Volume 123, Issue 8 p. 6533-6547
Research Article
Free Access

The Role of the Parallel Electric Field in Electron-Scale Dissipation at Reconnecting Currents in the Magnetosheath

F. D. Wilder

Corresponding Author

F. D. Wilder

Laboratory of Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO, USA

Correspondence to: F. D. Wilder,

frederick.wilder@lasp.colorado.edu

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R. E. Ergun

R. E. Ergun

Laboratory of Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO, USA

Department of Astrophysical and Planetary Sciences, University of Colorado Boulder, Boulder, CO, USA

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J. L. Burch

J. L. Burch

Southwest Research Institute, San Antonio, TX, USA

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N. Ahmadi

N. Ahmadi

Laboratory of Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO, USA

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S. Eriksson

S. Eriksson

Laboratory of Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO, USA

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T. D. Phan

T. D. Phan

Space Sciences Laboratory, University of California, Berkeley, CA, USA

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K. A. Goodrich

K. A. Goodrich

Laboratory of Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO, USA

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J. Shuster

J. Shuster

NASA Goddard Space Flight Center, Greenbelt, MD, USA

University of Maryland, College Park, MD, USA

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A. C. Rager

A. C. Rager

NASA Goddard Space Flight Center, Greenbelt, MD, USA

Department of Physics, Catholic University of America, Washington, DC, USA

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R. B. Torbert

R. B. Torbert

Department of Physics, University of New Hampshire, Durham, NH, USA

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B. L. Giles

B. L. Giles

NASA Goddard Space Flight Center, Greenbelt, MD, USA

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R. J. Strangeway

R. J. Strangeway

Department of Earth, Planetary and Space Sciences, University of California, Los Angeles, CA, USA

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F. Plaschke

F. Plaschke

Space Research Institute, Austrian Academy of Sciences, Graz, Austria

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W. Magnes

W. Magnes

Space Research Institute, Austrian Academy of Sciences, Graz, Austria

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P. A. Lindqvist

P. A. Lindqvist

Royal Institute of Technology, Stockholm, Sweden

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Y. V. Khotyaintsev

Y. V. Khotyaintsev

Swedish Institute of Space Physics, Uppsala, Sweden

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First published: 10 July 2018
Citations: 40

Abstract

We report observations from the Magnetospheric Multiscale satellites of reconnecting current sheets in the magnetosheath over a range of out-of-plane “guide” magnetic field strengths. The currents exhibit nonideal energy conversion in the electron frame of reference, and the events are within the ion diffusion region within close proximity (a few electron skin depths) to the electron diffusion region. The study focuses on energy conversion on the electron scale only. At low guide field (antiparallel reconnection), electric fields and currents perpendicular to the magnetic field dominate the energy conversion. Additionally, electron distributions exhibit significant nongyrotropy. As the guide field increases, the electric field parallel to the background magnetic field becomes increasingly strong, and the electron nongyrotropy becomes less apparent. We find that even with a guide field less than half the reconnecting field, the parallel electric field and currents dominate the dissipation. This suggests that parallel electric fields are more important to energy conversion in reconnection than previously thought and that at high guide field, the physics governing magnetic reconnection are significantly different from antiparallel reconnection.

Key Points

  • We observe ion diffusion regions and electron jets in the magnetosheath for multiple events
  • The dissipation due to the parallel electric field becomes more significant at increasing guide magnetic field
  • This may be associated with a dissipative electric field along the direction of the electron jet

1 Introduction

In March 2015, NASA launched the Magnetospheric Multiscale (MMS) mission to study the phenomenon of magnetic reconnection on the electron scale (Burch et al., 2015). Magnetic reconnection is a fundamental process in space plasma that can change the topology of a magnetic field and convert magnetic energy into particle kinetic energy and heat. Significant progress has been made over the past decade in understanding magnetic reconnection on the ion scale, particularly with regards to how the Hall effect allows for observed fast reconnection rates; however, the dissipation of the magnetic energy into kinetic energy and heat on the electron scale is still not well understood (Birn et al., 2001; Yamada, 2011, and references therein). On 16 October 2015, MMS encountered an antiparallel electron diffusion region (EDR) and observed significant dissipation in the electron frame of reference (Burch et al., 2016). Nongyrotropic electron crescent distributions were also observed, and the divergence of the electron pressure at least partially balanced the electric field in the EDR (Torbert et al., 2016). Since then, several encounters with the EDR by MMS at the dayside magnetopause (Burch & Phan, 2016; Chen et al., 2016; Torbert et al., 2017) as well as within the Kelvin-Helmholtz instability on the magnetospheric flanks (Eriksson et al., 2016) have been reported.

