Switchbacks near Boundaries of Small-scale Magnetic Flux Ropes in the Young Solar Wind from Parker Solar Probe Observations

The Parker Solar Probe (PSP; N. J. Fox et al. 2016; N. E. Raouafi et al. 2023) mission has revealed frequent occurrences of switchbacks (SBs—sharp magnetic field deflections accompanied by radial velocity spikes; S. Bale et al. 2019; J. C. Kasper et al. 2019) as key structures within the solar wind. These structures have been reported by many authors (e.g., S. Kahler & R. Lin 1994; M. Neugebauer et al. 1995; S. Kahler et al. 1996; N. Crooker et al. 2004; M. Owens et al. 2013; J. Huang et al. 2017; T. Horbury et al. 2018; T. Woolley et al. 2021), particularly in the young solar wind (e.g., S. Bale et al. 2019; J. C. Kasper et al. 2019; T. Dudok de Wit et al. 2020; T. S. Horbury et al. 2020; F. Mozer et al. 2020; C. Froment et al. 2021).

However, the origin and generation mechanisms are still under debate (N. E. Raouafi et al. 2023), with two prevailing perspectives: a solar origin or local generation within interplanetary space. The solar origin hypothesis suggests that SBs form due to processes occurring near the Sun, including surface-driven mechanisms such as photospheric flows (i.e., granulation and supergranulation) and network magnetic field evolution (S. D. Bale et al. 2021; J. Kasper et al. 2021; D. de Pablos et al. 2022; N. Fargette et al. 2022; C. Shi et al. 2022; S. Bale et al. 2023), small-scale jet-like eruptions like spicules or coronal jets injecting plasma into the solar wind (A. C. Sterling & R. L. Moore 2020; M. Neugebauer & A. C. Sterling 2021; D. Telloni et al. 2022; J. Lee et al. 2024; N. Bizien et al. 2025), and interchange reconnection at the boundary between open and closed magnetic field regions (Y. Yamauchi et al. 2004; L. Fisk & J. Kasper 2020; T. S. Horbury et al. 2020; A. C. Sterling & R. L. Moore 2020; G. Zank et al. 2020; S. D. Bale et al. 2021; J. F. Drake et al. 2021; J. He et al. 2021; P. F. Wyper et al. 2022; J. Huang et al. 2023a; Y. J. Rivera et al. 2024). F. S. Mozer et al. (2021) suggested that SBs form in transition regions near the Sun, further supporting the idea that their origin may be linked to dynamic changes in solar wind properties close to the solar surface. Unlike the solar origin hypothesis, the in situ formation of SBs gains credibility from the findings of V. K. Jagarlamudi et al. (2023), who reported that their occurrence increases with heliocentric distance.

Various mechanisms may also generate SBs within interplanetary space. Alfvén waves and firehose-like instabilities have been proposed as possible drivers of switchback formation (A. Larosa et al. 2021). Additionally, SBs could evolve above the Alfvén point due to dynamic instabilities in the expanding solar wind (N. A. Schwadron & D. J. McComas 2021). Another mechanism involves the expansion of the solar wind coupled with turbulence-driven processes, which can stretch and amplify preexisting magnetic field fluctuations, potentially leading to SB formation (S. Landi et al. 2006; L. Matteini et al. 2015; A. Tenerani & M. Velli 2018; D. Ruffolo et al. 2020; J. Squire et al. 2020, 2022; A. Tenerani et al. 2020; A. Mallet et al. 2021; M. M. Martinović et al. 2021; N. A. Schwadron & D. J. McComas 2021; M. Shoda et al. 2021; G. Toth et al. 2023).

Distributions and dynamics of the rotation angle of SBs have been studied extensively (T. S. Horbury et al. 2020; A. R. Macneil et al. 2020; N. Fargette et al. 2022; R. Laker et al. 2022; M.-M. Meng et al. 2022). SBs tend to rotate in a clockwise direction relative to the Parker spiral in the ecliptic plane in the quiet solar wind, as reported based on the measurements from the first PSP encounters (N. Fargette et al. 2022; M.-M. Meng et al. 2022) or Helios (A. R. Macneil et al. 2020). T. S. Horbury et al. (2020) and R. Laker et al. (2022) showed that SBs predominantly deflect in the tangential (T) direction, rather than the normal (N) direction, in the RTN coordinates. Here, R indicates the radial direction from the Sun to PSP, T is defined as the cross product of the solar rotation axis and the R axis, and N results from the third vector completing the right-handed orthogonal rule. Moreover, they observed that successive SBs often maintain similar orientations over several hours. R. Laker et al. (2023) reported a coherent deflection signature along arc polarized on the T–N plane, suggesting an association with proton core enhancements. O. V. Agapitov et al. (2023) demonstrated a relationship between the deflection angle and the Alfvénicity of SBs, emphasizing the constraint of SB’s Alfvénicity.

