Mechanism of Reconnection on Kinetic Scales Based on Magnetospheric Multiscale Mission Observations

We examine the role that ions and electrons play in reconnection using observations from the Magnetospheric Multiscale (MMS) mission on kinetic ion and electron scales, which are much shorter than magnetohydrodynamic scales. This study reports observations with unprecedented high resolution that MMS provides for magnetic field (7.8 ms) and plasma (30 ms for electrons and 150 ms for ions). We analyze and compare approaches to the magnetopause in 2016 November, to the electron diffusion region in the magnetotail in 2017 July followed by a current sheet crossing in 2018 July. Besides magnetic field reversals, changes in the direction of the flow velocity, and ion and electron heating, MMS observed large fluctuations in the electron flow speeds in the magnetotail. As expected from numerical simulations, we have verified that when the field lines and plasma become decoupled a large reconnecting electric field related to the Hall current (1–10 mV m−1) is responsible for fast reconnection in the ion diffusion region. Although inertial accelerating forces remain moderate (1–2 mV m−1), the electric fields resulting from the divergence of the full electron pressure tensor provide the main contribution to the generalized Ohm’s law at the neutral sheet (as large as 200 mV m−1). In our view, this illustrates that when ions decouple electron physics dominates. The results obtained on kinetic scales may be useful for better understanding the physical mechanisms governing reconnection processes in various magnetized laboratory and space plasmas.

Turbulent magnetic fields play an important role in plasmas, e.g., leading to magnetic reconnection (Vasyliunas 1975;Burlaga 1995;Biskamp 2000;Treumann 2009;Figura & Macek 2013;Treumann & Baumjohann 2013), and the redistribution of kinetic and magnetic energy in space environments and laboratory plasmas. Reconnection occurs when the electrons cannot supply the current needed to support antiparallel magnetic fields. This is a complex phenomenon that still remains a challenge for contemporary physics. Notwithstanding great progress in magnetohydrodynamic (MHD; Hall-MHD, twofluid) simulations, the physical mechanisms for reconnection are still not clearly understood. The dynamic variability of plasma and fields at very small electron scales in the solar system is not well known. However, collisionless space and astrophysical plasmas can be considered natural laboratories for investigating the complex dynamics (Bruno & Carbone 2016). Moreover, reconnection processes may play an important role in mixing heliospheric and interstellar plasmas, as postulated by Macek & Grzedzielski (1985), a hypothesis supported by numerical simulations (Strumik et al. 2013(Strumik et al. , 2014. Reconnection at the heliopause, which is the ultimate boundary separating the heliosphere from the very local interstellar medium, has yet to be confirmed by experimental data. One of the main objectives of the Magnetospheric Multiscale (MMS) mission is to determine the role of turbulence in the reconnection processes and the roles of ions and electrons in these processes. The MMS mission may also be useful for better understanding the physical mechanisms governing reconnection processes in various laboratory and space plasmas. Evidence for the reconnection diffusion region on the dayside magnetopause using MMS measurements has recently been found by Burch et al. (2016b) in a case study on 2016 October 16, which was further discussed by Torbert et al. (2016). Kinetic simulations of magnetopause reconnection have also been reported by Daughton et al. (2014), while simulation results for a magnetotail case are provided by Nakamura et al. (2018). MMS observations of an electron-scale magnetic cavity embedded in a proton-scale cavity have been recently reported (Liu et al. 2019). One can hence expect that a detailed analysis of the high-resolution MMS data can provide better insight into the nature of reconnection processes in space plasmas.
Magnetopause reconnection is relatively easy to recognize. A list of 32 such magnetopause events has been reported by Webster et al. (2018). Observations of electron-scale structures and magnetic reconnection signatures in the turbulent magnetosheath using MMS measurements have been provided by Yordanova et al. (2016), and reconnection jets at the magnetopause have been analyzed by Øieroset et al. (2016). Because the tail is highly dynamic and nightside reconnection is limited to the vicinity of the current sheet, it is much more difficult to find reconnection events here. A current sheet on electron scales in the near-Earth magnetotail without bursty reconnection has been identified by Wang et al. (2018). The first tail reconnection event on 2017 July 11 was reported by Torbert et al. (2018). Although MMS barely resolves electron scales during reconnection, the latter authors reported that the spacecraft entered the electron diffusion region (EDR) in the magnetotail, suggesting that the electron dynamics in this region was mostly laminar despite turbulence near the reconnection region. Even if the spacecraft remains in the much larger ion diffusion region (IDR), one can can study reconnection from approaches to the EDR in the tail current sheet.
