Parker Solar Probe Observations of Alfvénic Waves and Ion-cyclotron Waves in a Small-scale Flux Rope

Magnetic flux ropes, which possess helical magnetic field topology, play important roles in transferring the mass, momentum, and energy in the interplanetary environment and in affecting space weather (e.g., Liu et al. 2014; Shen et al. 2014, 2017; Huang et al. 2017, 2018; Kilpua et al. 2017). Interplanetary magnetic flux ropes are usually classified into two categories: small-scale magnetic flux ropes (SFRs; e.g., Moldwin et al. 1995, 2000; Hu et al. 2018), and magnetic clouds (large-scale magnetic flux ropes; e.g., Klein & Burlaga 1982). Generally, SFRs have durations from a few minutes to a few hours, which is much shorter than the duration of magnetic clouds ∼20 hr (e.g., Feng et al. 2008; Cartwright & Moldwin 2010). Contrary to magnetic clouds that are widely thought of as originating from the Sun (e.g., Klein & Burlaga 1982), the source of SFRs is still controversial: the Sun and/or the interplanetary space (e.g., Feng et al. 2007, 2008; Cartwright & Moldwin 2008, 2010; Zank et al. 2017; Hu et al. 2018; Zheng & Hu 2018). To study the source and the distribution of SFRs, statistical analyses have been performed for SFRs at heliocentric distances from 0.29 to 7–8 au through observations from Helios, Wind, Advanced Composition Explorer, Ulysses, and Solar TErrestrial RElations Observatory (Moldwin et al. 1995, 2000; Feng et al. 2007, 2008; Cartwright & Moldwin 2008, 2010; Tian et al. 2010; Yu et al. 2014, 2016; Hu et al. 2018; Zheng & Hu 2018; Chen et al. 2019; Chen & Hu 2020). Recently, using the Parker Solar Probe (PSP), Zhao et al. (2020a, 2020b) and Chen et al. (2020) explored the distribution of SFRs at the heliocentric distance down to ∼0.13 au.

Similar to SFRs, Alfvénic structures in the solar wind also exhibit helical magnetic field configuration (e.g., Zhao et al. 2020a, 2020b). To exclude these Alfvénic structures, different criteria are employed in different automated identification programs of SFRs. For example, Chen et al. (2020) use a criterion, i.e., the Walén slope smaller than 0.3, to distinguish SFRs from Alfvénic structures and fluctuations in the Grad–Shafranov-based program. Zhao et al. (2020a, 2020b) identify SFRs with parameters including normalized magnetic helicity ∣σ_m∣ ≥ 0.7, normalized cross helicity ∣σ_c∣ ≤ 0.3, and normalized residual energy σ_r ≤ −0.5 through an automated program based on the wavelet analysis (Telloni et al. 2013). In fact, Alfvénic waves can embed within an SFR. Gosling et al. (2010) identified such an event (the duration ∼3 hr) in which the Walén slope is ∼0.62. Since SFRs with medium and high Alfvénicity were removed in previous identification programs (e.g., Cartwright & Moldwin 2008, 2010; Yu et al. 2014, 2016; Hu et al. 2018; Zheng & Hu 2018; Chen et al. 2019, 2020; Chen & Hu 2020; Zhao et al. 2020a, 2020b), we have little knowledge of these kinds of SFRs.

Using PSP measurements, this paper gives direct observational evidence for the SFR with medium Alfvénicity in the inner heliosphere. Also, we find this SFR contains both large-scale Alfvénic waves and small-scale electromagnetic waves, and the latter waves are identified as the ion-cyclotron mode wave based on the wave theory in the spacecraft frame. This paper uses the data detected by the Electromagnetic Fields Investigation (FIELDS; Bale et al. 2016) and Solar Wind Electrons Alphas and Protons (SWEAP; Kasper et al. 2016) instruments on PSP (Fox et al. 2016), which provide vector magnetic fields with temporal resolution 0.0137 s and the plasma parameters with temporal resolution 0.874 s during the time interval including our SFR event.

