Recent progress on magnetic reconnection by in situ measurements

Abstract

In the last decades, a few spacecraft missions have been launched to investigate the process of magnetic reconnection in space, during which magnetic free energy is explosively released into plasma kinetic energy and heating. Due to the sophisticated in situ measurements of the spacecraft missions, a big progress has been achieved over the last decades. The mystery of the core region of the reconnection ion and electron diffusion regions is uncovered for the first time. The coupling between the local magnetic reconnection and the global-scale disturbance is deeply understood. More evidence for the relation between magnetic reconnection and turbulence is accumulated. This paper is aimed to simply review these advances.

1 Introduction

Magnetic reconnection is a fundamental plasma process in various environments (Hesse and Cassak 2020; Ji et al. 2022; Lu et al. 2022a; Paschmann et al. 2013; Yamada et al. 2010), e.g., the terrestrial magnetosphere, plasma turbulence, interplanetary space, solar corona, astrophysical jets. In the process of magnetic reconnection, magnetic topology is reconfigured rapidly, leading to the explosive release of the stored magnetic free energy into plasma energy in the form of plasma heating, kinetic energy, and super-thermal electrons as well as ions. According to the collision-less reconnection theoretical model, it is triggered in the diffusion region, where the frozen-in condition of magnetohydrodynamics is violated (Sonnerup 1979; Vasyliunas 1975). In magnetic reconnection without a guide field, the ions are decoupled from magnetic field lines at the ion inertial length scale while the electrons are decoupled from magnetic field lines at the smaller electron inertial length scale, as they drift toward the current sheet center. As for the more generic case of magnetic reconnection with a guide field, it occurs while the current sheet thins down to the ion sound Larmor radius (Kleva et al. 1995; Rogers et al. 2001; Cassak et al. 2007; Egedal et al. 2007; Ji and Daughton 2011). In this process, the charged particles can be efficiently energized.

Magnetic reconnection can affect a large volume in space but is initiated in the very localized diffusion region (Angelopoulos et al. 2020; Angelopoulos et al. 2008; Pu et al. 2010). Therefore, it is easy to observe its resulting consequence but is very challenging to capture the diffusion region by in situ spacecraft measurement. Magnetic reconnection extensively occurs in the interplanetary space (Davis et al. 2006; Gosling 2012; Gosling et al. 2005; Voros et al. 2021; Wang et al. 2022; Wei et al. 2003) and planet’s magnetospheres (Burch et al. 2016b; Deng and Matsumoto 2001; Wang et al. 2010b; Xiao et al. 2006; Zhong et al. 2018a). As a natural laboratory of the Earth’s magnetosphere, a few spacecraft missions have been launched to explore the effect on the large volume and the microphysics inside the diffusion region of magnetic reconnection (Angelopoulos 2008; Burch et al. 2016a; Liu et al. 2005; Nishida 1994; Shen and Liu 2005). In last decades, a large progress has been achieved on the knowledge of magnetic reconnection. This paper is aimed to simply review these main progresses.

2 The reconnection diffusion region

2.1 The reconnection outflow jet

According to the reconnection model, the bi-directional plasma bulk flows, dubbed plasma jets, would be generated and transferred away from the magnetic reconnection X-line, as illustrated in Fig. 1, and the speed of the plasma jets can be as large as the local Alfvén speed based on the plasma conditions upstream of the reconnection current sheet. The high-speed plasma jets were first observed in the Earth’s magnetotail at ~ 15–20 Earth radii (Re) and was thought to be related to substorm (Baumjohann 1991; Baumjohann et al. 1990). In the magnetotail, the high-speed flows were as high as 1000 km/s and supposed to be the product of magnetic reconnection. The high-speed plasma flows were detected at the magnetopause as well (Paschmann et al. 1979). These accelerated plasma flows show good agreement with the reconnection theoretical prediction. It indicates that the reconnection plays a key role for the substorm in the magnetosphere and for the coupling between the solar wind and the magnetosphere.

Fig. 1

A schematic illustration for the diffusion region of magnetic reconnection. The black curves with an arrow represent magnetic field lines. The blue arrows denote the ion bulk flows. The gray arrows are the Hall electric field. The dashed arrows are the electron bulk flows. The pink area exhibits the electron diffusion region

The high-speed plasma flows were found to be bursty and most of the flows lasted less than 10 min, called bursty bulk flows (BBFs) in the magnetotail (Angelopoulos et al. 1992; Angelopoulos et al. 1994; Cao et al. 2006; Nakamura et al. 2005; Sergeev 2004). One BBF event (Zhang et al. 2020) observed by the Magnetospheric Multiscale Mission (MMS) spacecraft (Burch et al. 2016a) was displayed in Fig. 2. This event was observed by MMS during 16:35–16:38 UT on 07 July 2017 when the spacecraft was at [− 24.3, 0.9, 4.7] $R_{E}$ in the GSE system. The bulk flows were continuously observed during more than 3 min (Fig. 2e) and the speed was as large as 1000 km/s. Inside the bulk flows, the ions were heated (Fig. 2g) primarily in the parallel direction (Fig. 2b) while the electron temperatures in the parallel and perpendicular directions increased significantly (Fig. 2c). During this time interval, MMS passed through the current sheet multiple times (Fig. 2a) and the plasma beta evolved accordingly (Fig. 2d), and thus the flow profile across the current sheet can be examined.

Fig. 2

a Magnetic field vector and the total magnetic field, b ion temperature in the parallel and perpendicular directions, c electron temperature in the parallel and perpendicular directions, d plasma beta, e ion bulk flows, f electron bulk flows, g electron velocity in the parallel and perpendicular directions, h ion energy–time spectrum and i electron energy–time spectrum, adapted from Zhang et al. (2020)

The statistical analysis on the BBFs presented the positive correlation between BBFs and the AE index, suggesting that BBFs could be the primary transport mechanism in the magnetotail and actively contributed to the substorm (Angelopoulos et al. 1994; Angelopoulos et al. 1999; Angelopoulos et al. 1997). Based on the MHD approximation and kinetic analysis, the contribution of the BBFs to the earthward transport of mass, energy, and magnetic fluxes during a substorm is quantified. The results show that the energy transport of the BBFs is responsible for up to 100% of the substorm energy consumption (Cao et al. 2013, 2012). Another statistical analysis found that the spatial scale of the BBFs in the near-Earth’s magnetotail is about 2 ~ 3 Re in the dawn-dusk direction and 1.5 ~ 2 Re in the north–south direction (Nakamura et al. 2004). This spatial scale of the flow channel indicates the length of the reconnection X-line in the magnetotail. Therefore, the BBFs should be common in the magnetotail and thus make major contribution to the substorms.

Accompanying with the BBFs, multi-scale magnetic field fluctuations are observed and magnetic field spectra display a power-law behavior (Li et al. 2022b; Vörös et al. 2006). These observations suggested that the BBFs drove the turbulence as they were ejected. Obviously, the turbulence driven by the BBFs could reinforce the energy dissipation and diffusion during magnetic reconnection (Li et al. 2022b). Since the insufficient measurement of the plasma moment, the energy dissipation in the kinetic sale inside the BBFs were unrevealed until recently. The Magnetospheric Multiscale Mission (MMS) provides the accurate measurement of plasma moments, including the electron moment. Thus, the electron bulk flow and the electron pitch angle distribution within the BBFs can be studied in detail.

In the BBFs event displayed in Fig. 2, the electron flows were investigated as well. The electron bulk flows were distinct with the ion flows of the BBFs in the magnetotail (Fig. 2e and f). Within the earthward BBFs, the tailward electron flows were frequently detected (Fig. 2f). To investigate the profile of these electron and ion bulk flows across the magnetotail current sheet, the distribution of these flows relative to $B_{x}$ and plasma beta $\beta$ is shown in Fig. 3. The ion flows had the maximum value just at $B_{x} = 0$ and gradually decreased as $|B_{x} |$ increased (Fig. 3a). So, the ion flow speed increased as $\beta$ increased (Fig. 3b). In contrast, the earthward electron flows got the maximum values at $|B_{x} |\sim 10$ nT and $\beta \sim 3$, away from the plasma sheet center. Moreover, the tailward electron flows were detected primarily further away from the plasma sheet center ($|B_{x} |\sim 14$ nT) at $\beta \sim 0.3$, nearly the boundary of the plasma sheet.

Fig. 3

The distribution of the ion and electron flows inside the magnetotail plasma sheet during the event displayed in Fig. 2. Each dot denotes the data measured by MMS in the plasma sheet. a The profile of the ion and electron flows across the plasma sheet, b dependence of the ion and electron flows on the plasma beta. This figure is adopted from Zhang et al. (2020)

Based on tens of the BBF events, our recent investigations further confirmed that the ion flows peaked near the center of the neutral sheet with a large plasma beta. However, the electron bulk flows peaked away from the neutral sheet and at $B_{x}$ ~ 10 nT. At the edges of the magnetotail plasma sheet, the tailward electron flows were detected and bounded the ion bulk flows. All these features are consistent with the reconnection picture in the magnetotail which will be introduced soon in the next section. It indicates that the observed BBFs in the magnetotail were very close to the reconnection X-line. Otherwise, the reconnection X-line could extend very long.