Another mesoscale structure in the solar wind is small-scale magnetic flux ropes (SMFRs; M. B. Moldwin et al. 1995), which are prominent structures within the heliosphere. Although SMFRs have been frequently observed (e.g., W. Yu et al. 2016; Q. Hu et al. 2018; Y. Chen et al. 2019; K.-E. Choi et al. 2021), particularly in the inner heliosphere (e.g., M. Cartwright & M. Moldwin 2010; L.-L. Zhao et al. 2020, 2021; Y. Chen et al. 2021, 2023; J. F. Drake et al. 2021; J. Eastwood et al. 2021; C. Shi et al. 2021; Y. Chen & Q. Hu 2022; H. Farooki et al. 2024), their origins and structural properties continue to be explored. Recently, N. Huang et al. (2023b) reported that the occurrence rate of small ejecta from the solar surface is comparable to the detection rate of SMFRs, supporting their solar origin (A. Rouillard et al. 2011, 2009). Alternatively, the helicity of in situ SMFRs (i.e., chirality, such as left-handed or right-handed), as derived from modeling, has not exhibited a clear pattern (K.-E. Choi et al. 2022; Y. Chen & Q. Hu 2025). This contrasts with large-scale flux ropes, whose helicity is consistently aligned between in situ observations and solar filaments (e.g., D. Rust 1994), with a dependence on the solar cycle, supporting their solar origin. Furthermore, the lack of a systematic helicity preference in SMFRs suggests that they may not share the same solar origin and could instead originate from interplanetary processes (e.g., M. Moldwin et al. 2000; M. Cartwright & M. Moldwin 2008; A. Greco et al. 2009; H. Tian et al. 2010; H. Feng et al. 2015; D. Telloni et al. 2016; J. Zheng & Q. Hu 2018; E. Sanchez-Diaz et al. 2019; B. Lavraud et al. 2020; V. Réville et al. 2020). This approximately even distribution of helicity may also indicate the presence of the counterhelicity type within SMFRs (Y.-D. Jia et al. 2024), adding complexity to their structural characteristics.

Several potential relationships between SBs and SMFRs have been proposed: (i) SMFRs may generate SBs (A. C. Sterling & R. L. Moore 2020), (ii) SBs may give rise to SMFRs (C. Shi et al. 2024), and (iii) SBs may be observed either within SMFRs (Y. Chen et al. 2021; J. F. Drake et al. 2021; O. V. Agapitov et al. 2022) or in the regions between them (K.-E. Choi et al. 2024). A. C. Sterling & R. L. Moore (2020) suggested coronal jets as a source of SBs, arguing that erupting minifilament flux ropes create Alfvénic fluctuations, which steepen into SBs during propagation. Recently, C. Shi et al. (2024) suggested, through a three-dimensional (3D) MHD simulation, the possibility that the reconnection between two SBs could generate a flux rope. J. F. Drake et al. (2021) and O. V. Agapitov et al. (2022) demonstrated that flux ropes formed through interchange reconnection exhibit signatures consistent with SBs. Y. Chen et al. (2021) investigated SMFRs that overlap with SBs and suggested that some SBs may be detected when the spacecraft traverses flux-rope-like structures, providing observational support for this theory. A recent study by K.-E. Choi et al. (2024) presented sequential observations of low-β SMFRs, which are embedded by blobs and distributed radially during PSP’s corotational orbits with the Sun, following a radial alignment within a narrow longitudinal zone. They reported that these flux rope structures exhibited relatively low fluctuations compared to the surrounding solar wind and the presence of SBs in between these flux ropes.