The MMS mission has made several important observations regarding the role of the out-of-plane magnetic field, or guide field, in magnetic reconnection at the dayside magnetopause. For the present study, we will discuss the guide field, Bg, as a ratio between the out-of-plane and the reconnecting components. This is a unitless quantity. Because it can often be difficult to determine local coordinates in magnetic reconnection, we will determine Bg based on the shear angle, θb, between the magnetic field vectors on each side of the reconnecting current sheet, as in equation 1.
urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0001(1)

We note that equation 1 assumes symmetry in the magnitude of B on each side of the current sheet. While most of the events analyzed in this study exhibited this symmetry, some did not, including the high guide field event discussed in section 4. It is therefore important to understand Bg as defined by equation 1 to be an indicator of the guide field rather than a direct measure. Additionally, equation 1 was explicitly chosen to neglect variation in the out-of-plane magnetic field within the current sheet. This is due to the fact that our study focuses on events near the EDR and within the ion diffusion region, where much of the out-of-plane variation is due to Hall physics. Regarding any asymmetry in the Hall fields, which could be related to asymmetry in the reconnecting field, use of the shear angle outside of the current sheet should not effect the qualitative interpretation of any trends with respect to the guide field.

The first EDR event found, reported by Burch et al. (2016), was an antiparallel reconnection event, with a shear angle of ~170°, implying Bg ≈ 0.1. During this event, agyrotropic “crescent” electron distributions were observed, and the DC electric field parallel to the background magnetic field, E||, was small (~3 mV/m). There was also a large asymmetry in density across the reconnecting current sheet, due to the difference in plasma characteristics between the magnetosheath and magnetopause, which led to an enhanced normal electric field (Malakit et al., 2010; Vaivads et al., 2004). Burch and Phan (2016) reported another asymmetric reconnection event where the Bg was near unity. In this event, the crescent distributions persisted, even in the presence of a moderate guide field. This could potentially make it difficult to maintain an agyrotropic electron distribution. Finally, Eriksson et al. (2016) reported observations of an electron diffusion region crossing where Bg > 2, and the density and magnetic field were near symmetric across the current sheet. In this event, there was a unipolar, out-of-plane E|| in excess of 15 mV/m. There was no evidence of agyrotropic electron distributions in the diffusion region, but rather, there was an electron population that had been accelerated along the background magnetic field by E||. These results suggested that under a large-enough guide field, the mechanisms that provide both dissipation and the breaking of the frozen-in condition may be significantly different from those in antiparallel reconnection.

Much of the focus of the first phase of MMS (September 2015 to March 2016 and September 2016 to February 2017) has been on magnetic reconnection at the dayside magnetopause, where there are differences between the higher density (tens of cubic centimeters) magnetosheath and the low density (<1 cm−3) magnetosphere (Paschmann et al., 1979). Thus, the observations have been ideal for comparing with theory regarding asymmetric magnetic reconnection. There are also complications associated with asymmetric reconnection that are not prominent in symmetric reconnection. These include an offset between the stagnation point and x point (Cassak & Shay, 2007) as well as turbulence driven by drift instabilities associated with finite gyroradius effects (e.g., Ergun et al., 2017). During the same mission phase; however, the MMS constellation also spent a significant amount of time in the Earth's magnetosheath. In this regime, nearly symmetric magnetic reconnection can be observed, both on solar wind current sheets that have crossed the bow shock (e.g., Øieroset et al., 2017; Phan et al., 2007) and during intervals of plasma turbulence behind the bow shock (Retino et al., 2007). Because the reconnecting current sheets are carried rapidly past the spacecraft by the magnetosheath bulk flow, the observations tend to be simple straight crossings, which make them easy to compare with both simulations and laboratory experiments. On 9 December 2015, the MMS constellation encountered the electron jet or “outer” EDR of symmetric magnetic reconnection in the magnetosheath (Wilder et al., 2017). In this event, Bg was approximately 0.5. Coincident with the electron jet, a significant unipolar E|| with an amplitude of ~5 mV/m was observed by all four spacecraft, despite the separation being 10 km, or 10 electron skin depths (de), which was significantly larger than the Debye scale (tens of meters). This electric field structure was partially oblique to the magnetic field, was highly dissipative, and appeared to heat electrons that passed through the structure. In the event, but the E|| structure consisted of electric fields along the jet direction, as well as the out-of-plane direction, suggesting it was more complicated than simply the reconnection electric field. The results suggested that parallel electric fields might play a significant role in the conversion of magnetic energy to kinetic energy and heat during guide field reconnection.

In the present study, we investigate additional electron-scale reconnection layers in the magnetosheath in order to understand the changing characteristics of symmetric reconnection as the guide field increases. We use data from the MMS mission. This includes electron and ion data from the Fast Plasma Instrument (FPI; Pollock et al., 2017), electric field data from the electric field double probes (Ergun, Tucker, et al., 2016; Lindqvist et al., 2016), and magnetic field data from the flux-gate magnetometer (Russell et al., 2016). We study events in the “outer” EDR, where there is a super-Alfvénic electron jet within the ion diffusion region, as these events are more straightforward to identify in the data. We investigate the scale sizes of the current sheets, as well as the dissipation and the relative contributions of parallel and perpendicular electric fields. We also compare the characteristics of the electron distribution functions as the guide field increases. We find that the agyrotropy becomes less prominent with increasing guide field. Additionally, we find that the dissipation becomes increasingly dominated by the parallel electric field in the presence of a guide field, even when Bg is less than 0.5.