2.2 The ion diffusion region

Although the high-speed plasma flow, as one typical signature of magnetic reconnection, has been extensively observed in the magnetotail and the magnetopause, the high-speed flow can be generated by other mechanisms as well. The definite evidence for the occurrence of magnetic reconnection is the so-called reconnection diffusion region (Sonnerup 1979; Vasyliunas 1975; Fu et al. 2006). In magnetic reconnection, the frozen-in field condition of magnetohydrodynamics is violated at the localized region, named the diffusion region. Considering the reconnection without a guide field, the ions would be decoupled from magnetic field lines at the ion inertial length scale, i.e., the ion diffusion region, while the electron frozen-in condition was broken in the much smaller electron inertial length, i.e., electron diffusion region. This kind of divergence of ion and electron trajectories is called the Hall effect. As a result, the electron diffusion region is embedded inside the ion diffusion region. Owing to the Hall effect, the Hall electric field and the Hall magnetic field structure are created inside the ion diffusion region, as shown in Fig. 1. Because the ions and electrons are separated at different spatial scale, the Hall electric field directed toward the electron diffusion region at both sides of the reconnecting current sheet is generated. The electrons are injected into the electron diffusion region along the magnetic field in the separatrices and formed the inflowing electron beam therein. After energized in the separatrix region and the electron diffusion region, the electrons are ejected away from the electron diffusion region. Then the electron current system generates the quadrupolar structure of the out-of-plane magnetic field, namely the Hall magnetic field. Therefore, the Hall electric field and magnetic field have been regarded one characteristic of the reconnection diffusion region.

The Hall electric field and magnetic field have been extensively detected in the magnetosphere and interplanetary space (Øieroset et al. 2001; Nagai et al. 2003; Eastwood et al. 2010a; Wang et al. 2017b). The observations show that they can greatly extend over the reconnection outflow direction (Khotyaintsev et al. 2006; Retinò et al. 2006; Shay et al. 2016b; Wang et al. 2012). It indicates that the Hall field signature alone is not the unique feature of the ion diffusion region. One must combine all the features related to the diffusion region, including the ion flow reversal, the Hall electric field, and magnetic field signatures, and the temperature increase to identify the reconnection diffusion region from in situ measurements. Based on tens of the reconnection ion diffusion regions observed by Cluster in the near-Earth tail, the Hall magnetic field strength was found to be ~ 39% of the inflow magnetic field and the Hall electric field was about ~ 33% of the inflow convection electric field (Eastwood et al. 2010a).

The guide field can modify the quadrupolar structure of the Hall magnetic field (Fu et al. 2006; Huang et al. 2010; Lapenta et al. 2010; Pritchett and Coroniti 2004). In antiparallel magnetic reconnection, where the shear angle of magnetic field prior to reconnection is 180° between both sides of the current sheet, the quadrupolar structure was symmetric. The Cluster spacecraft encountered one reconnection event without a guide field during 07:45–08:05 UT on 10 September 2001 in the magnetotail (Wang et al. 2010a, b, c). The distribution of $B_{y}$ in the plane $V_{x} - B_{x}$ is shown in left column of Fig. 4. The black (red) circles denote the negative (positive) values of $B_{y}$, and the sizes of the circles mean magnitude of $|B_{y} |$ or $|B_{y} - B_{g} |$. It is clear that the Hall magnetic field was nearly symmetric relative to the neutral plane ($B_{x} = 0$ nT). In contrast, the quadrupolar structure was distorted by the guide field in the component magnetic reconnection (Eastwood et al. 2010b; Wang et al. 2012). In the component magnetic reconnection, the addition of a guide field would deflect the electron outflow jets away from the neutral sheet, which causes the distortion of the quadrupolar structure of the Hall magnetic field, as shown in right column of Fig. 4. This reconnection event was detected by Cluster as well during 09:30–11:10 UT on 28 August 2002. These were a guide field in this event and the ratio of $B_{g} /B_{o}$ was 0.3, where $B_{o}$ is asymptotic reconnecting magnetic field. It can be found that $B_{y} - B_{g}$ changed sign at $B_{x} \sim 10$ nT rather than at $B_{x} \sim 0$ nT as the left column.

Fig. 4

The distribution of $B_{y}$ in a magnetic reconnection without a guide field and of $B_{y} - B_{g}$ during a magnetic reconnection with a guide field $B_{g}$ in the plane of $V_{x} - B_{x}$, where $V_{x}$ is ion speed in $x$ direction

The inflowing electrons are frequently observed along the separatrices bounding the ion diffusion region (Øieroset et al. 2001; Retinò et al. 2006; Wang et al. 2010b). Generally, the inflowing electrons are low energy and show the beam-like distribution. As moving toward the center of the diffusion region, the electrons are accelerated primarily by electrostatic structures/waves (Divin et al. 2012; Drake et al. 2005; Lapenta et al. 2015a, 2016; Wang et al. 2014b). As the electrons in the separatrix region were persistently accelerated, the electrons are depressed, and thus an electron density cavity is produced (Drake et al. 2005; Khotyaintsev et al. 2006; Wang et al. 2013; Wang et al. 2012). Therefore, the density cavity is regarded as one typical feature of the boundary of the ion diffusion region. Since the beam-like electron distributions are formed in the separatrices, the electrostatic instabilities would occur, and thus intense electric fluctuations are created.

The magnetic flux rope is a kind of helical magnetic field structure (Slavin et al. 2003a; Wang et al. 2016b). It is commonly embedded inside the reconnection outflow or within the ion diffusion region (Eastwood et al. 2007; Wang et al. 2010a, 2010c), as one byproduct of magnetic reconnection. Generally, the current enhancement can be observed inside magnetic flux ropes (Slavin et al. 2003b; Wang et al. 2016b, 2017a, 2019, 2020b) and the observations show that the flux rope can be associated with some kinds of wave emissions, energetic electrons, intense electric field, strong energy dissipation, and so on. More details on the flux ropes can be found in the section of turbulent magnetic reconnection.

Strictly speaking, the ion diffusion region can only be demonstrated by the definition. Thanks to the Magnetospheric Multiscale Mission launched by NASA, the ion diffusion region can be unambiguously identified. Based on the accurate measurements of magnetic field and electric field vectors, and ion as well as electron distribution, the ion diffusion region was first observed at the magnetopause and an electron diffusion region was detected at the center of the ion diffusion region (Burch et al. 2016b; Li et al. 2019a, b; Wang et al. 2017b; Zhou et al. 2019). Based on the comprehensive measurements of magnetic field, electric field, and plasma from the MMS, the frozen-in condition (${\mathbf{E}} + {\mathbf{V}} \times {\mathbf{B}} = 0$) can be strictly verified (e.g., Burch et al. 2016a, b; Eastwood et al. 2016). Many reconnection diffusion regions and the characteristics mentioned above are validated.

2.3 The electron diffusion region

The electron diffusion region was detected recently based on the MMS measurement in the magnetosphere (Burch et al. 2016b; Nakamura et al. 2019; Norgren et al. 2018; Torbert et al. 2018; Wang et al. 2020a), in the magnetosheath (Phan et al. 2018; Stawarz et al. 2019) and in the solar wind (Wang et al. 2022). The observations were in good agreement with the simulation results (Hesse et al. 2016, 2011; Lu et al. 2020a; Shay et al. 2016b; Zenitani et al. 2011a, 2011b). However, some unexpected new results were found (Li et al. 2022c; Wang et al. 2022) also, e.g., the electron diffusion region can be fragmented into a large number of filamentary currents. Since both the ion and electron moment data can be obtained from the MMS observations, the current density can be directly calculated by the equation ${\mathbf{J}} = qN({\mathbf{V}}_{i} - {\mathbf{V}}_{e} )$, where $q$ is elementary charge, $N$ is the plasma number density, ${\mathbf{V}}_{i}$ and ${\mathbf{V}}_{e}$ denote the ion and electron velocity. The obtained current density is compared with that calculated from the magnetic field measurement at four points via the Ampere’s law (Burch et al. 2016b; Eastwood et al. 2016). The comparison shows that the current densities from both methods are basically consistent at the scale of ion gyro-period. It means that the ion and electron moment data from the MMS spacecraft were accurate and the plasma moment data with a time resolution higher than the ion gyro-period are reliable as well. Thus, the detailed microphysics inside the electron diffusion region can be investigated by in situ measurement for the first time.

The electron diffusion region is expected to be a thin current layer. The electrons are moving primarily along the X-line direction while the ions are propagating oppositely to the electrons surrounding the electron diffusion region, resulting in a thin current layer (Li et al. 2019a, b; Nagai et al. 2013). Since the speed of the ions is much weaker than the electrons, the electric current inside this current layer is primarily carried by the electrons. This current layer can be elongated along the outflow direction and its length can be as large as tens of the electron inertial lengths (Phan et al. 2007; Le et al. 2013; Wang et al. 2017b). On the other hand, the electron flows are complicated inside the layer, especially away from its center. At the boundary of the current layer, the electrons are moving toward the center along the local magnetic field lines while they are ejected away from the center (Li et al. 2019a, b; Wang et al. 2010b). This outflow electron jets, called outer EDR sometimes (Shay et al. 2007, Karimabadi et al. 2007), were detected recently (Phan et al. 2007). The inflowing and outflowing electrons constitute a current loop at both outflow regions of the electron diffusion region. The width of the current loop in the vicinity of the electron diffusion region can be as thin as a few electron inertial lengths and the resulting Hall magnetic field was very narrow also with a spatial scale of a few electron inertial lengths (Wang et al. 2018; Wang et al. 2017b). Thus, the Hall magnetic field observed inside the EDR could be the extension of the Hall magnetic field inside the IDR.