While K.-E. Choi et al. (2024) have predominantly centered on the properties and behaviors of SMFRs, this study shifts the focus to the relationship between SMFRs (gray area) and SBs (light-blue area), focusing on SB properties and their distribution to better understand SBs’ association with SMFRs and shared origins. In this paper, we present the notable patterns of SBs occurring at the boundaries of low-β SMFRs based on published SB databases by J. Huang et al. (2023a) and O. V. Agapitov et al. (2023). Our results reveal well-organized relative orientations of leading and tailing SBs’ axes in these cases, with the SBs exhibiting directional flipping of the magnetic field, meaning the radial direction remains constrained while the transversal magnetic field reverses within the SBs. Especially, this tendency is pronounced at the leading and trailing edges of SMFRs, suggesting a systematic interaction between SBs and SMFR boundaries.

We focus here on PSP’s Encounter 1 (E1) and Encounter 4 (E4), when PSP observed a series of SMFRs while the PSP’s azimuthal speed closely matched the solar rotation for 106 and 84 hr, respectively. Figures 1(b) and 1(c) illustrate the longitudinal variation and spatial distribution of SMFRs and SBs during the inbound corotating interval of E4. Across the total 190 hr intervals for E1 and E4, encompassing 36 low-β SMFRs and 343 SBs, we infer a common origin for each corotating interval from the same source region with longitudinal variation of less than 15. These observations span a heliocentric distance range of 34.7–45.7 R_S (solar radii).

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Figure 1 presents a series of low-β SMFRs detected within the corotating interval of PSP, indicated on the orbital trajectory of PSP in Figures 1(j) and (k). The interval contains multiple SB structures located between SMFRs (K.-E. Choi et al. 2024). In these intervals, SMFRs in the PSP data were identified by visually analyzing the magnetic field and plasma properties obtained from the corresponding measurements. The magnetic field intensity is enhanced by approximately 20%–40% compared to the average over a 2 hr window surrounding each event, and smooth rotation of magnetic field direction is observed. The proton density (Figure 1(g)) and/or proton temperature (Figure 1(h)) are typically lower than the surrounding solar wind, consistent with transient SMFR events (highlighted by gray regions in Figure 1(a)–1(i)). Furthermore, the power spectrum of magnetic field perturbations exhibits a notable reduction within SMFRs. While this specific feature is not visually presented in this paper, it aligns with broader observational trends and supports the classification of SMFR events. These features collectively signify transient flux rope structures in the young solar wind (see K.-E. Choi et al. 2024 for details on previous event selection). In determining SMFRs, the consideration of specific physical quantities, along with the characteristic features of the B-spectrum, provides the most effective approach in the young solar wind for distinguishing them from torsional Alfvén waves (e.g., K. Marubashi et al. 2010), which can appear as pseudomagnetic flux ropes.

Alfvénic background solar wind conditions (Y. Chen et al. 2021) and wave activities (C. Shi et al. 2021) make determining the boundaries of SMFRs in the young solar wind challenging. To address this, we have optimized the boundaries of SMFRs (start and end times) by minimizing the rms error (Erms < 0.35) in the force-free modeling for the cases of plasma beta (the ratio of plasma and magnetic pressure) less than 1 (β < 1) and incorporating plasma parameters into the analysis, enabling more precise and reliable event identification compared to the prior analyses in K.-E. Choi et al. (2024). The plasma beta inside SMFRs is not necessarily low as low beta is not a defining criterion for SMFRs in general. However, it serves as a useful indicator for distinguishing pseudo-SMFRs. We have allowed plasma beta to be lower than that of the background solar wind and noted in Table 1 cases where model fitting was not appropriate due to β ≥ 1 within the SMFR or fitting failure. The magnetic field data used in this study are from the PSP Fluxgate Magnetometer, which is part of the FIELDS suite (S. Bale et al. 2016), and plasma data are from the Solar Wind Electrons Alphas and Protons suite (J. C. Kasper et al. 2016), which includes the Solar Probe Cup (SPC; A. W. Case et al. 2020) and Solar Probe Analyzers (SPAN-i and SPAN-e; P. L. Whittlesey et al. 2020; R. Livi et al. 2022). We use the SPC data collected during E1, while the SPAN-i data were used for the fitted proton in the interval from E4. The electron density is derived from the analysis of the plasma quasi-thermal noise (QTN) spectrum measured by the FIELDS Radio Frequency Spectrometer (M. Pulupa et al. 2017 ; M. Moncuquet et al. 2020). Additionally, we use SPAN-e to process electron pitch-angle distribution data.