Our SFR event arises during the time interval of 08:34:45 UT−08:46:05 UT on 2018 November 1, and its duration is about ∼11 minutes. We identify the SFR edges arising at 08:34:45 UT and 08:46:05 UT through the obvious changes of the magnetic field direction (Figure 1(a)) and of the solar wind bulk flow V_∥ along the magnetic field (Figure 1(f)) therein. Figure 1(a) also shows that this event is embedded in a highly variable magnetic field environment. Different from varying magnetic field, the solar wind is steadily flowing outward from the Sun at a speed of ∼325 km s⁻¹, which corresponds to the slow solar wind condition, as shown in Figure 1(b). Moreover, Figures 1(c)–(e) zoom in the magnetic field and the velocity during 08:25:00 UT−08:55:00 UT, and here the magnetic field data are averaged down to the plasma measurement cadence 0.874 s. Figures 1(c)–(e) show positive correlations between magnetic field and velocity perturbations. Figure 1(f) presents the distributions of V_∥ and the Alfvén speed ${V}_{{\rm{A}}}=B/{\left({\mu }_{0}{m}_{p}{n}_{p}\right)}^{1/2}$, where n_p is the proton number density. Inside SFR, V_∥ approximates 300 km s⁻¹, which is much larger than V_A ≃ 60 km s⁻¹. V_∥ becomes smaller than V_A nearby the SFR edges. Large V_∥ could result in a significant Doppler frequency shift of the waves in our event. The plasma parameters, e.g., proton number density n_p (Figure 1(g)), proton temperature T_p (Figure 1(h)), and proton beta β_p (Figure 1(i)), are nearly stable both inside and outside of this SFR, where n_p ≃ 220 cm⁻³, T_p ≃ 12 eV, and β_p ≃ 1. Furthermore, Figure 1(j) presents the pitch angle distribution of electrons at the energy of 315 eV. The E_e = 315 eV electrons observed by PSP are proposed to be proxy of strahl electrons in the solar wind (Nieves-Chinchilla et al. 2020). Figure 1(j) shows that bidirectional electrons with E_e = 315 eV arising at θ = 0° and θ = 180° inside SFR. The enhanced bidirectional strahl electrons are considered robust signatures for the flux rope in the solar wind (Nieves-Chinchilla et al. 2020). We also see antiparallel and bidirectional E_e = 315 eV electrons arising in upstream and downstream regions, respectively, indicating that this SFR resides between open and closed magnetic field structures.

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Figures 1(k)–(m) present normalized magnetic helicity ${\sigma }_{m}\left(s,t\right)=2\mathrm{Im}\left({B}_{T}^{* }\left(s,t\right){B}_{N}\left(s,t\right)\right)/| {\boldsymbol{B}}\left(s,t\right){| }^{2}$, normalized cross helicity ${\sigma }_{c}\left(s,t\right)=2\langle {\boldsymbol{V}}\left(s,t\right)\cdot {{\boldsymbol{V}}}_{{\boldsymbol{B}}}\left(s,t\right)\rangle$/$\left(\langle V{\left(s,t\right)}^{2}\rangle +\langle {V}_{B}{\left(s,t\right)}^{2}\rangle \right)$, and normalized residual energy ${\sigma }_{r}\left(s,t\right)=\left(\langle V{\left(s,t\right)}^{2}\rangle -\langle {V}_{B}{\left(s,t\right)}^{2}\rangle \right)$/$\left(\langle V{\left(s,t\right)}^{2}\rangle +\langle {V}_{B}{\left(s,t\right)}^{2}\rangle \right)$ distributions using the wavelet transform method (Grinsted et al. 2004), where s is the wavelet scale, and ${{\boldsymbol{V}}}_{{\boldsymbol{B}}}={\boldsymbol{B}}/{\left({\mu }_{0}{n}_{p}{m}_{p}\right)}^{1/2}$ denotes the magnetic field in the Alfvén speed unit. Figures 1(k)–(m) show that σ_m ∼ −0.20, σ_c ∼ 0.55, and σ_r ∼ −0.79 at the scale of ∼11 minutes. Moreover, we find σ_c within SFR can reach 0.69 in the scale of ∼0.1–1 minute, which implies the existence of Alfvénic waves (also see Figure 2). Alfvénic waves with the scale of ∼0.1–1 minute also exist in SFR surrounding regions where σ_c can reach 0.88.

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To further show the structure of our identified SFR, Figures 1(n) and (o) give the results by using the Grad–Shafranov reconstruction technique (Hau & Sonnerup 1999; Hu & Sonnerup 2001, 2002). The Grad–Shafranov reconstruction map (Figure 1(n)) clearly shows the existence of the flux rope structure, and its scale size is about 0.0009 au. Moreover, the Grad–Shafranov reconstruction indicates the duration of this SFR, i.e., from 08:34:23 UT to 08:43:15 UT, which is largely consistent with the result based on the change of the magnetic field and plasma parameter distributions (see Figures 1(c)–(j)). This indicates that although the Grad–Shafranov reconstruction technique uses the ideal MHD equation and the rigid body assumption for the flux rope, it can reconstruct the SFR with modest Alfvénicity over the time interval 08:34:23 UT−08:43:15 UT for which the Walén test slope is about 0.32 (Chen et al. 2020).