2 Event Examples

2.1 Antiparallel Reconnection Event

The first example event we will show is a reconnection event with a very small guide field, so that the merging magnetic fields are nearly antiparallel. Figure 1 shows data from MMS on 28 January 2017 at 05:32 UT, spanning an approximately 3-s interval. The Geocentric Solar Ecliptic position of the spacecraft is shown at the top of the figure, and it was near local noon. From the ion and electron spectra (Figures 1a and 1b), it can be determined that the spacecraft is in the magnetosheath. Figure 1c shows the ion and electron number density, measured by FPI, in red and blue, respectively. The number density, which is between 10 and 20 cm−3, is also consistent with typical values in the magnetosheath (e.g., Paschmann et al., 1979). Figure 1d shows the ion and electron temperatures both perpendicular and parallel to the background magnetic field. In the middle of the interval, there is a local enhancement in the parallel electron temperature, which can occur as long as B is nonzero. In this event and others shown here, the enhancement in parallel electron temperature is largely associated with the dynamics of electrons with energies of a few hundred electron volts. The total pressure balance on the current sheets presented in this study is maintained by this enhancement of the electron temperature. Figures 1e and 1f show the electron and ion bulk velocities, respectively, which are color coded by the local coordinate system labeled, L, M, and N. The magnetic field, shown in Figure 1g is also presented in the LMN coordinate system. This coordinate system is determined using minimum variance analysis (MVA) of the magnetic field over the interval from 05:32:32 and 05:32:33 UT (e.g., Sonnerup & Scheible, 1998). Here the unit vectors urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0002, urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0003, and urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0004 correspond to the directions of maximum, intermediate, and minimum variance in B, respectively, with urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0005 = [0.29, 0.91, 0.51], urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0006 = [−0.35, 0.59, −0.72], and urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0007 = [−0.89, 0.03, 0.45], in geocentric solar equatorial coordinates. The eigenvalues from the MVA associated with the three coordinates are λ1 = 1039.8, λ2 = 100.1, and λ3 = 1.6, with a ratio between the intermediate and minimum eigenvalues of 61, which exceeds the typical threshold for accurate determination of an MVA-based coordinate system (Sonnerup & Scheible, 1998). LMN coordinates relate to magnetic reconnection in the following manner: L corresponds to the axis along both the reconnecting field and the reconnection jets, M is the out-of-plane direction that corresponds to the direction of the current and the reconnection electric field, and N is normal to the current sheet and corresponds to the inflow direction (Sonnerup & Scheible, 1998).

Details are in the caption following the image
Overview of the magnetosheath reconnection event on 28 January 2017. From top to bottom: Omnidirectional (a) electron and (b) ion energy spectra, (c) ion and electron number density, (d) ion and electron parallel and perpendicular temperature, (e) ion bulk velocity in LMN coordinates, (f) electron bulk velocity in LMN coordinates, (g) magnetic field vector in LMN coordinates, (h) parallel electric field with uncertainty in orange, (i) electric current density in LMN coordinates, (j) J · E decomposed into the contributions from parallel and perpendicular currents, and (k) electric field vector in LMN coordinates. The vertical dashed line indicates the time where BL crosses 0; the vertical dotted line is the timestamp of the distributions in Figure 3. MMS = Magnetospheric Multiscale.

Figure 1h shows the electric field parallel to the background magnetic field, with uncertainty given in orange. The details of the calculation of this uncertainty are discussed by Ergun, Tucker, et al. (2016) and Ergun, Holmes, et al. (2016). Figure 1i shows the electric current density in LMN coordinates, = ne(Vi − Ve), where n is the number density, e is the electron charge, Vi is the ion bulk velocity, and Ve is the electron bulk velocity as measured by the FPI. All currents shown in this study are associated with enhancements in electron bulk velocity. Finally, Figure 1j shows the nonideal conversion of electromagnetic energy into kinetic energy and heat, as determined by J · E, where E = E + Ve × B is the electric field in the electron frame of reference. J · E is also decomposed into the contribution from currents and electric fields parallel (blue line) and perpendicular (pink line) to B. We define our energy conversion in the electron frame to focus specifically on the electron scale dynamics. While J · E is typically qualitatively similar to J · E for the current sheets presented in this study, small variations in the ion diffusion region account for differences that likely are not directly related to the electron dynamics. Figure 1k shows the electric field vector in LMN coordinates.

