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tokens: the contribution of a magnetic background turbulence, like that provided by an SSD, to α . Here, α M can be obtained already by SOCA (Rädler Rheinhardt 2007 ). Second, it can be interpreted as reflecting the quenching of α by such that with its magnitude growing, α M also grows, but opposite in sign to α K , resulting in a reduced total α . This can be obtained via closure approaches like the τ or eddy-damped quasi-normal Markovian approximations (Pouquet et al. 1976 ). Turbulent diffusivity in incompressible flows is estimated asIf the Strouhal number u rms τ / l , l a characteristic scale of the flow, is assumed to be unity, we can estimate τ = 1/ k f u rms . To obtain the fluctuating fields b ′, j ′, we have removed the large-scale field via filtering out the contributions of the k = 1 mode from the magnetic field snapshots. We estimated the growth rates by first calculating α and η t for individual snapshots using data from runs with high snapshot frequency during exponential growth. Then, we used Equation ( 10 ) to get λ for an individual snapshot and subsequently time-averaged over the growth phase. We find results that are at least approximately aligned with the directly measured values with better agreement at low ; see Figure 18 . Toward high , the results begin to diverge, most strongly at the highest . This appears to indicate that the closure estimates can work surprisingly well but do not catch all of the details. Figure 18. Growth rates ( 10 ) based on closure estimates of α and η t at the exponential growth stage, compared to directly estimated ones. But how does α behave at the saturation stage? Brandenburg et al. ( 2008 ) measured α and η t quenching, with both decreasing as functions of . For comparison, we calculated α K,M from the saturation stages of our runs and discovered similar results; see Figure 19 . The normalized α K approaches a constant, whereas α M keeps getting stronger with . Our results are close to Brandenburg et al. ( 2008 , their Figure 3) within our range of , including substantially more points though. The total α decreases with growing , reaching eventually a tentative plateau. Figure 19. α K and α M at the saturated stage as functions of , normalized by α 0 = u rms /3. Bars represent the fluctuation level of α derived from their standard deviations. The jump at is due to an unclear disagreement between resolutions 128 3 , 64 3 , and 256 3 , while that at is due to different saturation stage lengths in the runs with resolutions 256 3 and 512 3 . 5.5. Magnitude Distribution of the Magnetic Field Next, we investigate how the probability density functions (pdf’s) of the magnetic field differ in the regimes where SSD or LSD alone and SSD and LSD together are acting. While spectra gave us information about the distribution of the magnetic field across different scales, pdf’s can further reveal details of the structure of the field in different spatial directions. Additionally, we calculated kurtoses of these