Figure 2 presents the wave analysis for low-frequency electromagnetic fluctuations during 08:25:00 UT–08:55:00 UT. Figures 2(b)–(e) exhibit the wavelet cross-coherence spectra of B_⊥ − V_⊥ through the wavelet coherence analysis (Grinsted et al. 2004). To obtain the correlation of B_⊥ − V_⊥ between 0.02 and 0.57 Hz, we first smooth B at a timescale of 60 s, which is considered as the background magnetic field B₀, and then transform B and V_p into (B_⊥, B_∥) and (V_⊥, V_∥) in the field-aligned coordinates. Figures 2(b) and (d) show that the coherence coefficient CC(B_⊥, V_⊥) can be larger than 0.6 for low-frequency fluctuations with f ∼ 0.02–0.3 Hz inside and outside of the SFR, indicating the existence of low-frequency Alfvénic waves. Figures 2(c) and (e) show that the coherence phase angle Ψ(B_⊥, V_⊥) is mainly around zero in regions with high CC(B_⊥, V_⊥), which corresponds to Alfvénic waves propagating against the magnetic field.

Figures 2(f)–(i) further give the distributions of degree of polarization (DOP), wave normal angle θ_k, ellipticity (), and power spectral density of B (B_PSD) using the singular value decomposition method (e.g., SantolíK et al. 2003). To clearly show quasi-monochromatic waves, we retain the data with DOP ≳ 0.7, ≲ −0.65 and θ_k ≲ 25° in Figures 2(f)–(h). It is interesting to see that quasi-monochromatic waves with frequencies f ≃ 0.3–4 Hz arise near the leading and trailing edges of this SFR, where the proton cyclotron frequency f_cp is about 0.3 Hz. These waves have small angles (θ_k ≲ 25°) and exhibit left-hand polarization ( < −0.65). Moreover, the observed quasi-monochromatic waves locate in the turbulent medium, as suggested by Figure 2(i). Figures 2(j) and (k) further compare B_PSD in different regions, e.g., the upstream region during 08:30:00 UT−08:34:00 UT, the leading region during 08:35:00 UT−08:38:00 UT, the middle region during 08:39:00 UT−08:43:00 UT, the trailing region during 08:44:00 UT–08:46:00 UT, and the downstream region during 08:47:00 UT−08:51:00 UT. Figure 2(j) shows that B_PSD in the range of ∼0.3–4 Hz enhances in both SFR leading and trailing regions, and B_PSD in the SFR middle region follows a power-law distribution, i.e., B_PSD ∝ f^−1.5 at f ≲ 1 Hz and B_PSD ∝ f^−3.3 at f ≳ 1 Hz. In Figure 2(k), both upstream and downstream B_PSD obey the power-law distribution similar to that in the SFR middle region. This implies the same turbulence cascade mechanism inside and outside of the SFR. Since the Doppler shift frequencies of the proton inertial length and the proton gyroradius are about 3.2 and 3 Hz, the observed B_PSD in the SFR middle region extends to sub-ion scales (f ≳ 3 Hz).

For the observed electromagnetic waves with f ≳ f_cp, one basic problem is the mode nature. Since SFR streams against the magnetic field (Figure 1), the observed left-hand electromagnetic waves can be either a backward Alfvén/ion-cyclotron (A/IC) mode wave or a forward fast-magnetosonic/whistler (FM/W) mode wave in the plasma frame (Zhao et al. 2020). Unfortunately, the plasma measurements from PSP do not include the high-resolution data, and consequently we cannot identify the wave mode by using the correlation between the velocity and magnetic field fluctuations (Zhao et al. 2020). Recently, Mozer et al. (2020) explore the distribution of the electric field effective antenna length L_eff as a function of the wave frequency with PSP measurements, and they identify the wave mode by comparing L_eff with the antenna half-geometric length. Here we follow their method to identify the wave mode. Since the measured differential potentials dV are restricted to (x–y) plane in the spacecraft frame, we will estimate L_eff in the spacecraft frame.

