tokens: the total magnetic fluctuations and of the parallel electric fluctuations, and (top and bottom rows, respectively) for (left column) and β i = 0.2 (right column). A classical intermittency analysis has been performed on both simulations at about the peak of the nonlinear activity. In order to define the large-scale limit of the inertial range, we evaluated the perpendicular and parallel autocorrelation functions, respectively defined as and (Frisch 1995 ). We assumed isotropy in the perpendicular xy -plane, with the parallel direction along B 0 , i.e., along z . The e -folding length approximately gives the integral scale, which is about in the perpendicular direction (corresponding to ), for both regimes. The situation is different in the parallel direction, where the parallel correlation length is for β p = 0.2, while it is for β p = 1 (corresponding to and ∼0.5, respectively). This is in qualitative agreement with the features spotted in Figure 1 and quantitatively with the corresponding spectra (see Figure 4 ), indicating differences already in the large-scale properties of the fluctuations possibly due to a different decorrelation mechanism along the mean field. The level of intermittency can be better quantified by the probability distribution functions (PDFs) of the magnetic field increments at a given scale r , defined asWe show here the statistics of the perpendicular increments, namely, , spanning this increment from lengths larger than the correlation scale , down to the smallest available scale (Δ x ∼ 0.08 d p ). These distributions are reported in Figure 3 (a) for the β p = 0.2 regime for three cases, namely, and 0.08. These PDFs, as expected, become increasingly intermittent going toward smaller scales. In order to compare among cases, and among different times, we measured the scale-dependent kurtosis χ —the fourth-order moment of the increments in Equation ( 4 )—that can be measured asThis quantity is reported in Figure 3 (b), as a function of the perpendicular scale r , for the two values of β , at two distinct times. At large scales, for r > 5 d p , the distribution becomes Gaussian, where χ ∼ 3, in agreement with the computation of the correlation lengths. At small scales, in the inertial range of turbulence, there is an enhancement due to the intermittent nature of the cascade, due to the presence of coherent structures and nonlinear waves. At the smallest scales, a saturation of the multifractality is observed, in agreement with observations in the SW. In fact, the study of high-order structure functions up to the sixth moment and of their exponents, shows deviation from monofractality (not shown here). Here, this process of saturation might also be slightly affected by the presence of artificial dissipation. It is important to note that at scales in the inertial-dispersive range, the case with β p = 0.2 is more intermittent than the β p = 1 regime, indicating a higher degree of coherency in the small-scale fluctuations.
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