Because of the narrow current layer, the electrons cannot complete one whole cyclotron motion, which causes a non-gyrotropic electron distribution inside the layer. Moreover, one striking feature of the electron velocity within the electron diffusion region is the so-called crescent-shaped distribution in the plane perpendicular to the magnetic field. It was first proposed in the numerical simulations where the electrons drift due to the Hall electric field, leading to the crescent distribution (Hesse et al. 2014; Shay et al. 2016b). The electron crescent distribution was first observed at the magnetopause (Burch et al. 2016b) and then in the magnetotail (Torbert et al. 2018). In the component magnetic reconnection as observed at the magnetopause, the electron crescent distribution was observed at the stagnation point rather than at the X-line point (Wang et al. 2017b). Furthermore, the electron crescent distribution was not only observed in the perpendicular direction but also downstream of the electron diffusion region in the parallel direction. In the antiparallel magnetic reconnection, multiple crescent distributions at different energies are detected (Li et al. 2019a, b). The crescent electron distribution will excite some kinds of high-frequency electrostatic waves, e.g., electron Bernstein waves which thermalize and diffuse electrons around the electron diffusion region (Li et al. 2020). Most recently, the crescent distribution was detected also away from the electron diffusion region (Tang et al. 2019).

The evolution of the electron non-gyrotropic distribution across the EDR was first resolved by Li et al. (2019a, b). Figure 5 shows a complete EDR crossing and the electron velocity distributions at different locations therein. The dependence of non-gyrotropic distribution on the electron energy and the normal distance from the EDR midplane is present (Fig. 5d). When the spacecraft was at the EDR edge, only the relatively high-energy electrons ($V_{ \bot }$ > 30,000 km/s) displayed the non-gyrotropic distribution (Fig. 5d1) and the electrons with energy below that energy show a gyrotropic distribution. As the spacecraft approached the EDR center, medium-energy (20,000 < $V_{ \bot }$ < 30,000 km/s) and low-energy (5000 < $V_{ \bot }$ < 20,000 km/s) electrons became non-gyrotropic distribution in turn and the multiple crescents distribution was observed (Fig. 5d4) in the low-energy range. The dependence of non-gyrotropic distribution on the electron energy and the normal distance from the EDR midplane suggests that the non-gyrotropic distribution was caused by the electron meandering motion (Bessho et al. 2018; Hesse et al. 2014; Lapenta et al. 2017; Shay et al. 2016a). The electrons with the higher energy had the larger gyroradius, and thus the non-gyrotropic distribution was observed further away from the EDR midplane for the electrons with the higher energy. Moreover, the electrons in all energy ranges displayed nearly gyrotropic distribution at the very center of the EDR (Fig. 5d5).

Fig. 5

The complete EDR crossing and the electron velocity distributions therein. (a) Three components of the magnetic field. b The electron bulk flows. c Three components of the electric field. d and e Electron velocity distribution in the perpendicular plane $V_{ \bot 1} = ({\mathbf{b}} \times {\mathbf{v}})$ and $V_{ \bot 1} = ({\mathbf{b}} \times {\mathbf{v}}) \times {\mathbf{b}}$, where b and v are unit vectors of B and Ve. The radiuses of the black dashed circle are 0.5 × 10⁴, 2 × 10⁴, and 3 × 10⁴ km/s, respectively. The scale indicating the normal distance from the midplane of EDR is marked at the top, and the magenta arrows marked in a represent the time of the electron velocity distribution shown in d and e

Inside this electron current layer, the electrons are no longer frozen in with the magnetic field and the non-ideal electric field would be generated according to the generalized Ohm’s law. Because of simultaneous measurement of the MMS spacecraft at four points, all terms in generalized Ohm’s law could be calculated. The initial results show that the Hall term and the term of the electron pressure tensor gradient are the major contribution to the measured reconnection electric field (e.g., Wang et al. 2020a). On the other hand, the electron velocity was substantially enhanced inside the electron diffusion region and nearly equal to the sum of the electric field drift and diamagnetic drift except for at the very center of the EDR midplane.

Given the energy dissipation and the energy conversion from magnetic free energy into the plasma energy during magnetic reconnection, the energy conversion rate ${\mathbf{J}} \cdot ({\mathbf{E}} + {\mathbf{V}}_{e} \times {\mathbf{B}})$ was expected to be positive inside the EDR (Zenitani et al. 2011a, b). Numerical simulations show that ${\mathbf{J}} \cdot ({\mathbf{E}} + {\mathbf{V}}_{e} \times {\mathbf{B}})$ was positive at the center of the EDR and was surrounded by a region with negative ${\mathbf{J}} \cdot ({\mathbf{E}} + {\mathbf{V}}_{e} \times {\mathbf{B}})$(Zenitani et al. 2011b). The MMS observations confirmed that ${\mathbf{J}} \cdot ({\mathbf{E}} + {\mathbf{V}}_{e} \times {\mathbf{B}})$ was indeed positive (Burch, et al. 2016b; Torbert et al. 2018; Wang et al. 2020a), namely magnetic free energy was converted into plasma energy. However, the negative ${\mathbf{J}} \cdot ({\mathbf{E}} + {\mathbf{V}}_{e} \times {\mathbf{B}})$ was common inside and surrounding the EDR, which is consistent with the simulation results. However, further investigation shows that the value of ${\mathbf{J}} \cdot ({\mathbf{E}} + {\mathbf{V}}_{e} \times {\mathbf{B}})$ is randomly negative or positive inside the turbulent EDR (Li et al. 2022c; Wang et al. 2022). The cumulative distribution functions (CDF) of the current density and energy conversion rate are established. The CDF of current density, at $|{\mathbf{J}}|$, was defined by $\sum\nolimits_{{|{\mathbf{J}}|}}^{\infty } f$ (black trace in Fig. 6), representing the probability of current density great than ${\mathbf{|J|}}$. Figure 6 shows that the CDF of ${\mathbf{J}} \cdot {\mathbf{E}}^{\prime } = {\mathbf{J}} \cdot \left( {{\mathbf{E}} + {\mathbf{V}}_{e} \times {\mathbf{B}}} \right)$ (curve with red squares) with its parallel component ($\sum\nolimits_{0}^{{|{\mathbf{J}}|}} {{\mathbf{J}}_{\parallel } \cdot {\mathbf{E}}_{\parallel } }$, curve in blue) and perpendicular component of ${\mathbf{J}} \cdot {\mathbf{E}}^{\prime}$ ($\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{ \bot } \cdot {\mathbf{E}}_{ \bot } }$, black line). It is clear that the energy dissipation depended on the current density intensity. In the weak currents (< 30 nA/m²), the negative ${\mathbf{J}} \cdot {\mathbf{E}}^{\prime }$ means a dynamo process there. In the strong currents (> 30 nA/m²), overall ${\mathbf{J}} \cdot {\mathbf{E}}^{\prime }$ increases gradually. In the direction parallel to magnetic field lines, the magnetic field energy is accumulated while it is released mainly in the perpendicular directions. On the turbulent magnetic reconnection, it will be further dicussed in more detail in the last part.

Fig. 6

Energy dissipation in the turbulent EDR. The black trace represents the cumulative distribution functions (CDF) of current density, defined by $\sum\nolimits_{{\left| {\mathbf{J}} \right|}}^{\infty } f$. The traces with color squares display the CDF of energy dissipation rate ($\sum\nolimits_{0}^{{|{\mathbf{J}}|}} {{\mathbf{J}} \cdot {\mathbf{E}}^{\prime }}$, red curve with squares), with its parallel component ($\sum\nolimits_{0}^{{|{\mathbf{J}}|}} {{\mathbf{J}}_{\parallel } \cdot {\mathbf{E}}_{\parallel } }$, blue curve with squares) and perpendicular component of ${\mathbf{J}} \cdot {\mathbf{E}}^{\prime }$ ($\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{ \bot } \cdot {\mathbf{E}}^{\prime }_{ \bot } }$, black curve with squares)

3 Turbulent magnetic reconnection

3.1 Onset of magnetic reconnection

It is a long outstanding issue that how magnetic reconnection is triggered in the magnetotail. Previous investigations show that the current sheet thinning is one necessary condition for reconnection onset (Baumjohann et al. 2007; Nakamura et al. 2006; Zelenyi et al. 2020). However, the sufficient condition has never been revealed. In the magnetotail, the component of magnetic field normal to the current sheet originated from the Earth’s dipolar magnetic field stabilizes the current sheet and prevents the occurrence of the tearing mode and the following process of magnetic reconnection (Galeev and Zelenyi 1976; Lembege and Pellat 1982; Pellat et al. 1991). The fact is that magnetic reconnection can be frequently detected in the magnetotail. It is controversial that how the normal component of magnetic field is removed. A few possible candidates have been proposed to reduce the normal component of magnetic field. One is the external driver decreasing the normal component to initiate the electron kinetics and finally trigger magnetic reconnection (Birn and Hesse 2014; Liu et al. 2014; Lu et al. 2020b, 2022c; Pritchett and Lu 2018). Another possibility is that the reconnection can be spontaneously triggered without external driver via the ion tearing mode after a hump of the normal magnetic field is transferred toward Earth (Sitnov et al. 2013; Sitnov and Schindler 2010). Recent studies show that the small-scale current sheet is generally vertical to the plasma sheet in the magnetotail (Hubbert et al. 2021, 2022; Leonenko et al. 2021; Wang et al. 2018). Therefore, the normal magnetic field is just along the small-scale current sheet rather than normal to the current sheet expected previously, under which condition, the tearing mode can be easily initiated.