During the interval shown in Figure 1, an intense, small-scale current sheet is embedded in a larger-scale current sheet. There is a reversal in BL, with the component crossing 0 at 05:32:32.274 UT (vertical dashed line). Coinciding with this reversal is a significant out-of-plane current (JM ≈ 4 μA/m2). Using Ampere's law, and a BL change of 95 nT, this corresponds to a current sheet scale size in the N direction of less than 18.9 km. For this event, the ion inertial length (c/ωpi) is approximately 50 km, while the electron skin depth (c/ωpe) is 1.2 km, suggesting that the current sheet is between the electron and ion scales in gradient scale length. This scale length is consistent with diffusion region observations by MMS at the dayside magnetopause (Burch et al., 2016; Burch & Phan, 2016; Eriksson et al., 2016).

Also, coinciding with the reversal of BL is a positive enhancement in VeL, with a perturbation from the background speed by ~1,000 km/s. This is in excess of the ion Alfvén speed, which in this event is 243.9 km/s, and therefore is consistent of an electron jet resulting from reconnection (e.g., Phan et al., 2007). There is no clear corresponding enhancement in ViL, suggesting that the spacecraft was in the ion diffusion region near the EDR, so the ion jet had not fully formed. Flanking the electron jet is a bipolar signature in BM, which is consistent with a Hall magnetic field set up by current loops in the ion diffusion region. No significant unipolar E|| is observed, which distinguishes the event from observed symmetric reconnection events in the presence of a guide field (Eriksson et al., 2016; Wilder et al., 2017). From Figure 1j, there is a J · E peak corresponding with the reconnecting current sheet, which is dominated by electric fields and currents that are perpendicular to B. This is also in contrast with the guide field events, where parallel electric fields and currents dominate the dissipation (Eriksson et al., 2016; Wilder et al., 2017). From Figure 1k, the electric field contributing to the J · E peak consists of both the L component (along the jet) and the M component (in the direction of the reconnection electric field). This suggests that the electron jet also contributes to nonideal energy conversion.

Similar features were observed on all four spacecraft. Figure 2 shows BL, BM, VeL, and J · E from all four spacecraft, as well as the spacecraft formation in LMN coordinates. The spacecraft separation is between four and five electron skin depths. All four spacecraft see a reversal in BL, bipolar BM signatures, an electron jet, and enhanced dissipation. The negative Hall perturbation in BM appears to be elongated in this event, but to the author's knowledge, there is no clear explanation for this. MMS2 encounters the current sheet first, followed shortly after by MMS1. After that, MMS4 encounters the current sheet, followed shortly after by MMS3. Looking at Figure 2e, this suggests that the current sheet crossed the spacecraft in the normal direction. This is consistent with all four spacecraft observing a single jet in the same direction. Additionally, it is consistent with reconnection in the magnetosheath, where the bulk plasma flow advects current sheets past the spacecraft, which in this case shows a positive ViN in agreement with the spacecraft traversal in the negative N direction.

Details are in the caption following the image
Data from all four spacecraft during the reconnection event on 28 January 2017, color coded by spacecraft. (a) BL, (b) BM, (c) VeL, and (d) J · E. Panel (d) shows the spacecraft formation in the L-N plane, with the position of MMS1 as a reference, and the relative position in the M direction shown by the size of the dots. MMS = Magnetospheric Multiscale.

Another important aspect of magnetic reconnection to investigate is the role of electron agyrotropy. Agyrotropy can produce off-diagonal terms in the electron pressure tensor, which in turn can sustain the reconnection electric field and contribute to energy conversion between electromagnetic and mechanical energy (Hesse et al., 2011). Figure 3 shows three electron distributions accumulated by FPI between 05:32:32.234 and 05:32:32.236 UT, which is the time shown by the vertical dotted line in Figure 1. These distributions are 2-D cuts along three axes in velocity space. V⊥1 is along (E × B), V⊥2 is along (Ve × B), and V is along B. The color scale is in units of energy flux.

Details are in the caption following the image
Two-dimensional cuts of a single electron distribution during the 28 January 2017 reconnection event. (a) Cuts in the perpendicular plane, with V⊥1 being along (E × B) and V⊥2 along (Ve × B). (b) A parallel cut with the abscissa, V, being along B and V⊥1 being the ordinate. (c) A parallel cut with V⊥2 being the ordinate. MMS = Magnetospheric Multiscale.

Figure 3a shows asymmetry in the V⊥1 versus V⊥2 cut of the distribution, which indicates that the distribution is nongyrotropic. This is also seen in the distributions in Figures 3b and 3c, which are cuts of the two perpendicular velocities versus V. In a gyrotropic distribution these would be identical. For this event, noticeable agyrotropy persists over six measured distributions or 180 ms. Often, electron agyrotropy related to magnetic reconnection is associated with “meandering” electron orbits along a field reversal; however, this is difficult to identify in the magnetosheath due to the typical symmetry in density and magnetic field strength across the current sheets (Bessho et al., 2016), additionally, at the dayside magnetopause those distributions are associated with a large EN, which is not observed in this event. Other potential forms of nongyrotropy could include Speiser-like orbits, such as those seen in the ions in the magnetotail (e.g., Hietala et al., 2017). In this case, the current sheet would need to be thin enough for electron orbits to bounce back and forth across the current sheet and rotate around the normal field. Further, one can get nongyrotropic distributions without meandering motion (e.g., Egedal et al., 2018). Because the normal field is difficult to estimate using minimum variance techniques, it is difficult to determine precisely what leads to the agyrotropy of the distribution.

