tokens: by the WIND spacecraft at 1 au on 2011 June 24, with n i = 2.4 cm −3 , V SW = 599.0 km s −1 , and . (a)–(c) Time variations of the magnetic field vector in geocentric solar ecliptic coordinates. (d) Time variation of field magnitude. (e) Power spectrum of the magnetic field obtained from the FFT method with 11-point centered smoothing. The spectrum with spacecraft frequency f 10 −3 Hz is not shown here, since there are not enough points at this domain when smoothing the spectrum. The two red solid lines show the linear fits to the spectrum in the low-frequency and high-frequency ranges, respectively. Red dots indicate the upper and lower frequency limits used to perform the fits. The obtained spectral indices for the low-frequency ( α L ) and high-frequency ( α H ) ranges and their uncertainties are shown, along with the values of f b , f di (blue arrow), f ρi (green arrow), f ri (black arrow), and β . The vertical dashed line denotes the frequency of the spectral break. Panel (e) of Figure 1 shows the power spectrum of the magnetic field fluctuations. The spectrum is computed by applying the Fast Fourier Transform (FFT) on the three components of B . The trace of the spectral matrix gives the total power spectrum (hereafter power spectrum for simplicity). The spectral break frequency is determined as follows. First, we estimate the location of the break point by eye, which is roughly at 0.3 Hz. The break point divides the power spectrum into two parts: a shallower low-frequency part and a steeper high-frequency part. We then perform linear least-squares fit to the spectrum on the two sides of the roughly estimated break point, respectively (see the two red solid lines in Figure 1 (e)). The upper and lower frequency limits (the red dots) used in the fitting procedure are determined by the frequency range that is best fitted by power law based on chi-square minimization. For the low-frequency part, the band used to perform the fit is between 0.008 and 0.1 Hz. The spectral slope as well as its 1 σ uncertainty is estimated as α L = − 1.694 ± 0.025, which is close to the typical Kolmogorov scaling f −5/3 in the inertial range of the solar wind turbulence (Matthaeus et al. 1982 ; Goldstein et al. 1995 ; Tu Marsch 1995 ; Podesta et al. 2006 ). The high-frequency part of the spectrum beyond the break point is also fitted by a red solid line in the same way, but at the frequency range between 0.4 and 1.2 Hz. The intersection of the two red solid lines associated with the power-law fits thus gives the exact frequency of the break point f b = 0.288 Hz (marked by the red vertical dashed line). This method about determining the break frequency has already been used in several previous studies (e.g., Leamon et al. 1998 ; Smith et al. 2006 ; Hamilton et al. 2008 ; Markovskii et al. 2008 ; Bruno Trenchi 2014 ; Wang et al. 2018 ). In addition, we notice that at the frequencies higher than 1.5 Hz, the power spectrum becomes shallower again, which
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