One example of such event is observed by the MMS spacecraft during 20:24:03–20:24:11 UT on 17 June 2017 in the magnetotail (Wang et al. 2018), as shown in Fig. 7. As the MMS spacecraft crossed the current sheet from south to north ($B_{x - gse}$ varied from − 10 nT to 12 nT in Fig. 7a), $B_{y - gse}$ and $B_{z - gse}$ changed sign as well in the GSE coordinates. It means that the current sheet is not lying inside the $x - y$ plane of the GSE coordinates as usual. The normal direction of the current sheet was found to be primarily in the $y$ direction. Thus, the current sheet is vertical. The magnetic field was displayed in the local current system (Fig. 7b) and the normal direction of magnetic reconnection $B_{N}$ was close to zero (red trace in Fig. 7b). Thus, the component of magnetic field normal to the current sheet originated from the Earth’s internal dipolar magnetic field is lying within the current sheet. Thus, the tearing mode can be easily excited inside this vertical current sheet.

Fig. 7

Overview of the electron-scale current sheet. a Three components of the magnetic field in the Geocentric Solar Ecliptic (GSE) coordinates. b Three components of the magnetic field in the LMN coordinates. c The ion bulk flows. d The electron bulk flows. e The current density vectors and total current density. f Three components of electric field in the frame of current sheet. g, h Electron and ion energy spectrum

In this event, the ion bulk flow is nearly constant during the whole crossing (Fig. 7c) and the flows are mainly in the $L$ and $N$ directions. This flow speed is consistent with the speed of the current sheet obtained from the Timing method which is based on the time delay between the four satellites (Schwartz 1998). In other words, the ion flow is close to zero in the frame of this moving current sheet, and also the current sheet is quiet. The electron flow was very weak also at the boundary of the current sheet. However, it sharply increases at the center of the current sheet (Fig. 7d). The electron flow is intense, up to 5$v_{A}$, where $v_{A}$ is Alfvén speed, and thus a strong current layer is created by the electron flow (Fig. 7e) at the current sheet center. Inside this electron electric current layer, the Hall magnetic field and electric field (Fig. 7f) can be clearly detected. All these features are consistent with the observation inside the reconnection diffusion region. Furthermore, the energy conversion rate is significant, and the positive values are observed at the center of the electron current layer and surrounded by negative values, consistent with simulations on the electron diffusion region. Therefore, this electron current layer is in good agreement with the electron diffusion region of magnetic reconnection.

One distinct feature in this event from the reconnection diffusion region is the ion flow and ion distribution. The ion energy spectrum shows that ions are not energized inside this current sheet (Fig. 7h) and the ion flow is very weak. It looks like that the ions did not included in this process of magnetic reconnection. This kind of phenomena is now called electron-only magnetic reconnection (Phan et al. 2018). In the magnetosheath, the electron-only reconnection primarily occurs in the electron-scale current layer where no broad ion-scale current sheet embraced the electron-scale current layer (Norgren et al. 2018; Phan et al. 2018; Stawarz et al. 2019). Therefore, the ions cannot be affected by the electron-only reconnection. However, the electron electric current sheet must be embedded inside a broad ion-scale current sheet in the magnetotail. Then why can the electron-only magnetic reconnection happen in the magnetotail?

Comparing the electron-only magnetic reconnection with a classical magnetic reconnection in the magnetotail, Wang et al. found that the electron-only magnetic reconnection actually is a very initial phase of the classical magnetic reconnection (Wang et al. 2020a). As the electron-only reconnection proceeds, the electrons are heated, and thus the electron current layer would spread thick gradually. Finally, the ions are involved in this process and the classical magnetic reconnection is triggered. So, the electron-only magnetic reconnection corresponds to the electron phase of classical magnetic reconnection. Using particle-in-cell simulations, we succeeded in simulating this transition from the electron-phase or electron-only magnetic reconnection to the classical magnetic reconnection (Lu et al. 2020b, 2022c). According to the simulations (Liu et al. 2021, 2020), the electron phase only maintains for a short time, and thus cannot be detected easily.

Based on the MMS observations in the magnetotail and the PIC simulations, it is found that magnetic reconnection in the magnetotail was initiated from the electron dynamics and then followed by the ion dynamics (Hubbert et al. 2021, 2022, 2022c; Lu et al. 2020b; Wang et al. 2018, 2020a). The electron-scale current sheet generally is not lying in the equatorial plane but is vertical to the equatorial plane. Then the normal magnetic field disappears, which could be the reason for the instability of tearing mode in the magnetotail. However, it is still open whether all magnetic reconnection in the large-scale current sheet is initiated from the electron dynamics.

3.2 Turbulent magnetic reconnection

What we addressed above is the electron diffusion region resulting from the laminar electron bulk flows, dubbed laminar EDR here. However, an EDR is not always a single laminar electron current layer. As the electrons are persistently accelerated in the EDR, the laminar electron flows would break up and transition into the turbulent flows, which naturally leads to the turbulent magnetic reconnection (Li et al. 2022c; Wang et al. 2022). A few mechanisms have been proposed to explain the excitation of turbulent magnetic reconnection. The tearing mode is one possibility to excite the turbulent reconnection according to a three-dimensional (3D) simulation (Daughton et al. 2011). In that simulation, the current sheet is deflected from the equatorial plane due to the common existence of the guide field and is repeatedly fragmented into magnetic flux ropes, and then these magnetic flux ropes coalesce. The repeated generation of magnetic flux ropes and their coalescence eventually lead the reconnection into turbulence (Daughton et al. 2011; Lu et al. 2015a). Using the 3D simulations, Che et al. concentrated on the formation of turbulence at the X-line, i.e., the EDR. In their simulations, the EDR disintegrates into a complex web of filamentary currents (FCs) leading to the development of turbulence inside the diffusion region (Che et al. 2011; Che and Zank 2020). A right-hand circularly polarized electromagnetic wave, as a part of the whistler/electron cyclotron branch, is suggested to drive the filamentation of the current sheet in the EDR (Che et al. 2011). However, the following simulations with larger simulation volumes and longer duration, which are sufficient to distinguish between transient effects and to allow coupling to 3D flux rope dynamics, suggested that the dominant instability is collision-less tearing, with no evidence of turbulent broadening in the electron current layers, and the turbulence can be triggered only in the very thin current layers where electron–ion streaming instabilities are unstable (Liu et al. 2013a, b, c). In their simulations, the electron diffusion region is composed of two or more current layers (Liu et al. 2013a, b, c). Recently, 3D simulations of an EDR encountered at the magnetopause show that turbulence develops at both the X-line and along the separatices due to the lower hybrid drift instability (Price et al. 2017, 2020). Lu et al. (2019) found that formation of numerous secondary magnetic islands can cause turbulent reconnection and change the spectral structures of the electromagnetic fields, leading to significant electron acceleration, which is verified later using ARTEMES observations (Lu et al. 2020c). Recent simulations proposed that the particles trapped in magnetic islands in 2D simulations may leak out due to its axial extension of the islands in the 3D system, and then are repeatedly accelerated in the acceleration regions (Dahlin et al. 2017). In 3D simulations, the flux rope kink instability generates strong field-line chaos in weak guide field regions, and thus the electrons can be accelerated more efficiently by the Fermi mechanism (Zhang et al. 2021). Due to the self-generated turbulence and chaotic magnetic field lines in 3D reconnection simulations, the electrons can be transported across the reconnection layer, and thus be continuously accelerated in several acceleration regions to form the power-law spectra (Li et al. 2019a, b).

Turbulence magnetic reconnection has been proposed 20 years ago (Lazarian et al. 1999), where the MHD turbulence is imposed to generate a weak stochastic component of the field structure for the reconnection of large-scale magnetic fields. This weak stochastic component has a dramatic effect on reconnection rate. However, the formation of this weak stochastic component remains unresolved. In situ evidence for turbulent magnetic reconnection is just provided recently by the Cluster and MMS missions (Vörös et al. 2006; Huang et al. 2015a; Eastwood et al. 2009; Fu et al. 2018). Using the Cluster observations in the magnetotail, many magnetic flux ropes are found in the ion diffusion region and the coalescence is first verified (Wang et al. 2016a, b), which is consistent with the 3D simulation results (Daughton et al. 2011; Nakamura et al. 2016). A similar event is reported also at the magnetopause based on the MMS measurement (Wang et al. 2020b; Wang, et al. 2019) and validated in the laser-generated plasmas (Ping et al. 2023). It means that the turbulent magnetic reconnection dominated by magnetic flux rope evolution can occur in both the symmetric and asymmetric current sheet. However, we investigate the Cluster observations in the magnetotail from 2003 to 2008 and found the turbulent reconnection dominated by magnetic flux ropes is not as often as expected. In most of the detected reconnection events, there is no regular flux ropes which is further verified by the MMS observations in the magnetotail. It suggests that turbulent magnetic reconnection dominated by flux rope evolution could not be the most general model in the magnetosphere.