2.2 Medium Guide Field Event

The second example event we show (Figure 4) is the moderate guide field event on 9 December 2015 that was reported by Wilder et al. (2017). In this particular event, the guide field is ~0.5, and the LMN coordinates are urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0008 = [−0.104, 0.59, 0.80], urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0009 = [0.38, −0.77, −0.514], and urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0010 = [0.920, 0.250, 0.302]. There are several features that the event shares with the one shown in Figure 1. For example, there is a significant out-of-plane current of 1.8 uA/m2 at the reversal of the BL, which changed by 40 nT. This corresponds to a current sheet normal thickness of 17.7 km, which again is between the electron skin depth and the ion inertial length. There is also a local enhancement of Te|| at the reversal in BL. Additionally, an electron jet in VeL that exceeds the ion Alfvén speed (~146 km/s) coincides with the current sheet and is in the middle of a bipolar fluctuation in BM.

Details are in the caption following the image
Overview of the magnetosheath reconnection event on 9 December 2015, given in the same format as Figure 1. GSE = geocentric solar equatorial; MMS = Magnetospheric Multiscale; MVA = minimum variance analysis.

There are two significant differences between the events shown in Figures 1 and 4. In Figure 4h, there is a unipolar parallel electric field signature reaching −4 mV/m that coincides with the reconnecting current sheet. Wilder et al. (2017) discussed this electric field structure in detail and found that it acted like an “acceleration channel” for electrons that is oblique to B. It was observed on all four spacecraft. In addition to this unipolar E||, Figure 4j shows that J · E is dominated by parallel electric fields and currents. From the electric field, this appears to again be associated with the L and M components of the electric field, which has become more parallel due to the presence of the guide field, as well as a deflection of the electron jet toward the separatrix, as discussed by Wilder et al. (2017).

Figure 5 shows electron distributions accumulated between 05:03:56.932 and 05:03:56.962 UT. This time corresponds to the vertical dotted line in Figure 4, and is also agyrotropic, although it is not as pronounced as in Figure 1. Additionally, while agyrotropic distributions appear throughout the dissipation region for the event from Figure 1, only a single one was observed on each spacecraft for the event from Figure 4 and is shown in Figure 5 for MMS1. This distribution is closer to the separatrix than the region of peak dissipation. Bessho et al. (2016) has suggested that agyrotropic distributions can persist along the separatrices outside of the core electron diffusion region. We note, however, that both events observe a nonzero electron jet for all four spacecraft, and it is therefore unlikely that the MMS constellation encountered the core EDR in either event. Therefore, the agyrotropy seems to extend over a broader cross section of the current sheet for the antiparallel case, as compared with the moderate guide field case.

Details are in the caption following the image
Cut of the most agyrotropic distribution observed by MMS1 during the 9 December 2015 reconnection event. Given in the same format as Figure 3. MMS = Magnetospheric Multiscale.

2.3 High Guide Field Event

The final event to be shown is an event with a higher guide field of 1.3, on 4 November 2015. The LMN directions for this event are urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0011 = [−0.49, 0.86, 0.13], urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0012 = [−0.39, −0.35, 0.85], and urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0013 = [0.77, 0.37, 0.51]. Figure 6 shows an overview of MMS1 observations of the event given in the same format as Figures 1 and 4. Again, there are features in common with the other two events shown. First, there is a significant out-of-plane current (JM) on the order of 4 uA/m2, which, with a change in BL of approximately 80 nT, implies a normal current sheet scale thickness of ~16 km. In this particular event, the electron skin depth is 0.84 km, while the ion inertial length is 36 km. The normal gradient scale therefore falls between the two scale lengths. Additionally, there is an enhancement in VeL that exceeds the ion Alfvén speed (206 km/s). Like the Bg = 0.5 case (Figure 4), there is an enhancement in E|| at the current sheet. In Figure 6, the amplitude of the E|| in the survey data is 8 mV/m. One feature of this event in comparison with the Bg = 0.5 event (Figure 4) is that the dissipation in the Bg = 1.3 event seems to be split between the parallel and perpendicular fields and currents, whereas the Bg = 0.5 event saw parallel dominated dissipation on all four spacecraft. Part of this might be that in the Bg = 1.3 event, there was an enhanced normal electric field of ~10 mV/m in the lower rate data, which appeared on all four spacecraft and is contributing to the dissipation.