SBs, denoted by blue vertical regions in Figure 1(b)–1(c), were identified using published catalogs (J. C. Kasper et al. 2019; O. V. Agapitov et al. 2023; J. Huang et al. 2023a). Remarkably often, during these intervals, SBs were located near the edges of SMFRs. In the pitch-angle distribution of suprathermal electrons, a beam consistently appears at 180°, indicating the toward polarity of the interplanetary magnetic field throughout in the interval during SBs, and the beam sometimes broadens, as seen in Figure 1(a). A more detailed investigation of the spatial and temporal relationships between SBs and SMFRs is provided in Figure 2 and summarized in Table 1.

Figure 2 presents two SMFRs—Cases A and B—recorded during E1 and E4, respectively, with SBs bounding each side of each SMFR. Within SMFRs, the radial component (B_r) is dominant, whereas it is significantly reduced or even reverses polarity during SBs. The tangential (B_t) and normal (B_n) components within SMFRs are consistent with the cylindrical model fitting (red curves in Figures 2(a) and 2(c)). The sign of leading and trailing SBs B_t or/and B_n changes when comparing the leading (blue) and trailing (red) SBs bounding each of the SMFRs. Figures 2(b) and 2(d) further illustrate these spatial characteristics in spherical coordinates, showing distinct deflection of the magnetic field in the SBs. To clarify the large-scale rotation within the SMFRs, the magnetic field vectors in Figures 2(b) and 2(d) are smoothed within the SMFR intervals (gray lines). The fitted impact parameters, referring to the minimum distance between the spacecraft trajectory and the modeled flux rope axis, are 0.90 for Case A and 0.95 for Case B, indicating that both crossings were significantly off-axis (black crosses).

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3.1. Case A: T-flipping Event on 2018 November 2

The T-flipping event observed on 2018 November 2, at 45.1R_S, provides an example of how SBs alter the tangential (T) component of the magnetic field in the solar wind, during PSP’s E1. This Case A event is characterized by a distinct reversal of the tangential component (B_t) within the leading and trailing SBs bounding the flux rope. Figures 2(a)–2(b) illustrate the temporal and spatial characteristics of this event. The time series in Figure 2(a) presents the SMFR and its surrounding SBs, while the magnetic field map in Figure 2(b) shows the polarity changes in B_t.

In Figure 2(a), the SMFR, lasting approximately 3 hr, exhibits wave-like structures near its trailing edge (∼1200 UT), accompanied by density fluctuations and a slight temperature enhancement. These features, located near the SMFR’s boundary, are consistent with similar observations reported by C. Shi et al. (2021), where such wave-like structures were found near the edges of SMFRs. The leading and trailing SBs are positioned about 10 minutes apart from the SMFR’s edges, a separation that may have arisen from the expansion of the SMFR or its surrounding structures during propagation. The leading SB is situated near the center of a blob-like structure with enhanced density, while the trailing SB is associated with a more perturbed region. Interestingly, the radial component (B_R) shows a clear reversal near the trailing SB, further emphasizing the localized polarity changes.

In Figure 2(b), the surrounding solar wind is dominated by the radial (R) direction, with a slight tangential (T) contribution (black cross symbol), consistent with Parker spiral characteristics. Following the definition of the magnetic axis in SBs, which treats them as magnetic tubes (V. Krasnoselskikh et al. 2020), we determined the SB axes (blue and red cross symbols) based on the average of the local magnetic field within each SB. A reference plane (black curve) is constructed geometrically from the leading and trailing SB axes and represents a geometric reference frame that captures their relative orientation. This plane is not fitted to the local magnetic field data but is defined solely by the two mean axis directions. While the plane is defined in this geometric manner, the locally measured magnetic field vectors within each SB show a notable tendency to align with it. Although the magnetic field within each SB is expected to be distributed around its axis, the observed alignment with the plane defined by the two axes is noteworthy. Black thick arrows denote regions within the SBs where alignment with the geometrically defined plane is more pronounced. This observation suggests that the plane reflects the local deflection of the magnetic field within each SB, indicating a strong geometric relationship between the two SBs despite the SMFR separating them. This provides a clue that the two SBs are dynamically or geometrically related.

The SMFR axis was compared with the plane formed by the two SBs. Interestingly, the flux rope axis is tilted at an angle of approximately 632 relative to this plane, indicating a significant inclination relative to the SB-defined plane. This notable tilt suggests a complex geometric relationship between the SB’s plane and the SMFR’s axes. While the exact nature of this relationship remains unclear, our preliminary analysis reveals intriguing trends that are further explored in Section 3.3.