By the MMS observations in the magnetotail, Li et al. found a dynamic 3D current network inside the EDR instead of a single compact electron current layer (Li et al. 2022c). The current network is composed of a large number of filamentary currents. Figure 8 shows an overview of this turbulent magnetic reconnection event observed by MMS at [− 19.2, − 11.3, 3.2] Re in the GSE coordinates. As the MMS passed through the magnetotail from south to north (Fig. 8a), the high-speed ion flow was detected (Fig. 8b) and the ion flow reversed from tailward to earthward at the plasma sheet center. The Hall magnetic field (Fig. 8a) and electric field (red trace in Fig. 8c) were clearly identified around the X-line. Many current spikes were detected in the vicinity of the reconnection X-line (Fig. 8e) and became the strongest just around the plasma sheet center, i.e., the EDR. A total of 254 current spikes were identified inside the X-line region, and Fig. 9 shows the statistical features of these current spikes. The current spikes with a current density below 70 nA/m² occupied about 80%, and all three components (blue, green, and red bars represent the current spikes were dominated by $J_{x}$, $J_{y}$, and $J_{z}$, respectively) could dominate in the spikes (Fig. 9a), suggesting that these current spikes were 3D in spatial distribution. The duration of the spikes was very short (Fig. 9b) and less than 180 ms for most of them (90%). Using Timing method, the thicknesses of these current spikes were roughly estimated to be several electron inertial lengths. These current spikes corresponded to filamentary currents. Because the current needs to be closed, these current spikes must be intertwined, thereby generating a 3D filamentary current network in the X-line region.

Fig. 8

Overview of the turbulent magnetic reconnection. a Three components of the magnetic field. b The ion bulk flows. c Three components of the electric field. d Parallel and perpendicular electron temperatures. e The magnitude of current density (black curve), and the background current density (red curve). f Energetic electron (47–500 keV) omnidirectional differential flux. g Electron (0.1–30 keV) omnidirectional differential flux. The shadow area represents the X-line region

Fig. 9

The histogram of the number (a) and duration (b) of the current spikes in the X-line region. The blue, green, and red bars represent the currents of spikes dominated in the x, y, and z components, respectively

Because of the thin and dynamic filamentary current in the X-line region, electric field and magnetic field fluctuations were very strong (Fig. 8a and c), and both followed the power laws in the power spectral density (Fig. 10a), suggesting that the X-line region had evolved into a turbulent state. In this turbulent X-line region, the fluxes of electrons above 50 keV increased by two orders of magnitude relative to the background value, and the energetic electrons displayed the power-law distributions with a nearly consistent index of 8.0 in the X-line region (Fig. 10b). The observations indicate that the electrons could be effectively accelerated while the X-line region evolved into turbulence with a complex filamentary current network.

Fig. 10

Power spectral density of electromagnetic fields and electron distribution functions. a Power spectral density of the electric field (purple curve) and the magnetic field (black curve) in the X-line region. b Electron distribution functions at different times (the black trace represents the background) with error bars

The turbulent magnetic reconnection not only occur in the magnetosphere but also in the solar wind (Wang et al. 2022). The earlier observations show that the reconnection in the solar wind is quasi-steady state, with the exhausts bounded by back-to-back rotational discontinuities or slow-mode shocks (Gosling et al. 2005, 2007; Mistry et al. 2017; Phan et al. 2006), which is quite different from these observed in the magnetosphere where the reconnection is generally bursty and turbulent. By imposing turbulent forcing, Lu et al. simulated turbulent magnetic reconnection (Lu et al. 2023), which well reproduces the MMS observation results in the reference (Li et al. 2022a, b). Most recently, the MMS observations reveal that the reconnection is turbulent also in the solar wind and a statistical work found that the turbulent reconnection can be common in the solar wind (Wang et al. 2022).

Figure 11 displays one example of the turbulent reconnection in the solar wind, which is detected by the MMS spacecraft at ~ 1AU. The data are displayed in the local current coordinates system (Wang et al. 2022). $B_{L}$ evolved from + 4 nT at ~ 10:03:00 UT to − 5 nT at ~ 10:03:20 UT (Fig. 11b). It means that MMS crossed a current sheet from one side to the other. In this crossing, the plasma density got the minimum near the center (Fig. 11a), and the ion bulk flows $v_{iL}$ varied from negative to positive with respect to a background flow of − 200 km/s (Fig. 11f), accompanying with the $B_{N}$ reversal at ~ 10:03:15 UT (the vertical dashed line) from negative to positive. The $v_{iL}$ variation before and after the $B_{N}$ reversal point exceeded 30 km/s, ~ 0.6$v_{A}$, where $v_{A}$ = 46.6 km/s is the Alfvénic speed based on $N$ = 3.5 cm⁻³ and $|B_{L} | =$ 4 nT. The simultaneously correlated reversals of $v_{iL}$ and $B_{N}$ in the current sheet indicate that the spacecraft passed through the diffusion region from one outflow region to the other. The reversal points of $B_{N}$ and $v_{iL}$ (the vertical dashed line) correspond to the so-called reconnection X-line, at which both parallel ($T_{i//}$) and perpendicular ($T_{i \bot }$) temperatures of the ions peaked (Fig. 11i) and energetic ions with energy above 10 keV can be observed (Fig. 11j). It indicates that the ions were significantly energized at the X-line region. After this X-line, the positive $v_{iL}$ flow relative to the background flow persisted for ~ 30 s and then fluctuated around the background value, and the $T_{i//}$ enhancement was detected in a much wide region. An ambient magnetic field $B_{M}$ of ~ 4 nT was detected (Fig. 11c), and could be the guide field. The ratio of $B_{M} /B_{L}$ was ~ 1. $B_{M}$ was depressed clearly around the X-line. Given the MMS crossed the second and forth quadrants of the diffusion region (Fig. 1), the depression of $B_{M}$ is consistent with the Hall magnetic field in the collision-less reconnection.

Fig. 11

A turbulent reconnection event observed by the MMS four satellites. a Plasma number density, b–e three components and intensity of magnetic field, f–h three components of ion bulk flow velocity, i ion temperature in the parallel and perpendicular directions, j ion energy spectrum at mms4

In this event, plenty of filamentary and magnetic flux ropes were detected at the X-line region. Figure 12a shows the magnetic field $B_{N}$ with many bipolar variations inside the EDR where the electron flows are enhanced (Figs. 12c and d) and the electron frozen-in condition was violated (Fig. 12e). It indicates that many flux ropes were generated inside the EDR. The electron flow variations in three components (Fig. 12f–h) were significantly amplified inside the EDR. The correlation between the flux ropes and the electron flow variations is established. The observations found a number of magnetic flux ropes and filamentary currents inside the EDR and also in the outflow regions. This turbulent reconnection scenario is consistent with the observations in the magnetosphere (Wang et al. 2016a, b; Li et al. 2022a, b) and the prediction of the simulations (e.g., Daughton et al. 2011; Nakamura et al. 2016; Lu et al. 2023). This turbulent reconnection event was detected by MMS in the solar wind at ~ 1 astronomical unit (AU) (Wang et al. 2022). Most recently, the similar reconnection event with magnetic flux rope in the X-line region was also detected as close as 56 AU away from the Sun (Wang et al. 2023). It indicates that the turbulent reconnection could be common also in the environment of solar atmosphere.

Fig. 12

a, b $B_{N}$ and $B_{M}$ at all four satellites, c, d $V_{eL}$ and $V_{eM}$ at all four satellites, e electric field $E_{L}$, $- ({\mathbf{V}}_{i} \times {\mathbf{B}})_{L}$, and $- ({\mathbf{V}}_{e} \times {\mathbf{B}})_{L}$ in the $L$ direction, f, g the electron velocity variation in three directions, i the parallel electric field to the local magnetic field

In turbulent magnetic reconnection, the energy conversion not only occur in the diffusion region but also in the outflow region (Huang et al. 2015a; Lapenta et al. 2015b; Osman et al. 2015; Vörös, et al. 2006; Wang, et al. 2017a; Wang et al. 2020b; Zhou et al. 2021). The turbulence can be excited also in the outflow regions due to the outflow jets (Vörös et al. 2006), which suggests that the outflow region in the turbulent stage may also play an important role in the energy conversion during reconnection. It is still unclear which impactor controls the energy conversion in the reconnection outflow region.

The energy conversion related to current density in the turbulent outflow region of reconnection is quantitatively studied by a recent work (Li et al. 2022a). This turbulent reconnection endured for a very long time (up to 2 h) (Fig. 13a), and thus the MMS spacecraft stayed more than 1 h in the reconnection outflow (Fig. 13b). The intensity and sign of the energy conversion rate (Fig. 13c) were almost random in this turbulent outflow region (Fig. 13b), and it was difficult to recognize the general rules of energy conversion from the data in the time series (Fig. 13c). By the same event mentioned above, the cumulative distribution functions (CDF) of the current density and energy conversion rate are found in the reconnection outflow. The CDF of current density at $|{\mathbf{J}}|$ was defined by $\sum\nolimits_{{|{\mathbf{J}}|}}^{\infty } f$ (black trace in Fig. 13d and e), and represents the probability of current density great than ${\mathbf{|J|}}$, where $f$ is the probability density function of current density. For example, the CDF of the total energy conversion rate (${\mathbf{J}} \cdot {\mathbf{E}}$) at $|{\mathbf{J}}|$ was defined by $\sum\nolimits_{0}^{{{\mathbf{|J}}|}} {{\mathbf{J}} \cdot {\mathbf{E}}}$, and represents the sum of energy conversion rate in the region where the current density was less than $|{\mathbf{J}}|$. Figure 13d shows the CDF of ${\mathbf{J}} \cdot {\mathbf{E}}$ (red dotted lines) with its parallel component ($\sum\nolimits_{0}^{{|{\mathbf{J}}|}} {{\mathbf{J}}_{\parallel } \cdot {\mathbf{E}}_{\parallel } }$, blue dotted line) and perpendicular component of ${\mathbf{J}} \cdot {\mathbf{E}}$ ($\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{ \bot } \cdot {\mathbf{E}}_{ \bot } }$, black dotted line), simultaneously. The perpendicular component dominated the energy conversion and contributed ~ 90% of the total ${\mathbf{J}} \cdot {\mathbf{E}}$.