Details are in the caption following the image
Overview of the magnetic reconnection event on 4 November 2015. Given in the same format as Figures 1 and 4 but with an extra panel (k) showing the electric field vector in LMN coordinates. GSE = geocentric solar equatorial; MMS = Magnetospheric Multiscale; MVA = minimum variance analysis.

It should be noted that the normal magnetosheath flow was over 200 km/s in the Bg = 1.3 event (Figure 6), and thus, the diffusion region was under sampled due to the speed at which it passed the spacecraft constellation. Figure 7 shows the burst electric field data measured at 8,192 samples per second during the current sheet crossing shown in Figure 6. There are two important features. First, the unipolar E|| reaches −19 mV/m. This is comparable in amplitude to the high guide field EDR event reported by Eriksson et al. (2016), where the E|| amplitude was ~16 mV/m. This amplitude is also 3 times larger than the burst E|| reported by Wilder et al. (2017) for the Bg = 0.5 event. While there appears to be a trend of increasing E|| with increasing guide field, more events with similar plasma conditions would be needed to determine this conclusively. Additionally, the EN enhancement is 70 mV/m in burst. This enhancement is an asymmetric bipolar Hall electric field, with the larger amplitude being on the side of the current sheet with the larger magnitude of B. The enhancement on the higher B side is a feature of asymmetric reconnection, where the x point is offset toward the side of the current sheet with lower B and the stagnation point is offset toward the side with lower ρ/B (Cassak & Shay, 2007). This can lead to finite gyroradius effects and a normal electric field to slow the inflow of ions (e.g., Malakit et al., 2010; Norgren et al., 2016). In the past, this has mostly been discussed in the context of the large density asymmetry at the Earth's magnetopause; however, the event on 4 November 2015 is in the magnetosheath where the density asymmetry across the current sheet is negligible. The electric field in Figure 7 suggests that this effect can persist, even in the presence of an asymmetry in B. It also suggests that in asymmetric reconnection, even with a significant guide field, perpendicular electric fields can still be important for dissipation. The importance of the normal electric field in dissipation for antiparallel reconnection was observed at the magnetopause during the 16 October 2015 event (Burch et al., 2018; Swisdak et al., 2018).

Details are in the caption following the image
(a) B in LMN at 128 samples per second, as well as (b) E|| and (c) ELMN data at 8,192 samples per second near the current sheet. The vertical dashed line denotes the point where BL = 0.

Figure 8 shows data from all four spacecraft, in the same format as Figure 2. Because the reconnection event passed the spacecraft rapidly, the VeL panel makes use of electron moments calculated at 7.5-ms cadence (Rager et al., 2018). As can be seen, all four spacecraft observed the reversal in BL, as well as perturbations in the BM component. The electron jet was observed on three of the four spacecraft, with the exception being MMS2. From Figure 8e, the spacecraft separation was larger in this event than the one shown in Figure 2. Additionally, since MMS1, MMS3, and MMS4 observed a negative VeL jet, and MMS2 is separated from the rest of the constellation in the +L direction, it is possible that MMS2 was closest to the electron diffusion region.

Details are in the caption following the image
Data from all four spacecraft and formation for the 4 November 2015 reconnection event, given in the same format as Figure 2. The vertical lines indicate the times when distribution slices are shown in Figure 9 and are color coded by spacecraft. MMS = Magnetospheric Multiscale.

Because of the larger separation and the possibility of the spacecraft sampling different parts of the diffusion region, Figure 9 shows 2-D cuts of the most agyrotropic distribution observed by each of the four spacecraft. The corresponding times are shown on Figure 8 as vertical dashed lines color coded by spacecraft. There are several important features apparent in Figure 9. First, similar to the distributions for the Bg = 0.5 event (Figure 5), the agyrotropy is not as prominent as for the antiparallel event shown in Figure 3. This is especially apparent when comparing the two V versus V slices (second and third columns in Figure 9), which while exhibiting some differences as an effect of agyrotropy, those differences are nowhere near as pronounced as in Figure 3. One interesting feature is that the agyrotropy is not any less apparent than in Figure 5 for the Bg = 0.5 event. Eriksson et al. (2016) reported that in the Bg > 2 case, there was no visible agyrotropy in the distributions. It could be the case that the cutoff point for the presence of agyrotropy is significantly higher than the Bg = 1.3 in the 4 November 2015 event. Additionally, the visibility of the nongyrotropic distributions may be impacted by the asymmetry in B across the current sheet. In particular, the enhanced normal electric field could accelerate electrons into the region where they undergo meandering orbits, as described by Bessho et al. (2016). The analysis of this event suggests that while the parallel electric field seems to increase with increasing guide field, the relative importance of the parallel electric field for dissipation as well as the role of agyrotropy may depend on the asymmetry in either magnetic field strength or density across the current sheet.

Details are in the caption following the image
Distributions from all four spacecraft, taken at the times of the vertical dashed lines in Figure 8. Each row is in the same format as Figures 3 and 5. MMS = Magnetospheric Multiscale.

