Small-scale Field-aligned Currents in the Magnetopause Boundary Layer

Based on high-resolution measurements from the Magnetospheric Multiscale mission from 2015 May to 2018 June, we statistically investigate the properties of small-scale field-aligned currents (SFACs) in the magnetopause boundary layer. A total of 2235 SFACs are successfully identified. The durations of SFACs mainly fall between 0.2 and 0.3 s. Over 90% of SFACs have a width of less than 1 ion inertia length and are primarily distributed from 5 to 25 electron inertia lengths, implying that the SFACs belong to the kinetic-scale current layer. The main carriers of SFACs are electrons, and over 70% of SFACs exhibit net energy dissipation (i.e., J · E ′ > 0) with the majority of energy dissipation taking place in the parallel direction. SFACs are widely distributed spatially, and the occurrence rate of SFACs is higher in the boundary layer closer to the magnetosphere. Additionally, less than half of the total SFACs are identified in well-known structures, including the magnetic reconnection region, flux transfer event, Kelvin–Helmholtz vortex, and exhaust region, and 54% of the SFACs are in the “others” unknown structures. These results improve our comprehension of the current system at the magnetopause and the roles of SFACs in the coupling between the solar wind and magnetosphere.


Introduction
The magnetopause acts as a boundary between two distinct plasma environments: the solar wind and the magnetosphere.It serves as a crucial pathway for the coupling between these two regions (e.g., Paschmann 1997;Hasegawa et al. 2004;Paschmann et al. 2005;Hasegawa 2012;Hwang et al. 2012;Taylor et al. 2012;Lin et al. 2014).Under the dynamic pressure fluctuations of the solar wind, the magnetopause can become highly unstable, resulting in various structures at different scales.These structures within the magnetopause can facilitate the penetration of solar wind into the Earth's magnetosphere (e.g., Shi et al. 2013), allowing for the transfer of energy, momentum, and mass.Magnetic reconnection is a fundamental process capable of explosively transferring the energy stored in the field to charged particles.Reconnection occurring in the current sheet at the magnetopause is one important mechanism for the solar wind-magnetosphere coupling (e.g., Phan et al. 2004;Dahlin et al. 2014;Ergun et al. 2016a;Burch et al. 2016;Eriksson et al. 2016;Russell et al. 2016;Huang et al. 2021;Lu et al. 2022;Xiong et al. 2022).Furthermore, solar wind can also be injected into the magnetosphere through the flux transfer events (FTE) and Kelvin-Helmholtz vortex (KHV) (e.g., Lee & Fu 1985;Hasegawa et al. 2004Hasegawa et al. , 2006;;Liu et al. 2008;Hasegawa et al. 2009;Taylor et al. 2012;Merkin et al. 2013;Pu et al. 2013;Li et al. 2016;Jiang et al. 2019;Guo et al. 2021).Using high-resolution data from the Magnetospheric Multiscale (MMS) mission, Man et al. (2021Man et al. ( , 2022) ) conducted a statistical investigation of intense current structures and intense energy conversion events within the magnetopause boundary layer (MBL).Their findings indicate that intense current structures are widely distributed throughout the MBL and play a crucial role in the dissipation of energy within the boundary layer, as well as the coupling between the solar wind and the magnetosphere.
Current structures are a common feature in the near-Earth space environment, and research has shown that field-aligned currents (FACs) are critical for coupling the magnetosphere and ionosphere (e.g., Keiling et al. 2005;Anderson et al. 2014;Stawarz et al. 2017).FACs, which exhibit multiscale features, are critical to the Earth's magnetosphere.Several previous studies have investigated the role of FACs at different scales in the coupling process of the Earth's magnetosphere and ionosphere (e.g., Sugiura 1984;Lysak 1990;Lu et al. 1995;Glassmeier 1997;Korth et al. 2014;McGranaghan et al. 2017;Chen et al. 2019aChen et al. , 2019b)).Large-scale FACs, which include Region 1 currents and Region 2 currents, establish a connection between the ionosphere and the magnetosphere (e.g., McGranaghan et al. 2017;Liu et al. 2021).Recently, Chen et al. (2019a) have reported FACs in the plasma sheet boundary layer.They found that, compared to low-time resolution observations, FACs exhibit stronger current density and smaller scales (even reaching the subproton scale) under high-time resolution observations.Furthermore, they suggest that large-scale FACs are the integrated result of these small-scale FACs.
However, the general characteristics of small-scale fieldaligned currents (SFACs) in the magnetopause boundary layer remain unknown, and their impact on the solar windmagnetosphere coupling is not yet well understood.Thus, the main objective of this study is to explore the properties of SFACs in the MBL, such as their spatial and temporal scales, spatial occurrence distribution, and the physical context in which they occur.Additionally, this study aims to investigate the energy conversion in SFACs and their role in the solar wind-magnetosphere coupling process.To address these objectives, we perform a statistical study of SFAC events in the MBL.