Finally, a schematic of this configuration is presented in Figure 4 and is discussed in detail in Section 4, where potential mechanisms underlying these dynamics are also explored.

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3.2. Case B: N-flipping Event on 2020 January 26

3.3. Basic Statistics for E4: Geometric Properties Depending on Heliocentric Distance

In this section, we focus on E4 for the statistical analysis. This selection is guided by previous studies (R. Laker et al. 2022), which reported that certain PSP encounters, including E1 and E4, lack the asymmetry axis commonly observed in SB deflections. This absence suggests a reduced influence of global magnetic structuring. In addition, E4 contains a particularly large number of well-defined SMFR events in the extended interval (see Figure 1(k)), offering a valuable data set to investigate their geometric relationship with SBs under relatively neutral background conditions.

To ensure a consistent comparison, we begin by noting that during E1 and E4, a total of 343 SBs were identified within a 15 latitudinal zone. For the detailed analysis presented in this section, however, we concentrate on the E4 extended range of 5° in Carrington longitude depicted by the gray box in Figures 1(j) and 1(k) in this section. We analyze the 22 SMFRs and 266 SBs identified over the 4 day interval within the range of 51.3 to 30.4 R_S. Figure 3(a) provides the distribution of SBs as a function of their temporal proximity to SMFRs, revealing that the majority of SB–flux rope (FR) intervals (dT_SB−FR) are observed within 15 minutes. This suggests that SBs predominantly cluster around SMFR boundaries, implying a significant connection. Figure 3(b) shows the deflection angles between successive SBs, differentiating cases where both leading and trailing SBs are present at SMFR boundaries from those without such associations. Specifically, we identify 17 SMFRs that are bounded by SBs on both sides, amounting to 34 SBs in total, depicted by red bars in Figure 3(b), whereas those without SMFR-related boundaries are marked in black. The results indicate a significant difference in angular deflections, with SMFR-related SBs exhibiting larger angular changes than their non-SMFR counterparts. As noted in the introduction, previous studies (T. S. Horbury et al. 2020; R. Laker et al. 2022) found that successive SBs tend to maintain similar orientations over several hours. Our result in Figure 3(b) is consistent with those for non-SMFR-related SBs, showing the consistency in deflection angles between adjacent SBs. However, we found that SMFR-related SBs experience stronger deflections, potentially due to the local magnetic restructuring processes associated with SMFRs.

Table 1 provides a summary of the 17 SMFRs with SBs at both ends, accounting for 77% of the total 22 SMFRs identified in E4. This high fraction suggests that the presence of SBs at both ends of SMFRs is not a rare occurrence but rather a characteristic feature in this region. The table lists the start and end times of each SMFR, the success of the force-free model fitting, and detailed properties of the leading and trailing SBs, including their duration, time difference, angle difference, flipping patterns (T and/or N), the angle , and distance from the Sun. Additionally, the angle represents the inclination between the SMFR axis (determined by the force-free model fitting) and the plane containing the SBs at SMFR edges. By systematically comparing these cases as a function of heliocentric distance, we find that the TN flipping pattern becomes more frequent at closer distances to the Sun. Furthermore, SMFRs exhibiting TN flipping tend to have larger values, indicating that the SBs in these cases form at a more inclined angle relative to the SMFR axis. The E1 corotating interval (<15 latitudinal zone) has a similar trend provided by Table A1 in the Appendix.