Fig. 13

Energy conversion and partition in the turbulent outflow region. a Three components of the magnetic field. b The ion bulk flows. c Energy conversion rate. d and e The cumulative distribution functions (CDF) of current density (black trace) and different type of energy conversion rates (dotted lines). The CDF of current density, at $|{\mathbf{J}}|$, was defined by $\sum\nolimits_{{\left| {\mathbf{J}} \right|}}^{\infty } f$, representing the probability of current density great than $|{\mathbf{J}}|$, where $f$ is the probability density function of current density. Take total energy conversion rate (${\mathbf{J}} \cdot {\mathbf{E}}$) as example, the CDF of ${\mathbf{J}} \cdot {\mathbf{E}}$, at $|{\mathbf{J}}|$, was defined by $\sum\nolimits_{0}^{{{\mathbf{|J}}|}} {{\mathbf{J}} \cdot {\mathbf{E}}}$, representing the sum of energy conversion rate in the region where the current density is less than $|{\mathbf{J}}|$. Different colored dotted lines represent different energy conversion rates: red ($\sum\nolimits_{0}^{{{\mathbf{|J}}|}} {{\mathbf{J}} \cdot {\mathbf{E}}}$), black ($\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{ \bot } \cdot {\mathbf{E}}_{ \bot } }$), blue ($\sum\nolimits_{0}^{{|{\mathbf{J}}|}} {{\mathbf{J}}_{\parallel } \cdot {\mathbf{E}}_{\parallel } }$), magenta ($\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{e} \cdot {\mathbf{E}}}$), and cyan ($\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{{\mathbf{i}}} \cdot {\mathbf{E}}}$) dotted lines

Figure 13e shows the energy partition between ions ($\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{{\mathbf{i}}} \cdot {\mathbf{E}}}$, where ${\mathbf{J}}_{{\varvec{i}}} = nq{\mathbf{V}}_{{\mathbf{i}}}$, cyan dotted line) and electrons ($\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{{\mathbf{e}}} \cdot {\mathbf{E}}}$, where ${\mathbf{J}}_{{\mathbf{e}}} = - nq{\mathbf{V}}_{{\mathbf{e}}}$ magenta dotted line). When the current density was weak (|J|< 26${\text{nA}} /m^{2}$ ~ 0.9$J_{rms}$, $J_{rms}$ ~ 30 nA/m², is the root mean square value of ${|}{\mathbf{J|}}$), $\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{{\mathbf{i}}} \cdot {\mathbf{E}}}$ rapidly increased, while $\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{{\mathbf{e}}} \cdot {\mathbf{E}}}$ decreased continuously. It indicates that electromagnetic energy was mainly transferred into ions, and the electrons lost their energy transferred into the electromagnetic field. However, when the current density became larger (30${\text{nA}} /m^{2}$ <|J|< 70${\text{nA}} /m^{2}$, 1.0–2.3$J_{rms}$), both $\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{{\mathbf{i}}} \cdot {\mathbf{E}}}$ and $\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{{\mathbf{e}}} \cdot {\mathbf{E}}}$ were enhanced as ${|}{\mathbf{J|}}$ increased. Moreover, $\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{{\mathbf{e}}} \cdot {\mathbf{E}}}$ increased much faster than $\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}}_{{\mathbf{i}}} \cdot {\mathbf{E}}}$, and contributed about 72% to the increase of $\sum\nolimits_{0}^{{\left| {\mathbf{J}} \right|}} {{\mathbf{J}} \cdot {\mathbf{E}}}$. It suggests that the electromagnetic energy was mainly transferred to the electrons (~ 72%) when the current was strong. Overall, the magnetic free energy was primarily released to energize the ions (Fig. 13e). The observations indicate that the released magnetic free energy was primarily converted into the ions in the turbulent reconnection outflow. However, the electron dynamics were crucial also for energy conversion in intense currents and turbulence evolution.

Another work on energy dissipation in turbulent reconnection should be noticed here (Fu et al. 2017). Based on the Cluster observation in the magnetotail, Fu et al. studied the energy dissipation inside the reconnection diffusion region and found that the energy dissipation primarily occurred at the spiral nulls (O-lines) and the separatrices, rather than the intense filamentary currents. Thus, they concluded that the energy dissipation in magnetic reconnection occurs at O-lines but not X-lines. More efforts are needed to finally figure out where and how the magnetic free energy is released during turbulent reconnection.

Based on recent investigation, it seems that the energy conversion becomes intense while the reconnection evolves from the laminar state into the turbulent state. In the turbulent state, the electrons are trapped inside the complex small-scale structures inside the diffusion region and are easily accelerated to high-energy by the non-ideal electric field generated therein. Furthermore, the turbulent magnetic reconnection can be common in the magnetosphere and in the heliosphere.

4 The separatrix region and transient magnetic structures in magnetic reconnection

4.1 The separatrix region of magnetic reconnection

The separatrices are the edges between the reconnecting magnetic field lines and the reconnected field lines during magnetic reconnection (Chang et al. 2022; Divin et al. 2012; Khotyaintsev et al. 2006; Lapenta et al. 2015a; Lu et al. 2010; Norgren et al. 2020; Yu et al. 2019). Thus, they extend very far from the reconnection X-line. Some researchers estimated its length as long as tens of ion inertial lengths (Retinò et al. 2006; Wang et al. 2012). It is very challenging to identify the separatrices by in situ observation. In general, the low-energy electrons are flowing toward the EDR along the separatrices, as the beam-like distribution. Given the separatrices with the inflowing electrons, the outer boundary of the Hall magnetic field is identified as the separatrix region.

A few electrostatic instabilities can be excited in the separatrix region, and thus the electrostatic solitary waves and electrostatic structures are frequently detected (Huang et al. 2021; Nan et al. 2022; Wang, et al. 2013, 2014b; Yu et al. 2021a, 2019), e.g., the electron hole, double layer, low-hybrid drift wave, whistler, electron cyclotron harmonic wave. The electrostatic waves/structures can affect the electron behaviors and cause the complicated physics in the separatrix region. The observations show that the double layer is moving fast, and thus efficiently accelerates the electrons in the separatrix region (Lu et al. 2010; Nan et al. 2022; Wang et al. 2014b). As the electrons experience multiple double layers, they would have already been accelerated to high-energy before they are injected into the EDR. The observations show that the energy of the inflowing electrons can be as high as 100 keV in the separatrix region. Recently, the non-ideal electric field is detected in the separatrix region close to the EDR (Yu et al. 2019). At the same time, the non-gyrotropic electron distribution, intense energy dissipation, and parallel electric field are detected in the separatrix region (Yu, et al. 2019). All these features are consistent with the characteristic of the EDR. It means that the EDR can extend along the separatrices in magnetic reconnection. Therefore, the separatrix region is an important place for the energy conversion during magnetic reconnection.

4.2 Magnetic flux ropes, magnetic islands, and plasmoids

Magnetic flux ropes, magnetic islands, and plasmoids are frequently observed during magnetic reconnection (Chen et al. 2008; Deng and Matsumoto 2001; Wang et al. 2016a, b). Magnetic flux ropes are helical magnetic structures and frequently observed inside the current sheet at the magnetopause (Wang et al. 2019) and in the magnetotail (Slavin et al. 2003a). The typical signature of the flux ropes is a bipolar magnetic field variation in the component normal to the current sheet, with a significant enhancement of the magnetic field component along the current. Magnetic islands have the similar bipolar magnetic field variation, however, without the enhancement of the magnetic field component along the current. The plasmoid represents a mass of plasma with a significant bulk speed in the current sheet and its magnetic structure can be flux rope or island.

The magnetic flux ropes are commonly observed in the planet’s magnetosphere (Zhang et al. 2012; Zhao et al. 2016; Zhong et al. 2018a; Zhong et al. 2020) and heliosphere (Cartwright and Moldwin 2008; Feng et al. 2007; Moldwin et al. 2000; Zhao et al. 2021; Zhao et al. 2018), and widely considered to be generated by magnetic reconnection (Guo et al. 2021; Lu et al. 2022b). In many reconnection events, the flux ropes are even found inside the reconnection diffusion region (Wang et al. 2010a, 2012; Zhong et al. 2018b), further confirms that the flux ropes are the byproduct of magnetic reconnection. Figure 14 presents one event where numerous flux ropes are embedded inside the ion diffusion region (Wang et al. 2016a). As the Cluster spacecraft traversed the plasma sheet (Fig. 14d and f), it detected the ion flow reversal from the tailward ($V_{L} < 0$) to earthward ($V_{L} > 0$) in Fig. 14a and many bipolar $B_{N}$ variations in Fig. 14b. Among these bipolar $B_{N}$ signatures, 19 were identified to be flux ropes. For other bipolar $B_{N}$ variations, they could be flux ropes but were excluded in our study.