Database and Methodology
The high-resolution data from MMS spanning from 2015 May to 2018 June are processed and analyzed in this study.For timing analysis purposes, we use data from all four satellites, but for the rest of the analysis, only the data from MMS1 are utilized.We use the magnetic field provided by the fluxgate magnetometer (Russell et al. 2016), the electric field provided by the electric double probe (Ergun et al. 2016b;Lindqvist et al. 2016), and the ion and electron measurements provided by the Fast Plasma Investigation (Pollock et al. 2016).Initially, the crossing of MBL is manually identified.Subsequently, the FACs in MBL are automatically identified by the computer using the following criteria: 1.The intensity of the current in the parallel direction is stronger than in the perpendicular one.2. The current intensity in the parallel direction within the FACs is larger than the background current intensity.3. The peak intensity of the FACs' current exceeds 0.46 μA m −2 .4. Identified FACs should be no less than five data points.5.The correlation coefficients of the magnetic field among the four satellites exceed 0.8, which can ensure the reliability of the timing analysis.
In this study, the current density is calculated using plasma moments, and the resolution of the ion data was interpolated to match that of the electron data, which is 0.03 s.
Figure 1 shows the distribution of current density |J || | in the MBL (about 10 million data values).The 5 times of the standard deviation of the |J || | distribution (0.46 μA/m 2 ) is selected as the threshold to identify FACs.
In addition, to understand the composition of the FACs, the contribution of electrons and ions to the FACs is calculated as follows: The contribution of electrons and ions to the current density for a given FAC event is calculated by computing the average value of their respective contribution proportions throughout the entire event.We set the threshold for particle contribution to the field-aligned current at 0.6.If the contribution of ions (electrons) to the current intensity is greater than 0.6, then ions (electrons) are considered the main current carriers, otherwise, the currents are carried by both ions and electrons.Based on the above criteria, we identified 2235 SFACs within the MBL.The relevant analysis and in-depth exploration will be carried out in the following section.Figure 2(j) shows the current intensity in the parallel direction using ion and electron data separately.Figure 2(k) displays the contribution ratio of ions and electrons to the total field-aligned current intensity.One can see that electrons dominate the fieldaligned current intensity in this event.

Case Study
Figure 3 presents the ion-dominated FACs event on 2016 November 27 at [9.9, 6.7, 0.7] R e in the GSE coordinates.Figures 3(a   13:48:09.72UT).Therefore, this FAC also belongs to SFACs.The contribution of the ions to the total field-aligned current intensity predominates in this SFAC, as is shown in Figures 3(j)-(k).The electron velocity has significant disturbances, and the three components of the ion velocity experience relatively minor disruptions throughout this SFAC.
By comparing (h)-(k) in Figures 2 and 3, it can be observed that regardless of whether SFACs are electron-dominated or ion-dominated, the velocity variations of ions during their duration are relatively small, while disturbances in at least one component of the electron velocity are quite noticeable.The trends in current density variations of SFACs are generally consistent with the ones computed using only electron data, while the field-aligned current density remains relatively constant when calculated using only ion data.Such characteristic is commonly observed in our statistical events, which implies that the changes in the current intensity of SFACs in the MBL are primarily caused by perturbations in electron velocity, thus supporting the statement that electrons serve as the primary carriers of SFACs.Additionally, these two example events are classified into the "reconnection" category in the subsequent statistical analysis based on the characteristics of their background environment.Therefore, it seems that reconnection is an important factor leading to the formation of SFACs.

Statistical Analysis of SFACs
The FACs with the scale around ion scales are named as SFACs in our study.Similar to the aforementioned analysis, there are a total of 2235 SFACs in MBL.To comprehensively understand the fundamental properties of SFACs in the MBL, a statistical work is performed as follows.