Table 1. Summary of SMFRs Bounded by SBs for E4

No.	FR		Leading SB			Trailing SB			Flipping Component (in RTN)	d	Heliospheric DistanceRS
	Time in Jan of 2020 (dd/hh:mm:ss - hh:mm:ss)	FF Modela	Duration (minute)	dTSB − FRb (minute)	dθc (°)	Duration (minute)	dTSB − FRb (minute)	dθc (°)
1	24/16:00:00 - 17:59:36	Success	1.2	−0.2	36.7	0.9	5.8	52.0	⋯	20.8	47.2
2	24/21:09:30 - 22:39:36	Success	3.0	0.5	94.1	1.9	5.3	60.6	⋯	38.9	46.1
3	24/23:47:24 - 25:19:54	Successe	1.1	−2.6	75.1	0.7	3.2	68.6	⋯	30.2	45.4
4	25/05:52:30 - 07:20:00	Successe	0.5	−1.9	42.1	0.2	−3.2	79.6	T, N	62.7	44.0
5	25/10:19:48 - 11:39:30	Successe	0.4	0.4	79.9	6.0	1.5	49.8	T	76.0	42.9
6	25/16:02:18 - 16:30:24	Success	22.0	−3.3	89.7	2.9	7.7	94.0	T	44.8	41.7
7	25/22:55:18 - 24:33:12	Success	3.3	10.2	128.9	5.0	1.8	37.7	⋯	3.1	40.0
8	26/00:50:24 - 01:15:00	Success	0.7	6.2	61.2	0.8	0.7	96.7	T	32.9	39.7
9	26/03:55:18 - 04:24:30	Success	0.1	7.0	83.7	4.0	0.5	35.6	T	37.8	38.9
10	26/04:40:18 - 06:07:12	Success	0.7	−3.9	44.9	1.2	−0.2	42.7	⋯	17.7	38.7
11	26/06:14:30 - 07:06:48	Success	1.2	7.5	42.7	0.1	3.8	82.4	T	56.0	38.4
12	26/07:23:18 - 08:06:24	Success	0.6	6.3	62.8	4.0	4.9	44.6	N	50.1	38.1
13	26/13:49:54 - 15:16:24	Success	0.1	5.7	77.2	4.6	7.1	71.5	T	33.0	36.6
14	26/19:20:06 - 19:45:06	Success	13.5	4.1	41.5	5.0	−0.1	36.2	T, N	68.8	35.6
15	27/11:19:30 - 12:39:30	Failure	0.7	1.3	40.5	0.5	0.9	20.1	T, N	⋯	32.4
16	27/14:00:06 - 14:30:18	Success	0.3	2.5	30.1	0.5	0.2	35.0	N	30.0	32.0
17	27/14:30:06 - 14:59:30	Success	0.5	−0.3	35.0	0.1	0.1	86.5	T, N	63.9	31.9

Notes.

^aFF model: Cylindrical linear force-free model. ^bTime difference from each SMFR’s edge to SB’s edge. ^cDeflection angle of SBs relative to background interplanetary magnetic field. ^dInclination angle of SMFR axis from the SB’s plane. ^eβ_plasma≃1 cases if β_plasma based on QTN electrons.

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In this paper, we present the results of the analysis of the relationship between SMFRs and SBs in the young solar wind based on PSP observations during E1 and E4. According to the statistical results for the SB deflection distributions in R. Laker et al. (2022), SBs demonstrate a preference for the tangential direction of their axial magnetic field (as illustrated in Figure 4 in R. Laker et al. 2022). While R. Laker et al. (2022) identified systematic magnetic configurations and specific symmetry axes in most of the PSP encounters (from the first eight PSP encounters), they noted that E1 and E4 deviated from this trend, suggesting a possible lack of alignment with large-scale solar wind structures. Our analysis focuses on these “exceptional” encounters, revealing that the more chaotic SBs orientation seen in E1 and E4 are, in fact, connected to smaller-scale solar wind structures. We identified distinct connections (alignment) of SBs with the boundaries of SMFRs and reversal of leading and trailing SBs axial magnetic filed polarity patterns by examining their spatial and magnetic configurations. Figure 4 schematically illustrates possible cases of SB polarity flipping. In this figure, two SBs—referred to as the leading and trailing SBs—are shown on either side of an SMFR, represented by blue and red arrows, respectively.

The observation of SB deflection angles demonstrates the relationship between successive SBs, suggesting coherent magnetic behavior across multiple events. As emphasized in T. S. Horbury et al. (2020) and R. Laker et al. (2022), successive SBs often maintain a consistent deflection angle over extended intervals, suggesting these coherent magnetic structures are shaped by large-scale solar wind dynamics. In contrast, the more recent findings of R. Laker et al. (2023) reveal cases of polarity reversals (TN flipping) in successive SBs, indicating localized and potentially transient magnetic interactions. One of our results shows that during E4, T- and/or N-flipping patterns are observed in 12 cases (about 70.6% of the total 17 SMFRs), illustrating the significant occurrence of polarity reversals. Our study aligns more closely with the findings of R. Laker et al. (2023), as we observe distinct TN polarity flipping patterns. However, unlike R. Laker et al. (2023), which reported these patterns in successive SBs over extended regions, we identify such behaviors specifically near SMFR boundaries.

