tokens: ρ instead. aswith B ∥ being the LOS component of the magnetic field. Beck et al. ( 2003 ) derived how an (anti)correlation between ρ and B changes this measurement of the mean magnetic field strength, which is exact for uncorrelated fields. For anticorrelated fields Equation ( 4 ) underestimates the true LOS B . This effect can be observed in Figure 4 (c), where the mean PDFs of the LOS B x (over the 512 2 available LOSs) are shown. With increasing anticorrelation from , , , , to the derived values of 0.1640(8), 0.1589(12), 0.1584(12), 0.1558(8), and 0.1533(11), respectively, deviate further from the real value 0.1667. More strikingly, the PDF of is much more peaked with a standard deviation of 0.058(3) compared to , , , and with 0.103(5), 0.104(4), 0.125(12), and 0.116(5), respectively. 3.4. Supersonic Simulations The supersonic simulations , , and exhibit a very similar behavior to their subsonic counterparts. All of the simulations reach a stationary regime after ≈2.5 T with the same , but different of 2.84(13), 1.96(19), and 1.62(7), respectively. Again, a higher for similar in the saturated regime implies less-effective magnetic field amplification in the case. Similarly, the ratio of compressive versus rotational power in the kinetic energy spectrum decreases from to to . However, the differences are less pronounced compared to the subsonic regime given that there is overall more power in compressive modes as expected from the supersonic regime. The dynamical alignment between velocity and acceleration field in the supersonic regime is virtually identical to the corresponding subsonic simulations shown in Figure 3 (b). Quantitative differences between both regimes are first observed in the ρ – B correlation, as illustrated in Figure 4 (d). and exhibit virtually no correlation with correlation coefficients of 0.04(5) and −0.09(7) whereas still shows a weak anticorrelation with a coefficient of −0.23(3). The logarithmic density PDFs of the supersonic simulations in Figure 4 (e) follow the same trend observed in the subsonic simulations. With decreasing power in the acceleration field the PDFs get a more pronounced negative skew. Finally, derived LOS magnetic field strength measurements are again systematically affected as shown in Figure 4 (f). The derived value in the simulation of 0.630(12) is closest the real value of 2/3 and the PDF is most peaked with a standard deviation of 0.229(17) whereas and underestimate the magnetic field strength with 0.562(19) and 0.544(15), respectively, and generally broader PDFs with deviations of 0.39(2) and 0.46(4), respectively. 4. Discussion 4.1. Unrealistic Large-scale δ-in-time Forcing While the idea of a δ -in-time forcing is appealing on first sight due to its random, uncorrelated nature, we argue that it is unrealistic for two reasons. First, no large-scale process (on some length scale L p ) in nature evolves instantaneously. 8 8 Small-scale processes, such as energy injection from supernovae
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