Therefore, this Letter focuses on the deviations from MHD, including Hall-MHD, electron pressure, and inertia effects on both ion and electron scales as seen in the MMS data. Following our previous study of turbulence and reconnection using MMS data (Macek et al. 2018(Macek et al. , 2019, we analyze in greater detail the electric fields on sub-ion scales at the magnetopause and in the magnetotail near the X-line within highly variable plasmas to compare the characteristics of reconnection processes in both regions when going from the ion to electron kinetic scales. This naturally leads to a description of space plasmas within kinetic theory, instead of an ideal MHD approach. We find experimental evidence for a somewhat turbulent (chaotic) reconnection in the magnetotail, as suggested by numerical simulations (see, e.g., Lazarian et al. 2015 and references therein). We observe rather large reconnecting electric fields resulting from the Hall currents for the plasma and magnetic field data at the highest resolution available within the MMS mission (see Yamada et al. 2016). The additional components are caused by a moderate inertial term followed by large pressure forces activated when approaching the reconnection site. Basically, the electric field related to the full electron pressure tensor becomes the main contribution there, showing that when ions decouple electron kinetic physics dominates.
In the classical one-fluid MHD theory the electric field , seen in the rest frame by the plasma moving with the velocity V, is often described by the ideal case ( = R 0; see, e.g., Krall & Trivelpiece 1973). In two-fluid theory, the sum of all the contributions to the electric field, E tot , consisting of various terms should be equal to the dissipation created by an anomalous resistivity η in the generalized Ohm's law. Basically, one should have (see Rossi & Olbert 1970, Equation (12.25)) where E H , E a , and E p denote the Hall, inertial, and pressure terms. Namely, the electric fields responsible for dissipative processes at reconnection sites must be described by nonideal terms (e.g., Baumjohann & Treumann 1996;Biskamp 2000;Yamada et al. 2016). Using the quasi-neutrality of plasma with density n=n i =n e (and the electron to ion mass ratio m e /m i = 1), the bulk velocity of the plasma is approximately equal to the velocity of ions, » V V i , provided that the velocities of ions and electrons are of the same order of magnitude,Ṽ V i e . For many astrophysical applications inside the ion IDR the main contribution to the electric field should come from the Hall term, ) (e is the electron elementary charge).
This means that electrons remain frozen and are convected by the magnetic field. It is worth noting that the Hall term is active on kinetic ion scales (Burch et al. 2016a). On the other hand, the new E a and E p terms describing the electric field resulting from the difference between accelerated electrons and ions and the thermal pressure of electrons relative to the ion background, respectively, should be important on both ion and electron scales (Spitzer 1956;Rossi & Olbert 1970). Therefore, these two other inertia and thermal terms should also be important in the kinetic regime.
In the reconnection region, the inertial forces resulting from separation of the electrons and ions should be taken into account. The first nonideal component to the electric field should come from the difference of the acceleration of electrons and ions = - ) . Namely, taking the time and space change of the convective derivative of the electrons for jets moving rapidly from the X-line for both the electron V e and ion V i flows, turning electrons and ions from inflowing into outflowing current directions, we have Next, using the continuity conservation equations, , for both the ion and electron fluxes, one obtains the following formula for steady-state conditions: corresponding to the conservation of the total anisotropic kinetic energy density flux in the stress tensor, which involves the divergence  of this tensor (Landau et al. 1984). The second (nonideal) contribution to the electric field results from the divergence of the fully anisotropic pressure (dyadic) tensor (e.g., Gurnett & Bhattacharjee 2005, Equation . Note that by averaging over velocity space for a given position = r x y z , , ( ) within an infinitesimally small fluid element of volume = r d dxdydz Spitzer 1956, Equation (2.6)). This means that the pressure term should have a somewhat similar structure to that of the inertial term, as given by Equation (3), but with the distribution function f for individual particles moving randomly with velocities V around the mean (bulk) velocity º á ñ = U V ò V V fd n 1 3 . Because m m 1 e i  , the contribution from the ion pressure tensor can be neglected and we only have the electron tensor electric field (e.g., Rossi & Olbert 1970):  Figure 1 shows the MMS trajectories for cases (a)-(c) that will be presented in Figures 2-4, respectively, in the Geocentric Solar Magnetospheric (GSM) coordinates (x toward the Sun, y toward dusk, with the dipole axis in the x, z plane), similar to the (L, M, N) coordinates used in by Torbert et al. (2016Torbert et al. ( , 2018 Table 1, we have 513 measurement points for the magnetic field and 133 (27) points for the electron (ion) velocity. However, it appears that reconnection in the magnetotail is much more difficult to identify. Inside the magnetosphere, when approaching the EDR in the magnetotail on 2017 July 17, the 4 s interval has only been reported by Torbert et al. (2018), and we analyze this case (b), as listed in Table 1. We also consider another interval lasting 8 s during a magnetotail crossing on 2018 July 24 consisting of 1026 points for the magnetic field B and 267 (53) points for the ion and electron V i,e velocity, case (c) in Table 1. The left panels ((A)-(H)) of Figures 2-4 display the data used for the analysis. Because all probes observed similar structures, we display the data for only one selected MMS spacecraft for each event. The magnetic field vector components including its magnitude are presented in panel (A), with all components of the ion (B) and electron (C) velocity vectors, the ion (D) and electron (E) energy omnidirectional spectrograms, the ion (F) and electron (G) perpendicular T ⊥ and parallel T P temperatures, and the ion and electron density n i and n e are shown in the bottom panel (H).
