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tokens: On the other hand, when V 0 = −2 V A (Figure 1 (c)), the forward LH-polarized Alfvén/proton-cyclotron wave at V 0 = 0 becomes backward RH-polarized mode, and the forward RH-polarized fast-magnetosonic/whistler wave with λ p k 1 at V 0 = 0 turns to the backward LH-polarized mode. For the forward fast-magnetosonic/whistler wave with λ p k > 1, its polarization remains the same as that at V 0 = 0. Comparing the ratio of to in the plasma frame to that in the spacecraft frame, we find that this ratio is independent of V 0 . Note that this conclusion can be confirmed by the expressions ( 6 )–( 8 ). Therefore, the correlation coefficient between B ⊥ and V ⊥ () is a useful parameter to identify the direction of the observed wave in the plasma frame, e.g., corresponding to the backward wave and for the forward wave. Then, by combining the information of the polarization and the direction of S ∥ , we can clearly identify the nature of the electromagnetic wave in the spacecraft frame. As shown in Table 1 , Alfvén/proton-cyclotron and fast-magnetosonic/whistler waves have different behaviors in the parameter space of , S ∥ , and polarization. Table 1 Linear Responses of Low-frequency Electromagnetic Waves in the Spacecraft Frame where V 0 > V A ( V 0 − V A ) 3. Application: Two Observation Events Figure 2 shows two events containing both LH- and RH-polarized low-frequency electromagnetic waves in the Earth’s magnetosheath by using Magnetospheric Multiscale ( MMS ) spacecraft observations (Burch et al. 2016 ). The particle moments are measured from the Fast Plasma Investigation (Pollock et al. 2016 ). The electric and magnetic fields are from the Electric Double Probe (Ergun et al. 2016 ; Lindqvist et al. 2016 ) and the FluxGate Magnetometer (Russell et al. 2016 ). These two events have the same distribution, that is, the waves with the ellipticity ∼−1 have frequencies larger than that with the ellipticity ∼1. The former and latter correspond to the LH-polarized and RH-polarized waves, respectively. Note that the ellipticity is defined as the ratio of the intermediate variance value to the maximum variance value in performing minimum variance analysis to the magnetic field. For nearly parallel and antiparallel waves, the definition of the ellipticity is consistent with the polarization defined in the field-aligned coordinates. The parallel Poynting flux is different for these two events, that is, in Event 1 and in Event 2. In these two events, ions have the perpendicular temperature anisotropy , and electrons exhibit the parallel temperature anisotropy . Furthermore, using the bulk ion flow velocity and the magnetic field data in Figure 2 , we find in Event 1 and in Event 2. Figure 2. Two examples of the wave event containing both LH- and RH-polarized low-frequency electromagnetic waves observed by MMS : (I) Event 1 occurred in the time interval of 12:27:00 UT−12:37:00 UT on 2018 October 7, and (II) Event 2 during 08:30:00 UT−09:00:00 UT on 2018 November