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tokens: range. Figure 2. Normalized (see Equations ( 1 )–( 3 )) power spectral densities observed by MMS1 at MHD scales in the quasi-perpendicular MSH during the time interval 07:00–08:00 UT on 2017 January 8. The parallel and perpendicular magnetic-field components measured by FGM are shown in red and dark blue, respectively. The parallel and perpendicular electric-field components measured by EDP are shown in orange and light blue, respectively. The density measured by FPI is displayed in green. The associated black solid lines represent the slope of the observed spectra. The vertical dashed line displays the electron gyrofrequency, while the dotted and dashed–dotted lines show the electron gyroradius and inertial length, respectively, estimated using Taylor’s hypothesis. The insert shows the anisotropy A at different frequencies. 3. Kinetic-scale Turbulence In order to study magnetic fluctuations in the sub-ion range, the burst-mode magnetic waveforms from FGM and SCM instruments are merged using an FIR filter (see, e.g., Breuillard et al. 2016 ), and B 0 and n 0 are defined as low-pass, filtered fluctuations at 0.1 Hz (i.e., below the frequency range of interest). Spatial and temporal scales are again determined as described in Section 1 ; however, as we will see below, intense whistler turbulence is detected in the quasi-perpendicular MSH, which might violate Taylor’s hypothesis. This is discussed in the next two sections. 3.1. Quasi-parallel Magnetosheath In this case, we have v bulk / v A > 3 and v bulk / v ms > 2 (see Table 1 , case 3), thus the Taylor hypothesis should not be significantly violated, and the frequency shift and flattening of the spectrum should be negligible (see Section 1 ). Figure 3 shows that at sub-ion scales (i.e., below the largest electron scale being f ρe here) the anisotropy of magnetic fluctuations is much smaller (here A ≈ 1) than in the MHD range, as noted in the previous section. Both perpendicular and parallel magnetic spectra follow the classical power law, f −2.8 , which is expected by KAWs and whistler turbulence. In this range, both parallel and perpendicular electric fluctuations follow an f −0.8 power law, i.e., , as expected from theoretical models (see Section 4 ). However, if the density spectrum also roughly follows an f −2.8 power law, , as in the MHD range, which is not expected from any of the models cited above. We note here that the density spectrum is affected by Poisson noise (for more details, see Gershman et al. 2015 ) above 10 Hz (not shown) and the flattening of the spectrum is not physical. Figure 3. Normalized (see Equations ( 1 )–( 3 )) power spectral densities observed by MMS1 at kinetic scales in the quasi-parallel MSH during the time interval 00:16–00:18 UT on 2017 January 18. The parallel and perpendicular magnetic-field components measured by FGM are shown in red and dark blue, respectively. The parallel and perpendicular electric-field components measured by EDP are shown in