Fig. 14

An overview of the reconnection diffusion region observed by the Cluster. a ion bulk flow in the $L$ direction, b–e three components and magnitude of magnetic field, f the electron energy spectrum. The vertical bars in b mark the flux ropes identified

These flux ropes inside the diffusion region were interacting with each other as the Cluster spacecraft passed through it. One coalescence event of a pair of magnetic flux ropes is present in Fig. 15. The two flux ropes were observed one after another. In the data sampled at 0.25/s (Fig. 15a), one cannot get any information on their interaction. If the data in the high-time resolution are used (Fig. 15b–d), the interaction can be easily confirmed. The two black vertical dashed lines denote the centers of two flux ropes and the pink vertical dashed line represents the coalescing current layer. The speed of the two flux ropes is estimated. The second flux rope is much faster than the first one. Thus, the second rope would compress the one ahead of it, leading to a current layer, dubbed coalescing current layer, and a high density in the trailing part of the first flux rope (Fig. 15e). The coalescing current layer is expanded in Figs. 15g–j. The current was strong and its direction was opposite to the current inside the flux rope. The energy dissipation ${\mathbf{J}} \cdot {\mathbf{E}}$ was positive. Therefore, the two flux ropes were coalescing. In the same way, more coalescing events were identified and the coalescing current as well as the electric field were superposed in Fig. 15k and l. Based on these observations, the observed diffusion region was full of magnetic flux ropes and other small-scale magnetic structures and these flux ropes were interacting, which is consistent with the PIC simulation results (e.g., Daughton et al. 2011).

Fig. 15

A coalescing event of a pair of magnetic flux ropes. a $B_{N}$ sampled at 0.25/s, b–d three components of magnetic field sampled at 67/s, e electron number density, f electron energy spectrum, g $B_{N}$ and $B_{L}$, h electron number density, i $E_{y}$, j the current density, k average $E_{y}$ and l average current density $j_{M}$ of all coalescence events

Earlier investigations show that the electrons can be accelerated inside the flux ropes (Drake et al. 2006; Chen et al. 2008; Wang et al. 2010a, c). However, the acceleration mechanism is still unclear. The waves due to the low-hybrid drift instability and whistler wave detected inside the flux ropes could be one potential one (Wang et al. 2016b, 2019, 2020b). The microphysics inside the flux ropes are investigated recently. The high-resolution electron pitch angle distributions observed inside flux ropes imply that the flux ropes can develop into complicated magnetic topologies after they are ejected away from the X-line (Hwang et al. 2016; Pu et al. 2013; Wang et al. 2019). The distribution of electrons inside flux ropes can provide free energy for plasma instabilities and the generation of waves. The whistler waves in multiple bands were first observed inside the flux ropes at the magnetopause (Wang et al. 2019), classified as the lower and upper bands according to the frequency range, as shown in Fig. 16. The lower band whistler waves have a frequency range between 0.1$f_{ce}$ and 0.5$f_{ce}$ (Fig. 16f–j,$f_{ce}$ is the electron gyrofrequency) and propagate in opposite directions, and therefore could be generated locally. The compressed tailing part of the flux ropes is one possible source region, since the electron anisotropy produced by betatron acceleration in the perpendicular direction can be formed therein (Fig. 16b–d). On the contrary, the upper band whistler waves (frequency range between 0.5$f_{ce}$ and 1.0$f_{ce}$) are mainly observed near the center of the flux ropes and all propagate antiparallel to the magnetic field, and therefore originated from the same source region. These upper band whistler waves are closely associated with the depression of the low-energy electron fluxes (0–200 eV) in the parallel direction (Fig. 16b). These observations reveal that flux rope is also a source of the whistler waves except for previously reported reconnection diffusion regions (Burch et al. 2018; Cao et al. 2017) and separatrix regions (Graham et al. 2016; Huang et al. 2016; Yu et al. 2021a, b).

Fig. 16

Whistler waves observed in a flux rope. a Three components and magnitude of the magnetic field in the geocentric solar ecliptic (GSE) coordinates. b Pitch angle spectrogram for 0–200 eV electrons. c Pitch angle spectrogram for 0.2–2 keV electrons. d Electron temperature. e Parallel electric field. f Power spectral density of electric field. g Power spectral density of magnetic field. h Wave angle. i Ellipticity. j Parallel component of the Poynting vector. The white lines superposed on f and g correspond to 1.0, 0.5, and 0.1 electron gyrofrequency

In general, the flux rope consists of a singular compact current layer primarily along the axis and exhibits a force-free field. With the high-time resolution measurements of the plasma moments from the MMS mission, it shows that the singular compact current layer is composed of many filamentary electron currents (Eastwood et al. 2016; Wang et al. 2017a), and the filamentary currents are directed in any direction other than primarily along the flux rope axis. Wang et al. (2020b) further examined the filamentary currents within two flux ropes observed at the magnetopause (Fig. 17a and g). They find direct evidence of reconnection in the filamentary currents (Fig. 17b and h) carried by the electrons (Fig. 17d and j). Specifically, the bi-directional electron outflow jets (Fig. 17c and i), the related Hall electric field (red traces in Fig. 17e and k), and significant energy conversion rate (Fig. 17f and l) are simultaneously observed inside some filamentary currents. Magnetic energy is released inside the flux ropes by these secondary reconnections (Wang et al. 2020b). Considering many flux ropes inside reconnection outflows and thus more filamentary currents, they may play a significant role in energy dissipation during reconnection.

Fig. 17

Direct evidence of reconnection in two filamentary currents within flux ropes. The data are shown in a local current (LMN) coordinate with L = (0.88, − 0.47, − 0.01)_GSE, M = (0.25, 0.50, − 0.83)_GSE, and N = (0.39, 0.73, 0.56)_GSE for filamentary current 1, and L = (− 0.92, 0.05, 0.39)_GSE, M = (− 0.18, 0.82, − 0.55)_GSE, and N = (− 0.35, − 0.57, − 0.74)_GSE for filamentary current 2. a, g Magnetic field B_LMN, with B_M shifted by − 40 nT for filamentary current 1 and − 75 nT for filamentary current 2. b, h The total current density intensity. c, i Electron velocity V_e,LN. d, j Electron velocity V_eM. e, k Perpendicular electric field in the spacecraft frame. The perpendicular electric field means the electric field components are perpendicular to the local magnetic field (f, l) ${\mathbf{J}} \cdot {\mathbf{E}}^{\prime } = {\mathbf{J}} \cdot \left( {{\mathbf{E}} + {\mathbf{V}}_{{\mathbf{e}}} \times {\mathbf{B}}} \right)$

The magnetic flux ropes are frequently observed at the magnetopause and in the magnetotail and are immersed in reconnection outflows. However, in the magnetosheath, the observations of flux ropes are rare compared to the magnetopause and magnetotail due to the absence of a large-scale background current sheet. Wang et al. (2021a) find a series of coherent structures with increased magnetic field magnitude in the magnetosheath (Fig. 18a) (Wang et al. 2021a). These coherent structures (Fig. 18b) are identified as flux ropes based on the magnetic field signals, magnetic curvatures, and the toroidal magnetic field lines. The density is significantly enhanced while the flux ropes are observed (Fig. 18c and g). These flux ropes are embedded inside ion flows (Fig. 18d) and found to be closely associated with intense current density (Fig. 18e and h), energy dissipation (Fig. 18i), and electron heating (Fig. 18a) in the turbulent magnetosheath.

Fig. 18

Flux ropes and associated current layers observed in the magnetosheath. a Electron energy–time spectrogram of differential energy fluxes (color scale, in units of keV cm⁻² s⁻¹ sr⁻¹ keV⁻¹). b Three components and magnitude of the magnetic field. c Electron number density. d Ion velocity. e Current density. f–i Enlarged view of observations: f Three components and magnitude of the magnetic field, g electron number density, h total (black trace) and electron (magenta trace) current density, i ${\mathbf{J}} \cdot {\mathbf{E}}^{\prime } = {\mathbf{J}} \cdot \left( {{\mathbf{E}} + {\mathbf{V}}_{{\mathbf{e}}} \times {\mathbf{B}}} \right)$. All the data are shown in the geocentric solar ecliptic (GSE) coordinates. The vertical cyan dashed lines mark the magnetic field maximum in five magnetic peaks

Figure 19 shows the observation of an extremely thin electron current layer observed in the magnetosheath (Wang et al. 2021a). Inside this current layer (shaded region in Fig. 19), $B_{L}$ presents a sharp rotation from positive to negative, accompanied by a significant decrease of $B_{M}$ and a positive enhancement of $B_{N}$ (Fig. 19b). Magnetic field and plasma density (Fig. 19c) both exhibit asymmetries on two sides of the current layer, like magnetopause reconnection. Near the center of the current layer, the MMS observed fast electron outflows $V_{eL}$ and out-of-plane electron flows $V_{eM}$ (Fig. 19d). Across the current layer, the perpendicular electric field presents a bipolar variation with a larger amplitude on the side with larger $|{\mathbf{B}}|$ (Fig. 19f). Simultaneously, a unipolar parallel electric field reaching ∼ − 20 mV/m is observed during the whole crossing of the current layer (Fig. 19g), implying that the parallel electric field is widely distributed therein. ${\mathbf{J}} \cdot {\mathbf{E}}^{\prime }$, where ${\mathbf{E}}^{\prime } = {\mathbf{E}} + {\mathbf{V}}_{{\mathbf{e}}} \times {\mathbf{B}}$, is positive inside the current layer (Fig. 19h). This suggests that magnetic energy is converted into plasma energy. Both the parallel and perpendicular components have an important role in energy dissipation. All these signatures indicate that the current layer is identified as an electron diffusion region. The strong electron pressure anisotropy in the exhaust suggests that the current inside the electron diffusion region could be generated by the firehose instability (Fig. 19j) (Le et al. 2013). The observations show that the large-amplitude parallel electric field can fill the entire electron diffusion region in the magnetosheath reconnection, and thus dominates electron dynamics therein (Wang et al. 2021b). This is dramatically different from electron diffusion regions in the magnetotail and magnetopause where the large-amplitude unipolar parallel electric field is rarely detected. The condition for the generation of this kind of strong parallel electric field in the magnetosheath remains an issue. Most recently, the strong parallel electric field is simulated at the extended current layer which is embedded in the exhaust of reconnection with a moderate guide field (Wetherton et al. 2022). It is generated by the strong gradient in the parallel electron pressure which is caused by a transition between magnetized electrons with the parallel temperature larger than the perpendicular temperature on one side of the extended current layer and demagnetized electrons nearly isotropic across the current layer (Wetherton et al. 2022).