Spatial and Temporal Scales of SFACs
Figure 4 shows the distribution of the time duration for all SFACs.The number of SFACs first increases from 0.15 to 0.27 s, and then gradually decreases.The duration of SFACs is mostly less than 0.5 s, and the majority of the SFACs have a duration between 0.15 and 0.39 s.
Figure 5 shows the distribution of the spatial scale of FACs normalized by the local ion and electron inertial lengths.The spatial scales of the SFACs are obtained by timing analysis as shown in Section 3. It is found that only ∼10% of the SFAC events have a spatial scale larger than 1 d i (Figure 5(a)), and the spatial scales of 62% of the SFACs are less than 0.5 d i .Most of the SFACs have a spatial scale mostly distributed in the range of 5-25 d e .Thus, it is clear that the FACs observed in the MBL are small-scale structures.

Spatial Distribution and Occurrence Rate Distribution of SFACs
Figure 6 depicts the spatial distribution of over 2235 SFACs in the MBL and the occurrence rate therein.One can see that the SFACs occur more frequently at the subsolar region in the X-Y plane (Figure 6(a)), and the SFACs occur mainly near the ecliptic plane with Z < 3 R e in the X-Z and Y-Z planes (shown in Figures 6(b) and (c)).In order to eliminate the effect from the orbit of the MMS mission, the occurrence rate is calculated.SFACs have a higher occurrence rate in the MBL closer to the Earth's magnetosphere, and demonstrate a preference for the dawn sector in the dawn-dusk distribution (Figure 6(d)).Figures 6(e) and (f) show that the occurrence rate of SFACs is asymmetric in the Northern and Southern Hemispheres (i.e., larger occurrence rate and broader spatial region in the Northern Hemisphere).

Contribution of Electrons and Ions to the Field-aligned Current Intensity
Figure 7 presents the contribution of electrons and ions to the SFACs.One can see that 62.9% of SFACs are mainly carried by electrons, while 23.7% of SFACs are primarily carried by ions.The equal contribution of both kinds of particles occurs in only 13.4% of SFACs.This indicates that the electrons have a significant impact on the composition of SFACs, which is in agreement with previous studies on field-aligned currents (e.g., Korth et al. 2014;McGranaghan et al. 2017;Chen et al. 2019a).+ ´is extensively employed as a measure of energy dissipation in space plasmas (e.g., Zenitani et al. 2011;Burch et al. 2016;Fu et al. 2017;Huang et al. 2018;Torbert et al. 2018;Huang et al. 2019;Hwang et al. 2019;Zhou et al. 2019;Huang et al. 2021).It can be seen that 77.36% of SFACs have J • E′ > 0 (Figure 8(a)), suggesting that the field's energy is converted into the plasma's thermal and kinetic energy for most of the SFACs.Parallel, perpendicular, and total J • E′ were calculated for data at each time point during the duration of the SFACs and then averaged separately.The results are displayed in Figure 8(b).Using 0.5 and 1.5 as the threshold dividers, one can find that the energy dissipation dominated in the perpendicular direction of the SFACs is only approximately 11%.Conversely, energy dissipation in the SFACs is primarily carried out in the parallel direction.