3 The Role of Parallel Electric Fields in Dissipation

For the three events shown, there are several clear differences. First, for the antiparallel case, there is no significant direct current parallel electric field above the background in the dissipation region. This was also the case for the antiparallel EDR event reported by Burch et al. (2016). In the two events with a stronger guide field, there is an increasingly large magnitude E|| that is also unipolar. Additionally, the dissipation in the cases of the antiparallel event is dominated by the perpendicular electric fields and currents. This is different from the guide field cases, where the parallel electric fields become important for dissipation. This can be associated with multiple factors, including the guide field diverting the electron jet toward one of the separatrices, as well as the reconnection electric field being the out-of-plane component, which becomes increasingly parallel in the presence of a guide field.

The third event, shown in Figure 7, suggests that the role of the parallel electric field in dissipation is complicated and may vary event by event based on the asymmetry in magnetic field and plasma density, even in the presence of a high guide field. It is therefore worthwhile to identify other electron-scale reconnecting current sheets. For the present study, we identified 10 additional magnetosheath current sheets on the subion scale by searching through events where J = ( × B)/μ0 exceeded 0.8 μA/m2. The list was then narrowed down by finding current sheets that coincided with a local enhancement in J · E and also included enhanced electron flow in the direction of the magnetic field reversals. The complete list of events is given in Table 1. Because the MMS data were searched manually for these events, the list is not exhaustive; however, it provides a basis by which to further study the role of parallel electric fields in the dissipation of electromagnetic energy associated with magnetic reconnection in the magnetosheath.

Table 1. List of Events Used to Generate Figure 10
Date Time (UT) Bg
25 October 2015 11:07–11:08 0.32
4 November 2015 04:35–04:36 1.32
9 December 2015 05:00–05:05 0.48
13 January 2016 04:30:30–04:31:30 2.10
29 January 2016 23:20–23:21 1.21
1 November 2016 09:56–09:58 1.18
24 November 2016 14:42–14:44 0.81
7 December 2016 05:21:30–05:22:30 1.95
27 December 2016 10:16:20–10:17:40 0.06
7 January 2017 04:01–04:04 0.35
27 January 2017 00:39–00:40 (CS1) 0.55
00:39–00:40 (CS2) 0.33
28 January 2017 05:31:43–05:32:43 0.10
  • Note. Includes the time of the Magnetospheric Multiscale burst interval containing the event, as well as the calculated guide field using equation 1.
To quantify the relative contribution of parallel and perpendicular electric fields and currents to dissipation, we introduce the dissipation ratio, given in equation 2:
urn:x-wiley:21699380:media:jgra54412:jgra54412-math-0014(2)

Here the “max” implies the maximum value of the quantity measured within the current sheet. The absolute value of (J · E)ratio can be greater than 1, which typically implies that either the perpendicular or parallel contributions to the dissipation were negative (e.g., mechanical energy was converted to electromagnetic by those particular currents and fields). Additionally, for each event, Bg was calculated using equation 1.

Figure 10 shows a plot of (J · E)ratio versus Bg for the 13 events in Table 1, as well as two previously published magnetopause events for context (Burch et al., 2016; Eriksson et al., 2016). The vertical dashed line indicates Bg = 0.5. This is chosen because if E = E · B/B, and the reconnection electric field is in the M component, the reconnection electric field throughout the diffusion region, and not just at the null point, will become parallel dominated at Bg = 0.5. The black diamonds indicate the mean (J · E)ratio observed by all four spacecraft in the constellation, and error bars signify the range from the minimum to the maximum values measured by individual spacecraft. The size of the error bars can be used as a metric of how well the observations across the constellation agree. Error bars for the magnetopause events are not included, since all four spacecraft did not observe enhanced dissipation for those events.

Details are in the caption following the image
Plot of (J · E)ratio versus Bg for the identified magnetosheath current sheets. Black diamonds indicate the mean across the four spacecraft constellation. The error bars correspond to the minimum to maximum values of (J · E)ratio measured by each of the four spacecraft. Red symbols indicate two previously published magnetopause observations, provided for context. The vertical dashed line indicates the point where Bg = 0.5.

There are several important features in Figure 10. First, as expected based on the example events shown, as well as the conclusions by Eriksson et al. (2016), the dissipation is dominated by contributions from parallel electric fields and currents as Bg increases. Second, the dissipation seems to become parallel dominated even in the presence of a guide field less than 0.5. If the dissipation were largely due to the out-of-plane reconnection electric field, EM, which is responsible for governing the reconnection rate, we would expect a switch from perpendicular- to parallel-dominated dissipation near 0.5, since EM would be completely parallel at the B minima associated with BL = 0. Since this parallel dissipation happens for Bg < 0.5, it is likely that the parallel electric field providing the energy dissipation is not necessarily the reconnection electric field. This same effect was seen in the Bg = 0.5 event reported by Wilder et al. (2017), where the parallel electric field consisted of both an EM near the dissipation region and an EL along the jet direction. It was also the case for the Bg = 0.1 event shown here, where the dissipation included both an L component and an M component. These results suggest that the electron jet itself can be a significant source of nonideal energy conversion. Additionally, in the 3-D symmetric case, the parallel electric field might be an effective way to dissipate the incoming magnetic energy into particle energy and heat away from the inner EDR itself, even in the presence of a moderate or small guide field.