At first, we use the minimum variance analysis (MVA; e.g., Sonnerup & Cahill 1967) to find out the direction of the wavevector k. Since MVA can result in the 180° ambiguity of k/∣k∣, we use the z-direction Poynting flux S_z to yield the uncertainty of k/∣k∣ through S_z · k/∣k∣ > 0. Figure 3(a) presents MVA results in the SFR leading region, where the smoothing timescale is 4 s. The ratio of intermediate to minimum eigenvalues λ_int/λ_min is larger than 10 in most time intervals, indicating that MVA is valid therein. The ratio of maximum to intermediate eigenvalue λ_max/λ_int approximates 1 in λ_int/λ_min ≳ 10 regions, indicating that the waves are circularly polarized (also see Figure 2). The observed waves have the wave normal angle θ ≃ 176°, which means that these waves are nearly antiparallel propagation with respect with the background magnetic field.

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Second, using the wavevector direction and observed parameters, we can directly give the dispersion relations and linear responses among all wave variables. We recently developed a wave theory in the spacecraft frame based on the cold two-fluid model, where the plasma bulk flow and the wavevector can be in arbitrary direction (J. Zhao 2020, in preparation). Under the averaged wave and plasma parameters during the time interval of 08:36:50 UT−08:37:10 UT (labeled by two dotted lines in Figure 3(a)), i.e., k/∣k∣ = [0.074, −0.73, − 0.68], n_p = n_e = 219 cm⁻³, V = [−63, 6, −356] km s⁻¹, and B = [−0.8, 23, 22] nT, the corresponding low-frequency electromagnetic wave modes are shown in Figure 3(b). There are two modes behaving the left-hand polarization ($\arg ({B}_{y}/{B}_{x})=-90^\circ$), i.e., the A/IC mode wave with V_⊥1/B_⊥1 > 1 (backward propagation in the plasma frame; labeled by dashed lines), and the FM/W mode wave with 0 > V_⊥1/B_⊥1 > −1 (forward propagation in the plasma frame; labeled by dotted lines). The candidates of the observed waves (0.3–3 Hz; see Figure 2) correspond to the A/IC mode wave with λ_p∣k∣ ≃ 0.1 − 1.1, E_x/V_AB_y ≃ −8.9 to −8.3, and E_y/V_AB_x ≃ 8.0 − 8.2 (thick dashed lines), and the FM/W mode wave with λ_p∣k∣ ≃ 0.2 − 4.7, E_x/V_AB_y ≃ −5.9 to −0.5, and E_y/V_AB_x ≃ 4.2 − 6.8 (thick dotted lines). It should be emphasized that the FM/W mode wave cannot explain the observed high-frequency waves with f ∼ 3 Hz.

Lastly, using the theoretical electromagnetic ratios and the observed electromagnetic fields, we can estimate the electric field effective antenna length through ${L}_{\mathrm{eff}}={\left({dV}/{V}_{{\rm{A}}}B\right)}^{\mathrm{obs}}/{\left(E/{V}_{{\rm{A}}}B\right)}^{\mathrm{theory}}$. The observed $\left({dV}/{V}_{{\rm{A}}}B\right)$ is shown in Figure 3(c), which also exhibits the power spectral densities of dV = EL_eff and B. Both the observed dV_x/V_AB_y and dV_y/V_AB_x are about 10 in the frequency range of 0.3–3 Hz. The theoretical predictions of L_eff are presented in Figure 3(d). For the A/IC mode wave, ${\bar{L}}_{\mathrm{eff}}\left({E}_{x}/{V}_{{\rm{A}}}{B}_{y}\right)$ and ${\bar{L}}_{\mathrm{eff}}\left({E}_{y}/{V}_{{\rm{A}}}{B}_{x}\right)$ are about 2.6 m and 1.2 m, respectively, where ${\bar{L}}_{\mathrm{eff}}$ is the mean electric field effective antenna length. The FM/W mode wave predicts longer L_eff than that estimated by the A/IC mode wave, even much longer than the antenna half-geometric length of 3.5 m (see L_eff for the FM/W mode wave with λ_p∣k∣ ∼ 2.5 − 4.5).