Spatial Structures Related to SFACs
Several previous studies have been conducted on the formation mechanisms of FACs.Ma & Otto (2013) provided a detailed presentation of the formation and characteristics of FACs using numerical simulations.Furthermore, Artemyev et al. (2018), through a combination of MMS observations at the plasma sheet boundary, equatorial ARTEMIS observations, and particle-in-cell simulations of magnetotail magnetic reconnection, demonstrated that the FACs observed near the plasma sheet boundary in the near-Earth magnetotail are likely generated by near-Earth magnetic reconnection.These two studies convincingly argued that magnetic reconnection can induce the formation of FACs.Considering that FTEs near the magnetopause are often considered as the products of magnetic reconnection, the possibility of generating FACs in FTEs is significant.Silveira et al. (2020) observed strong FAC features in the FTEs.Additionally, some studies utilized a quasistatic magnetosphere-ionosphere coupling model driven by a vortex in the boundary layer to determine how FACs depend on ionospheric and boundary layer parameters (e.g., Johnson et al. 2021).
To explore in which background conditions SFACs are more likely to form, we statistically analyzed the background environment of each SFAC.Based on the characteristics of the environmental conditions, as described in previous studies (e.g., Man et al. 2022), we categorized the SFACs into wellknown magnetopause structures: (a) magnetic reconnection region: a reversal of the magnetic field in the L-direction, coupled with a magnitude difference in electron velocity within the L-direction that exceeds 3 times the standard deviation during the continuous duration of FACs; (b) FTE: the bipolar variations in the normal component of the magnetic field and an enhancement in the core field; (c) KHV: the magnetic field exhibits quasiperiodic variations, with the total pressure reaching the maximum (minimum) at the edge (center); (d) exhaust region: the ion outflow speed V iL is greater than 100 km s −1 .Any remaining events were classified as "others," as some SFACs satisfy various feature criteria, for instance, SFACs present in FTE are identified in the exhaust region.We classify the SFACs according to the following order of priority: reconnection region > KHV > FTE > exhaust region > others.Figure 9 displays the proportions of different structures related to SFACs.One can see that 12% of SFACs occur in the magnetic reconnection region, 1% in FTE, 8% in KHV, and 24% in the exhaust region.The remaining 54% of events are classified as "others," which correspond to spatial regions that do not belong to the four aforementioned structures.Thus, this indicates that SFACs in the MBL exist widely outside the wellknown structures.

Conclusions and Discussions
In this study, 2235 SFAC events are successfully identified in the MBL.The main statistical results are summarized as follows: 1. Most SFAC events have a duration of less than 0.5 s, and the events with a spatial size of less than 1 d i approach 90%. 2. SFACs have a higher occurrence rate in the MBL close to the magnetosphere.The occurrence of SFACs has a dawn-dusk symmetry distribution.Furthermore, the occurrence rate of SFACs is asymmetric in the Northern and Southern Hemispheres (preference in the Northern Hemisphere).3. Electrons are the dominant current carriers in 62.9% of the SFAC events.4. Strong energy dissipation (J • E′ > 0) from the fields to the plasmas occurs in 77.36% of SFACs.The energy dissipation in the SFACs is primarily in the parallel direction.5.The percentage of SFACs observed in the "others" is as high as 54%, which is higher than in the well-known structures, such as magnetic reconnection region, FTE, KHV, and exhaust region.This suggests that the occurrence of SFACs does not solely depend on these well-known structures and that other factors may contribute to their formation.
SFACs are frequently observed in the MBL and exhibit strong energy dissipation.Our results provide us with a deeper insight and understanding of the SFACs observed in the MBL.Based on the analysis presented in this study, SFACs have been observed within structures such as the magnetic reconnection region and FTE, which are recognized as crucial pathways for the coupling of the solar wind and magnetosphere.Thus, it suggests that SFACs may play an essential role in the coupling between the solar wind and magnetosphere.However, there are still many issues that merit discussion.For example, the SFACs are observed in a large proportion in "others," and the mechanisms of SFAC formation in these structures remain a mystery.Thus, it is worthwhile to explore the mechanism of the generation of SFACs.
Recently, Du et al. (2023) have used a reconstruction method named as FOTE at the magnetopause to reveal that strong current filaments are driven by the twist of the local magnetic field.In our two events (Figures 2 and 3), it can be observed that they are also associated with strong current filaments in their vicinity; similar characteristics are prevalent in the events we tallied.Strong currents generally correspond to strong magnetic field variations, and twist magnetic is a type of strong magnetic field variation, but it is necessary to check whether it corresponds to a twisted magnetic structure using the FOTE method (Fu et al. 2015).The findings of Du et al. (2023) have provided some new ideas and insights for us to explore the formation of SFACs.We will conduct further analysis on our events in the future.

Data Availability Statement
This work was supported by the National Natural Science Foundation of China (42074196 and 41925018), and the Special Fund of Hubei Luojia Laboratory.We thank the entire MMS team and instrument leads for data access and support.MMS data are publicly available from the MMS Science Data Center at http://lasp.colorado.edu/mms/sdc/.