Given the narrow longitudinal detection region, it is clear that these features originate from the same coronal structures, which can be traced back to the source surface. However, subtle variations in these structures may account for the observed differences in their properties and spatial configurations. It is also worth emphasizing that the SMFRs examined in this study are characterized by their transient nature and low-β. Furthermore, while some SMFR-related SBs occur within the same series of SMFRs, their properties are not uniform. The distance between SBs and SMFR boundaries, the obliqueness of SB orientations relative to the SMFR axes, and their characteristics also vary with heliospheric distance, as mentioned in Section 3.3. In general, SMFRs and SBs are influenced by the background solar wind conditions and the surrounding magnetic environment, with their properties varying depending on factors such as heliocentric distance and solar cycle phase. However, due to the limitations of the detection region, finer structural details may remain unresolved. To better understand these variations, it is necessary to examine a broader range of heliocentric distances and different phases of the solar cycle. Further statistical analysis and simulations incorporating diverse solar wind conditions will be essential for a more comprehensive interpretation.

Extending the results reported in R. Laker et al. (2023, 2022), our study highlights how SMFR boundary affects the behavior of SB deflection angles. Furthermore, the suggested cogeneration of SBs and SMFRs, which could emerge from interactions between multiple SBs, as shown in recent 3D MHD simulations (C. Shi et al. 2024), suggests a tightly coupled relationship between these structures. In summary, our key findings in this paper are as follows:

(1) Most of the 22 SMFRs recorded during PSP E 4 were surrounded by SBs near the SMFR boundary: SBs were present at 86.4% of the SMFR boundaries, and 77.3% of the SMFRs were bounded by SBs at the leading and trailing edges.

(2) In all, 35.9% of the 266 SBs observed during PSP E4 demonstrated a statistically significant (with the significance level α < 0.05) relation to the SMFR boundary in the 15 minute vicinity. In contrast, 64.1% of the SBs were randomly distributed in the inter-SMFR regions.

(3) Successive SBs associated with SMFRs showed systematic variations in their axial magnetic field direction. In particular, a large majority (71%) of SMFR-related SBs exhibited T and/or N component polarity reversal patterns between the leading and trailing SBs.

K.E.C. and O.V.A. were supported by NASA contracts 80NSSC22K0433, 80NNSC19K0848, and 80NSSC21K1770 and NASA’s Living with a Star (LWS) program (contract 80NSSC20K0218). We thank the NASA Parker Solar Probe Mission, the SWEAP team led by Justin Kasper, and the FIELDS team led by Stuart Bale for the use of the data.

Table A1 summarizes 7 SMFRs from the inbound and outbound corotating interval of E1 out of a total 25 SMFRs and shows that the occurrence of TN flipping is associated with larger values, consistent with the trend observed in E4.

Table A1. Summary of SMFRs Bounded by SBs for E1

No.	FR		Leading SB			Trailing SB			Flipping Component (in RTN)	d (°)
	Time	FF Modela	Duration (minute)	dTSB − FRb (minute)	dθc (°)	Duration (minute)	dTSB − FRb (minute)	dθc (°)
1	2018-11-02/09:31:36 - 12:20:36	Success	3.9	6.7	39.1	1.7	7.5	113.9	T	63.2
2	2018-11-02/16:05:00 - 18:00:18	Success	1.1	0.2	44.3	1.4	−0.6	67.9	T, N	58.5
3	2018-11-02/20:14:54 - 23:40:06	Success	1.6	0.7	51.1	5.8	−1.5	43.7	N	63.9
4	2018-11-03/14:20:00 - 17:45:00	Failure	23.4	−6.7	67.6	16.9	2.3	33.7	N	⋯
5	2018-11-08/03:05:12 - 03:59:30	Success	2.5	0.2	65.6	1.1	−0.4	85.9	⋯	24.8
6	2018-11-08/08:19:30 - 09:19:42	Success	2.0	0.2	51.3	1.5	7.2	86.5	N	50.4
7	2018-11-08/09:59:30 - 12:30:06	Success	1.8	3.9	67.1	7.4	2.0	61.4	N	41.6

Notes.

^aFF model: Cylindrical linear force-free model. ^bTime difference from each SMFR’s edge to SB’s edge. ^cDeflection angle of SBs relative to background interplanetary magnetic field. ^dInclination angle of SMFR axis from SB’s plane.

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