Fig. 19

A reconnecting current sheet observed in the magnetosheath. a Electron energy–time spectrogram (color scale, in units of keV cm⁻² s⁻¹ sr⁻¹ keV⁻¹). b Magnetic field. c Electron number density. d Electron velocity. e Current density and its parallel and perpendicular components. f Perpendicular electric field. g Parallel electric field. h ${\mathbf{J}} \cdot {\mathbf{E}}^{\prime } = {\mathbf{J}} \cdot \left( {{\mathbf{E}} + {\mathbf{V}}_{{\mathbf{e}}} \times {\mathbf{B}}} \right)$ and its parallel and perpendicular components. i Electron temperature. j Firehose instability parameter $\mu_{0} \left( {p_{||} - p_{ \bot } } \right)/B^{2}$. The shaded region represents the electron diffusion region

4.3 Dipolarization fronts

Another kind of transient magnetic structure associated with the magnetotail magnetic reconnection is the so-called dipolarization front (DF) (Nakamura et al. 2002; Runov et al. 2009; Sergeev et al. 2009; Wang et al. 2014a). In general, the dipolarization front is embedded within the high-speed ion bulk flows and characterized by a sharp increase of the normal magnetic field ($B_{z}$) and preceded by a much smaller negative dip of $B_{z}$(Deng et al. 2010; Runov, et al. 2009; Zhou et al. 2009). The DFs are extensively explored by the Cluster, THEMIS, and MMS observations. They show a relative stable structure for at least several minutes and energize ions and electrons as propagating earthward (Fu et al. 2011, 2012a; b; Wu et al. 2013). They might be related to magnetospheric substorm and the substorm ground as well as space magnetic signatures.

Dipolarization fronts were first proposed based on spacecraft observations, but it is still unclear what dipolarization front essentially is. The conventional scenario is that a dipolarizing flux bundle (DFB) is formed by single X-line reconnection and connect directly to the geomagnetic field (Liu et al. 2013a, b). The DFB propagates earthward, which can be well described by plasma bubble model (Chen and Wolf 1993, 1999; Pontius and Wolf 1990; Yang et al. 2019). More recently, THEMIS observations (Vogiatzis et al. 2015) and 3D global hybrid simulations (Lu et al. 2015a) suggest an alternative scenario: DFs are highly evolved, earthward propagating flux ropes formed and bracketed by two reconnection X-lines (Lu et al. 2015b; Slavin et al. 2003a). Figure 20 shows the global hybrid simulation result of this DF scenario. This new scenario of depleted flux rope describing DFs has been verified by recent MMS observations (Man et al. 2018; Poh et al. 2018).

Fig. 20

3D global hybrid simulation showing the structure of a flux-rope-type dipolarization front adopted from Lu et al. (2015a). a Typical magnetic field lines of the DF and contour of ${B}_{z}$ in the −10° meridian plane. The red and blue dots denote two virtual satellite located at $\left(X,Y,Z\right)=\left(-\mathrm{12,2},0\right) {R}_{E}$ and $\left(-\mathrm{12,2},0.25\right) {R}_{E}$, respectively. b, c Virtual satellite observations of the magnetic field ${B}_{z}$ versus time at these two locations

Because these two scenarios of DFs have different geometries and structures, the particle acceleration by DFs is consequently different in the two scenarios. Particle-in-cell (PIC) simulations have been performed to investigate particle acceleration by these two types of DFs: flux-bundle type (FB-type) and flux-rope type (FR-type).

Electrons are lighter than ions, so they are usually magnetized and their acceleration is usually adiabatic. Figure 21 shows the result of a PIC simulation (Huang et al. 2015b). As shown by the magnetic field lines (white curves), a DF formed by single X-line reconnection is located at $\sim 131c/{\omega }_{pi}$. Therefore, this DF is an FB-type DF. This figure also shows that electrons are accelerated by the FB-type DF with a peak energy flux right at the front with ${B}_{z}$ peak. By analyzing their representative trajectories, these energetic electrons are found to be accelerated through a betatron mechanism which is summarized as follow. The electrons are magnetized to the earthward moving DF, with the increase of the magnetic field ${B}_{z}$, the electrons are accelerated through the conservation of the first adiabatic invariant.

Fig. 21

Particle-in-cell simulation result adopted from Huang et al. (2015b). Energy flux of energetic electrons with energy higher than $0.1{m}_{e}{c}^{2}$

Electron acceleration in FB-type DF has also been studied using PIC simulations (Lu et al. 2016a). Because FB-type DF has an eroded flux rope at the center of the DF region (e.g., see Fig. 1a), this flux rope is playing an important role in particle acceleration. Most of the energetic electrons are confined to the center of the flux rope. These confined electrons are accelerated through multiple reflections between the two ends of the flux rope, which is a Fermi-like process. Ions can also be accelerated by (FR-type) DFs according to global hybrid simulations and PIC simulations. For example, the hybrid simulations show that the high-energy part of the ion energy spectra increases more than ten times after passage of several (FR-type) DFs (Lu et al. 2015a). PIC simulations further show that the energetic ions, similar to the energetic electrons, are confined to the center of the flux rope and accelerated through the Fermi-like process (Lu et al. 2016a).

As for the FB-type DF, according to the PIC simulation results, most of the energetic ions are located ahead of the DF. These ions are reflected by the earthward propagating DF and accelerated during the reflection: the ion ahead of the DF moves into the front region (with strong ${B}_{z}$) and gyrates for about half an orbit in the magnetic field ${B}_{z}$, during which the ion is accelerated in the y direction by the electric field ${E}_{y}\approx {V}_{x}{B}_{z}$. After the half-orbit gyration, the accelerated ion leaves the DF with a larger velocity. These accelerated ions through reflection contribute to the precursor ion flow ahead of DFs (Zhou et al. 2010, 2011).

Particle acceleration around the DF is controlled by the DF’s configuration such as magnetic field and electric field structures, current system, etc. (Wu et al. 2013). On the other hand, the accelerated particles also have feedback effects on the DF configuration. To study this self-consistent process with theory or simulation, one needs to consider particle kinetics in advancement of electric and magnetic fields. This underlines the importance of kinetic simulations (hybrid simulation, PIC simulation) in the study of particle acceleration around DFs. For example, THEMIS observations show that the cross-tail current density ${j}_{y}$ reduces significantly ahead of DFs. Lu et al. (2016b) performed PIC simulations and explained this current density reduction which is summarized as follows: ions reflected and accelerated by the DFs cause positive charge density buildup ahead of the DFs (Lu et al. 2016b). This positive charge density generates an electrostatic field ${E}_{z}$ and a duskward electron ${E}_{z}\times {B}_{x}$ drift, significantly reducing the cross-tail current density ${j}_{y}$ ahead of the front.

5 Perspectives

In situ spacecraft measurement in the near-Earth space is very important for studying collision-less magnetic reconnection. In the twentieth century, single spacecraft was generally launched to study the plasma processes in space, including the process of magnetic reconnection. Single satellite measurement cannot distinguish the temporal and spatial variation in space. Thus, multiple spacecraft mission is proposed and launched in this century, e.g., the Cluster mission, the Themis mission, and the MMS mission. Both the Cluster and MMS missions consist of four satellites with identical instruments, and are designed to investigate the plasma processes at the ion scale and the electron scale, respectively. Thanks to these two missions, the microphysics inside the reconnection ion and electron diffusion regions have been explored extensively. However, it is still unclear that how the ion and electron diffusion region evolve during magnetic reconnection. For example, when and how the laminar electron diffusion region transitions to turbulent electron diffusion region. During this transition, it is still poorly understood how the electron kinetics evolves from the laminar to the turbulent state. It is very challenging to study the evolution of magnetic reconnection by in situ spacecraft. The soft X-ray imaging of the reconnection region is one potential method to explore their evolution. The Solar wind-Magnetosphere-Ionosphere Link Explorer (SMILE) which will be equipped with a wide-field-of-view Soft X-ray Imager (SXI) and launched in late 2024 or early 2025 is designed to remotely detect magnetopause boundary (Branduardi-Raymont et al. 2016; Wang et al. 2017a, b, c; Wang and Branduardi-Raymont 2018), and can be a good chance to resolve the evolution issue at the magnetopause.

The cross-scale coupling is another issue on magnetic reconnection. It is well known that magnetic reconnection occurs in a localized region but can affect a large volume in space. Magnetic reconnection in the near-Earth magnetotail has been widely accepted to be the main driver of magnetospheric substorm. The Themis mission has addressed the temporal evolution of reconnection onset and the subsequent geomagnetic activity and the aurora, with five satellites locating in different places along the Sun–Earth direction. However, the coupling between the physics at the kinetic scale and the activities at the large scale or global scale is still open. A new mission AME (self-Adaptive Magnetic reconnection Explorer) is proposed to assess the role of magnetic reconnection in the context of space weather and to resolve the cross-scale coupling ranging from kinetic scale to macro scale (Dai et al. 2020). The AME mission consists of a cross-scale constellation of 12 + CubeSats and one mother satellite. Each CubeSat is equipped with magnetic field and plasma measurements to fulfill the purpose.