Figures 2
Figures 2 and 3 show two examples of FACs in the MBL.Figure2shows the electron-dominated FACs event.This event was observed on 2015 December 28 at [7.7, −6.7, −0.8] R e (R e is the Earth's radius) in the geocentric solar ecliptic (GSE) coordinate system.Figures2(a)-(e) display the crossing of the MBL.The Z-component of the magnetic field changes from positive to negative (Figure 2(b)), the number density gradually increases (Figure 2(d)), and the ion flux changes from highenergy particles in the magnetosphere to low-energy particles in the magnetosheath (Figure 2(a)).These features indicate that the MMS crossed the magnetopause.Many filamentary FACs are detected during the crossing of the magnetopause (Figure 2(e)), and one of them is selected to study (as marked by the blue vertical dashed line in Figures 2(a)-(e)).Figures 2(f)-(k) show the detailed observations.The peak value of the current intensity of this current structure is higher than 0.46 uA m −2 (Figure 2(j)).The duration dt of the structure is 0.28 s, the moving speed V m determined by timing analysis is ∼150 km s −1 , and thus the spatial scale is estimated as V m * dt ∼ 42 km (i.e., ∼0.56 d i or ∼24.3 d e , where d i ∼ 74.7 km is the ion inertial length, and d e ∼ 1.73 km is the electron inertial length based on averaged plasma parameters N i = N e ∼ 10.1 cm −3 from 22:21:42.82 to 22:21:43.1 UT).Thus, this FAC belongs to SFACs.The two red vertical dashed lines in Figures 2(f)-(k) mark the locations of the corresponding SFACs.The three components of the electron velocity change significantly, especially the Z-direction component (Figure2(i)), while the perturbation of the ion velocity is slight (Figure2(h)).Figure2(j) shows the current intensity in the parallel direction using ion and electron data separately.Figure2(k) displays the contribution ratio of ions and electrons to the total field-aligned current intensity.One can see that electrons dominate the fieldaligned current intensity in this event.Figure3presents the ion-dominated FACs event on 2016 November 27 at [9.9, 6.7, 0.7] R e in the GSE coordinates.Figures3(a)-(e) display the overview of this FAC.It can be seen that B z changes from positive to negative (Figure 3(b)), the plasma density shows a clear increase (Figure 3(d)), and the ion flux changes from the high-energy component of the magnetosphere to the relatively concentrated low-energy component of the magnetosheath (Figure 3(a)), indicating that the MMS spacecraft was crossing the magnetopause.The two red vertical dashed lines in Figures 3(f)-(k) correspond to FAC events, and the peak value of the parallel current intensity of this current structure (Figure 3(j)) is above the set threshold.The duration of this FAC is about 0.32 s, and the moving speed derived from the timing analysis is ∼178 km s −1 .Then, the spatial scale can be estimated as ∼57 km (i.e., ∼0.6 d i or ∼27.1 d e , where d i ∼ 93.44 km, and d e ∼ 2.1 km based on averaged plasma parameters N i = N e ∼ 15.2 cm −3 from 13:48:09.4 to Figures 2 and 3 show two examples of FACs in the MBL.Figure2shows the electron-dominated FACs event.This event was observed on 2015 December 28 at [7.7, −6.7, −0.8] R e (R e is the Earth's radius) in the geocentric solar ecliptic (GSE) coordinate system.Figures2(a)-(e) display the crossing of the MBL.The Z-component of the magnetic field changes from positive to negative (Figure 2(b)), the number density gradually increases (Figure 2(d)), and the ion flux changes from highenergy particles in the magnetosphere to low-energy particles in the magnetosheath (Figure 2(a)).These features indicate that the MMS crossed the magnetopause.Many filamentary FACs are detected during the crossing of the magnetopause (Figure 2(e)), and one of them is selected to study (as marked by the blue vertical dashed line in Figures 2(a)-(e)).Figures 2(f)-(k) show the detailed observations.The peak value of the current intensity of this current structure is higher than 0.46 uA m −2 (Figure 2(j)).The duration dt of the structure is 0.28 s, the moving speed V m determined by timing analysis is ∼150 km s −1 , and thus the spatial scale is estimated as V m * dt ∼ 42 km (i.e., ∼0.56 d i or ∼24.3 d e , where d i ∼ 74.7 km is the ion inertial length, and d e ∼ 1.73 km is the electron inertial length based on averaged plasma parameters N i = N e ∼ 10.1 cm −3 from 22:21:42.82 to 22:21:43.1 UT).Thus, this FAC belongs to SFACs.The two red vertical dashed lines in Figures 2(f)-(k) mark the locations of the corresponding SFACs.The three components of the electron velocity change significantly, especially the Z-direction component (Figure2(i)), while the perturbation of the ion velocity is slight (Figure2(h)).Figure2(j) shows the current intensity in the parallel direction using ion and electron data separately.Figure2(k) displays the contribution ratio of ions and electrons to the total field-aligned current intensity.One can see that electrons dominate the fieldaligned current intensity in this event.Figure3presents the ion-dominated FACs event on 2016 November 27 at [9.9, 6.7, 0.7] R e in the GSE coordinates.Figures3(a)-(e) display the overview of this FAC.It can be seen that B z changes from positive to negative (Figure 3(b)), the plasma density shows a clear increase (Figure 3(d)), and the ion flux changes from the high-energy component of the magnetosphere to the relatively concentrated low-energy component of the magnetosheath (Figure 3(a)), indicating that the MMS spacecraft was crossing the magnetopause.The two red vertical dashed lines in Figures 3(f)-(k) correspond to FAC events, and the peak value of the parallel current intensity of this current structure (Figure 3(j)) is above the set threshold.The duration of this FAC is about 0.32 s, and the moving speed derived from the timing analysis is ∼178 km s −1 .Then, the spatial scale can be estimated as ∼57 km (i.e., ∼0.6 d i or ∼27.1 d e , where d i ∼ 93.44 km, and d e ∼ 2.1 km based on averaged plasma parameters N i = N e ∼ 15.2 cm −3 from 13:48:09.4 to