We see that the components of the magnetic field B x and B z change sign at 7:49:33, 22:34:03, and 17:47:10, respectively, and that the ion V ix velocity usually changes sign nearly simultaneously, followed by distinct fast electron jets V ex . When densities are low in the magnetotail (0.1-0.3 cm −3 ) we reduce the noise caused by local photoelectrons from the spacecraft by including only particles with energies greater than 56 eV (165 eV) for electrons and 975 eV for ions (panels E) in the respective partial distribution functions for cases (b) and (c), see Supplementary Materials of Torbert et al. (2018). Because the highest resolutions available for the ion distributions are 5 times lower than that for electrons, we have also verified that the fluctuations in the electron speeds could be smoothed by using somewhat lower resolutions for electrons. A reversal in ion flow is still clearly seen in all panels (B) but substantial variations in electron speeds are present in panel (C) only in case (c), smoothed by the same running averages of 0.3 s (twice the resolutions for ions, 0.15 s), and to be consistent with quasi-neutrality achieved in panel (H). Contrary to case (b) of 2017 July 11, when MMS crossed the EDR region (Torbert et al. 2018), in case (c) representing the current sheet crossings in 2018 we see large chaotic fluctuations in the electron velocities. In fact, this may exhibit some turbulent processes responsible for reconnection when approaching or  Table 1. passing by the X-line. Besides the flow reversal, some heating is observed here for both ions (up to energies of a few tens keV) and electrons (1-10 keV), but compared with the temperature asymmetry observed in the EDR of 2017 July 11, for the current sheet crossing on 2018 July 24 roughly isotropic ion (3-6 keV) and electron temperatures (2-3 keV), are seen in panels (D) and (E).
The main results for the reconnecting electric fields are shown in the right panels from (I) to (P) of Figures 2-4. First, the current j obtained from the curl of the magnetic field B is displayed in panel (I). The relatively large components during the crossing of the current sheet are seen especially at the magnetopause, case (a). Next, besides the ideal field +É V B (1-10 mV m −1 ) seen in the frame of the plasma moving with the bulk speed V (panel J), we display nonideal electric fields resulting from the following terms: the Hall E H (panel K), inertial acceleration E a (L), and electron pressure E p (M) electric fields, respectively. The Hall electric fields of Equation (2) have been calculated using two methods, from Ampere's law (curl of the magnetic field) and from plasma ion and electron data, to check the consistency of the calculations of moments of electron distribution functions (only the curlometer current is shown in panel (I)). The divergence of the ion and electron velocity tensors in Equation (3) and the electron pressure tensor of Equation (4) have been calculated using the probability distribution functions with the tools developed for analysis of multispacecraft data employing a linear interpolation within the tetrahedral configuration of four spacecraft (in case (c), only MMS 1, 2, and 3 are taken; Chanteur 2000, chapter 14).
It is interesting to compare the electric fields contributing to the generalized Ohm's law as displayed in panels (J)-(M). We see that the electric field resulting from the Hall current (1-10 mV m −1 ) is the same order as the ideal field, and as expected the Hall term still plays an important role for fast reconnection, especially in the IDR. The contribution from the inertial term is rather small at the magnetopause, case (a) (fraction of mV m −1 ), and moderate in the magnetotail (1-2 mV m −1 ) in cases (b) and (c). In particular, we have recovered the current and magnetic field at the magnetopause, case (a), but we have noticed that = -É j B en H ( ) can provide values up to 10 mV m −1 , i.e., larger than the inertial contribution, contrary to Webster et al. (2018; owing to the corrected multiplication error in their Figure 8).
On the other hand, as compared with the rather small reconnection electric fields of 1-2 mV m −1 at the magnetopause, case (a), and in the EDR in 2017, case (b), we see a very large electric field up to 200 mV m −1 resulting from the divergence of the electron pressure gradient in the neutral sheet crossing in 2018, case (c). Please note that Hall physics is in principle dissipationless, = =-´= j E j j B W en 0 H H · ·( ) ( ) . Hence, the secondary Hall electric field can only accelerate a small group of electrons. However, the divergence of the electron pressure term is clearly dissipative, because it introduces electron velocities, Equation (4). This shows that, when electrons decouple from ions, electron kinetic physics should play a major role in the neutral sheet reconnection site.  Table 1.