high-conductivity limit. In both limits, the is positive and, therefore, both eddy diffusivity and diamagnetic pumping are magnetically quenched rather than amplified (“anti-quenched”). 3.1. Numerical results Fig. 5 Two horizontal components ( top : , bottom : ) of the turbulence-induced electromotive force for background fields without helicity. Left panels : , (only homogeneous magnetic field in direction); right panels : , (only homogeneous electric current in direction). The averages over all snapshots are noted in the plots. The two horizontal components of the electromotive force are calculated for two different cases. In the first simulation, the applied magnetic fields are assumed to be free of helicity, i.e. . The other possibility works with . If the results of both setups