Figure 1 .
Figure 1.The distribution of current density |J || | in the MBL.The vertical line is 0.46 uA m −2 , which is the current intensity threshold to identify FACs.

Figure 2 .
Figure 2. Electron-dominated SFAC event.(a) Ion omnidirectional differential energy flux; (b) three components of the magnetic fields and the magnetic field strength; (c) three components of the ion bulk velocity; (d) electron number density; (e) field-aligned current; panels ((f)-(k)) shows the zoomed-in view around this FACs; (f) three components of the magnetic fields and the magnetic field strength; (g) electron number density; (h) three components of the ion bulk velocity; (i) three components of the electron bulk velocity; (j) the field-aligned current intensity calculated by plasma moments; (k) the ions' and electrons' individual contributions to the overall field-aligned current intensity.

Figure 3 .
Figure 3. Ion-dominated SFAC event.The format is the same as Figure 2.

Figure 4 .
Figure4.The distribution of the duration of all SFAC events.Since there are at least five data points for the statistical SFACs, the minimum duration of SFACs is 0.15 s.

Figure 5 .
Figure 5. Distribution histograms of the spatial scales of SFACs normalized by the ion (a) and electron (b) inertial lengths, respectively.

Figure
Figure 8 depicts the overall performance of energy dissipation in the SFACs.J E J E V B e • •( ) ¢ =+ ´is extensively employed as a measure of energy dissipation in space plasmas (e.g.,Zenitani et al. 2011;Burch et al. 2016;Fu et al. 2017;Huang et al. 2018;Torbert et al. 2018;Huang et al. 2019;Hwang et al. 2019;Zhou et al. 2019;Huang et al. 2021).It can be seen that 77.36% of SFACs have J • E′ > 0 (Figure8(a)), suggesting that the field's energy is converted into the plasma's thermal and kinetic energy for most of the SFACs.

Figure 6 .
Figure 6.The spatial distribution and the occurrence rate of SFACs in the MBL.The upper panels (a)-(c) depict the spatial distribution of SFACs, while the lower panels (d)-(f) illustrate the occurrence rate of SFACs at the corresponding positions.The radius of the Earth [R e ] is the scale unit in the figure.

Figure 7 .
Figure 7. Histogram of the different dominant contributions to the SFACs.

Figure 9 .
Figure 9.The percentage of the SFACs in different structures.

Figure 8 .
Figure 8.(a) The distribution of J • E′ for all SFACs, where the red vertical line is the position where J • E′ is zero; (b) histogram of the proportion of the ratio of the energy dissipation in the parallel direction J E ( • ) || ¢ vs. the energy dissipation in the perpendicular direction J E ( • ) ¢ ^.