Similarly, Figure 4 gives the L_eff distributions in the SFR trailing region. For the A/IC mode wave, ${\bar{L}}_{\mathrm{eff}}\left({E}_{x}/{V}_{{\rm{A}}}{B}_{y}\right)$ and ${\bar{L}}_{\mathrm{eff}}\left({E}_{y}/{V}_{{\rm{A}}}{B}_{x}\right)$ are about 1.4 m and 1.5 m, respectively. For the FM/W mode wave with λ_p∣k∣ ≃ 0.1 − 1.4, ${\bar{L}}_{\mathrm{eff}}\left({E}_{x}/{V}_{{\rm{A}}}{B}_{y}\right)\simeq 1.7$ m and ${\bar{L}}_{\mathrm{eff}}\left({E}_{y}/{V}_{{\rm{A}}}{B}_{x}\right)\simeq 1.9$ m. For the short-scale FM/W mode wave (λ_p∣k∣ ≃ 7.7 − 9.0), ${\bar{L}}_{\mathrm{eff}}$ is much larger than 3.5 m, and it is unreasonable.

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Combining the results of the wave dispersion and L_eff in Figures 3 and 4, we conclude that the A/IC mode wave gives L_eff closer to the values given by Mozer et al. (2020), i.e., L_eff = 1.15 m at 1 Hz and 0.98 m at 3 Hz, and the FM/W mode wave cannot explain the high-frequency branch of the observed waves in the SFR leading region. Therefore, we propose that the observed waves with f ≳ f_cp are A/IC mode waves.

Figure 5 further gives the wave frequency f_plas and wavelength λ of the observed f ≳ f_cp waves in the plasma frame. Since the observed waves are nearly antiparallel to the background magnetic field, we calculate f_plas and λ using the analytical dispersion relations of parallel and antiparallel A/IC and FM/W mode waves in the spacecraft frame (Zhao et al. 2020). Using the dispersion relations of the A/IC mode wave,

$$\begin{eqnarray}\begin{array}{c}\begin{array}{rcl}2\pi {f}_{{\rm{sc}}} & = & {V}_{\parallel }k-{V}_{{\rm{A}}}k\left({\lambda }_{p}k/2\right.\\ & & +\left.\sqrt{1+{\lambda }_{e}^{2}{k}^{2}+{\lambda }_{p}^{2}{k}^{2}/4}\right)/\left(1+{\lambda }_{e}^{2}{k}^{2}\right),\end{array}\end{array}\end{eqnarray} \tag{ 1 }$$

and the FM/W mode wave,

$$\begin{eqnarray}\begin{array}{c}\begin{array}{rcl}2\pi {f}_{{\rm{sc}}} & = & {V}_{\parallel }k-{V}_{{\rm{A}}}k\left({\lambda }_{p}k/2\right.\\ & & -\left.\sqrt{1+{\lambda }_{e}^{2}{k}^{2}+{\lambda }_{p}^{2}{k}^{2}/4}\right)/\left(1+{\lambda }_{e}^{2}{k}^{2}\right),\end{array}\end{array}\end{eqnarray} \tag{ 2 }$$

we can obtain both λ = 2π/∣k∣ and f_plas = ∣f_sc − V_∥k/2π∣. Here we only consider minimum and maximum f_sc of the observed quasi-monochromatic waves at each time. Figure 5(a) shows f_plas ∼ 0.03–0.3 Hz and λ ∼ 60–1000 km for A/IC mode waves in the SFR leading region, where the proton inertial length λ_p and the proton gyroradius ρ_p are about 15 km and 19 km, respectively. Figure 5(b) shows f_plas ∼ 0.02–0.3 Hz and λ ∼ 60–2000 km for A/IC mode waves in the SFR trailing region, where λ_p ≃ 15 km and ρ_p ≃ 20 km. Since f_plas is close to f_cp, the observed waves are indeed ion-cyclotron waves. Besides, as the frequency of the FM/W mode wave is cutoff at ∼2 Hz in the SFR leading region (see Figure 3), there exist gaps in the f_plas and λ distributions relating to FM/W mode waves therein.