4 Summary and Conclusion

In the present study, we investigated several reconnecting current sheets in the Earth's magnetosheath. Three events were shown in detail, with special attention given to the scale of the current sheet, the presence of the electron jet, and the relative contribution of parallel and perpendicular electric fields and currents to electromagnetic energy dissipation. We also showed the changing features of agyrotropic distributions, both in the presence of a guide field, as well as asymmetries in magnetic field magnitude across the current sheet. Finally, we investigated the relative contributions of parallel and perpendicular fields to dissipation as a function of the guide field using additional events.

Several important features were found in the study. First, as the guide field increases, unipolar parallel electric fields coincident with the electron jet and diffusion region become increasingly prominent. Further, their contribution to the conversion from magnetic energy to thermal and kinetic becomes increasingly important. The fact that these parallel electric fields become important when the guide field is less than half the reconnecting field suggests that these parallel electric fields are not necessarily the out-of-plane reconnection electric field but are still important for energy conversion. This parallel dissipation might be due to the fact that when the reconnecting fields annihilate, there is a nonzero field due to the guide field, and it is easy to accelerate electrons along the field in response to pressure gradients. Wilder et al. (2017) showed that for at least one event, divergence of the pressure tensor was balanced by the parallel electric field. In the large guide field case (>2), the reconnection appears to be completely dominated by parallel electric field (Eriksson et al., 2016). Additionally, Ergun, Holmes, et al. (2016) suggested that the detwisting of secondary flux ropes by parallel electric fields could be an example of extreme guide field reconnection. Conversely, for the antiparallel case examined here, the perpendicular electric fields and currents dominate the dissipation of energy. These results suggest a continuum of types of dissipative current sheets from antiparallel reconnection to low-shear current sheets where the dynamics are governed by parallel electric field structures such as double layers.

Another observed feature of antiparallel reconnection is the agyrotropy found in the electron distributions, even for symmetric reconnection. The present study shows that even in the presence of a guide field, this agyrotropy can still persist, which is consistent with observations of guide field reconnection at the dayside magnetopause (Burch & Phan, 2016). The present study also suggested that in the presence of a guide field, the agyrotropy was less prominent. This is consistent with electrons being magnetized even in the diffusion region. Observations of a large guide field event, reported by Eriksson et al. (2016), displayed no clear agyrotropy in the electron distributions but rather an electron population that was accelerated along the background magnetic field. One hypothesis is that the presence of agyrotropy may be governed by whether or not the gradient scale size of the electron diffusion region (usually the electron skin depth) exceeds the Larmor radius of electrons associated with the guide field, as suggested by Hesse et al. (2016).

Finally, we showed that while the parallel electric field becomes increasingly important for dissipation with increasing guide field, the asymmetry in magnetic field or density across the current sheet may offset this effect. Most of the reconnection events in the magnetosheath are symmetric; however, we showed an event from 4 November 2015 where there was a significant (factor of 2) asymmetry in the magnetic field magnitude across a reconnecting current sheet in the magnetosheath. Despite there being significant guide field (~1.3), the perpendicular contributions to dissipation were significant. This perpendicular dissipation was due to a large normal electric field on the large B (and low ρ/B) side of the current sheet and is likely a feature of asymmetric reconnection, as opposed to symmetric reconnection. A recent simulation study by Dahlin et al. (2016) showed that at high guide field, the parallel electric field accounts for all electron heating, although no energetic tail is produced. The results of the present study are consistent with these findings and also do not show any energetic tail (greater than a few tens of kiloelectron volts) in the electron distribution.

The results from this study show that magnetic reconnection in the magnetosheath provides an opportunity to investigate how different conditions around the x-line can impact the dissipation process in magnetic reconnection. Because they are rapidly advected past the spacecraft, the current sheet crossings tend to be simple to study, particularly when compared to the varying motion of Earth's magnetopause and plasma sheet. This makes the observations optimal for comparison with simulations and laboratory experiments. Additionally, because the density across the x-line is relatively constant, especially when compared to the Earth's magnetopause, it provides an opportunity to study symmetric reconnection in a manner that complements the observations by the MMS mission in the magnetotail. While the results of this study focus on the first two dayside phases of MMS, the spacecraft are anticipated to spend a significant time in the magnetosheath during the extended mission phase.

Acknowledgments

This work was funded by the NASA MMS project. French involvement (SCM instruments) on MMS is supported by CNES, CNRS-INSIS, and CNRS-INSU. MMS spacecraft data are available via the MMS Science Data Center (https://lasp.colorado.edu/mms/sdc/public/).