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Using PSP measurement at 0.23 au, this paper reports an interesting SFR event in the slow solar wind, which contains both Alfvénic waves and ion-cyclotron waves. This SFR event is surrounded by Alfvénic waves and Alfvénic structures. Alfvénic waves inside and outside of this SFR have frequencies below ∼0.3 Hz, and are mainly propagating outward from the Sun. Moreover, the turbulence composed by these Alfvénic waves cascades to sub-ion scales (corresponding to f ≳ 3 Hz), and the spectral index changes from −1.5 (f ≲ 1 Hz) to −3.3 (f ≳ 1 Hz). For the source of the observed Alfvénic waves and Alfvénic turbulence, referring to the suggestion given by Gosling et al. (2010), they may exist within the flux rope if this SFR originates from a small-scale coronal mass ejection. However, if this SFR results from the MHD turbulence in the solar wind (Zank et al. 2017), it would be a natural result that SFRs contain the waves and turbulence coming from the surrounding environment. Besides, Alfvénic waves can be produced due to the change of the magnetic field topology through magnetic reconnections, and the nonlinear interaction among Alfvénic waves could further produce the Alfvénic turbulence (e.g., Cranmer et al. 2007). These three possible sources cannot be distinguished via single spacecraft observation. It should be noted that Alfvénic waves and Alfvénic turbulence also exist in magnetic clouds (e.g., Li et al. 2017; Guo et al. 2019).

We also identify quasi-monochromatic and left-hand polarized electromagnetic waves with f ≳ f_cp at SFR leading and trailing edges. As the outward A/IC and inward FM/W mode waves in the plasma frame are two candidates to explain these high-frequency electromagnetic waves, to distinguish these two modes, we investigate the wave dispersion relation and estimate the electric field effective length based on the wave theory in the spacecraft frame. We find that FM/W mode waves cannot explain the observed waves with ∼2–3 Hz at the SFR leading edge. Moreover, the electric field effective length corresponding to the FM/W mode wave is larger than that estimated from the A/IC mode wave, and the latter seems to be closer to the values given by Mozer et al. (2020). Therefore, we conclude that the observed f ≳ f_cp electromagnetic waves correspond to A/IC mode waves. In addition, PSP also detects ion-cyclotron waves in steady solar wind (Bowen et al. 2020; Verniero et al. 2020), and this study gives direct observational evidences of ion-cyclotron waves in SFR.

The observed ion-cyclotron waves can be driven by the ion perpendicular temperature anisotropy instability or the ion beam instability (e.g., Gary 1993; Liu et al. 2019; Sun et al. 2019). Since the SFR flow velocity is nearly the same as the speed of ambient solar wind, SFR cannot significantly compress the ambient plasma, inducing large ion perpendicular temperature anisotropy therein. On the other hand, the proton beam can produce both A/IC and FM/W mode waves along the beam direction (e.g., Liu et al. 2019), which is inconsistent with the presence of only one wave mode, i.e., outward A/IC mode waves. As a consequence, we propose that the observed waves may not be locally produced by the ion perpendicular temperature anisotropy instability or the ion beam instability.

Besides, SFRs with medium and high Alfvénicity are normally discarded in automated identification procedures, which use a low Walén slope threshold (≤0.3) or low normalized cross helicity (≤0.3) (e.g., Chen et al. 2020; Zhao et al. 2020a, 2020b). The Walén slope in our event is about 0.37 during 08:34:45 UT−08:46:05 UT in a de Hoffman–Teller (HT) frame where the HT speed is [332.34, 5.83, 12.99] km s⁻¹, and this event is not listed in the database given by Chen et al. (2020) and Zhao et al. (2020a, 2020b). It should be noted that Gosling et al. (2010) have examined the SFR database recognized by several identification procedures (e.g., Moldwin et al. 1995, 2000; Feng et al. 2007; Cartwright & Moldwin 2008), and they concluded that SFRs with high Alfvénicity are relatively rare in solar wind. Actually, the SFR event database analyzed by Gosling et al. (2010) suffer a low Walén slope limit. There may be still no robust conclusion on the occurrence rate of SFR with medium and high Alfvénicity. Moreover, Hu et al. (2018) found that the duration of SFRs (from 10 minutes to several 100 minutes) follows a power-law distribution. Most events detected by PSP have durations of the order of 10 minutes (also see Chen et al. 2020; Zhao et al. 2020a, 2020b). Alfvénic structures can also arise at a timescale of 10 minutes (e.g., Bale et al. 2019; Kasper et al. 2019). Therefore, an effective identification method needs to be developed in order to discriminate SFRs with medium and high Alfvénicity from Alfvénic structures, which will be studied in the future.

This work was supported by the NNSFC 41974203, 41531071, and 11673069. We acknowledge the NASA Parker Solar Probe Mission and the SWEAP team led by J. Kasper and the FIELDS team led by S. D. Bale for use of data. The data can be downloaded from the NASA CDAWeb (https://cdaweb.gsfc.nasa.gov/pub/data/psp/). The SWEAP and FIELDS experiments on the Parker Solar Probe spacecraft were designed and developed under NASA contract NNN06AA01C.