Investigation of a Magnetic Reconnection Event with Extraordinarily High Particle Energization in Magnetotail Turbulence

Magnetic reconnection and plasma turbulence are ubiquitous and key processes in the Universe. These two processes are suggested to be intrinsically related: magnetic reconnection can develop turbulence, and, in turn, turbulence can influence or excite magnetic reconnection. In this study, we report a rare and unique electron diffusion region (EDR) observed by the Magnetospheric Multiscale mission in the Earth’s magnetotail with significantly enhanced energetic particle fluxes. The EDR is in a region of strong turbulence within which the plasma density is dramatically depleted. We present three salient features. (1) Despite the turbulence, the EDR behaves nearly the same as that in 2D quasi-planar reconnection; the observations suggest that magnetic reconnection continues for several minutes. (2) The observed reconnection electric field and inferred energy transport are exceptionally large. However, the aspect ratio of the EDR (one definition of reconnection rate) is fairly typical. Instead, extraordinarily large-amplitude Hall electric fields appear to enable the strong energy transport. (3) We hypothesize that the high-energy transport rate, density depletion, and the strong particle acceleration are related to a near-runaway effect, which is due to the combination of low-plasma-density inflow (from lobes) and possible positive feedback between turbulence and reconnection. The detailed study on this EDR gives insight into the interplay between reconnection and turbulence, and the possible near-runaway effect, which may play an important role in other particle acceleration in astrophysical plasma.


Background
Magnetic reconnection is a fundamental and energetically important plasma process in a wide range of astrophysical and laboratory environments.It has been observed and studied in the solar corona (Smartt et al. 1993;Xue et al. 2016;Dahlin et al. 2019), solar wind (Gosling et al. 2005;Phan et al. 2020;Wang et al. 2023), Earth's and planetary magnetospheres (Burch et al. 2016;Guo et al. 2018;Phan et al. 2018;Torbert et al. 2018;Zhong et al. 2020;Ebert et al. 2022;Ergun et al. 2022;Montgomery et al. 2022), and laboratory plasmas (Yamada et al. 1990;Ji et al. 1998).Magnetic reconnection acts across multiple scales and enables energy conversion between fields and particles while modifying the magnetic field topology.The complex nature of magnetic reconnection makes it challenging to fully understand how it facilitates explosive plasma energization and how it interacts with turbulence.
Turbulence is a key process that governs energy flow across scales that ultimately dissipates.Two of the energy sources for turbulence are known to be (1) magnetic field annihilation enabled by magnetic reconnection (Drake et al. 2006;Eastwood et al. 2009;Price et al. 2017) and (2) braking of a plasma flow, for example, at a shock front (Fredricks et al. 1968;Scarf et al. 1981;Blandford & Eichler 1987).Turbulence driven by magnetic reconnection can occupy a much larger volume than the diffusion regions (Ergun et al. 2020a).Moreover, a number of studies suggest that magnetic reconnection and turbulence are intrinsically related, and that turbulence may increase the magnetic reconnection rate (Che 2017;Shi et al. 2019).
Earth's magnetotail is ideal for studying magnetic reconnection and turbulence (Rogers et al. 2019;Hubbert et al. 2022;Rogers et al. 2023).The cross-tail current sheet provides a large enough volume for these processes to develop and interact.Magnetic reconnection in the magnetotail is characterized by Alfvénic plasma outflow jets (Gosling et al. 2005;Cassak & Shay 2007, 2008), magnetic flux transport (Li et al. 2021a;Qi et al. 2022;Li et al. 2023) showing a change in magnetic connectivity, Hall fields indicating a decoupling of ions and electrons (Graham et al. 2016;Lu et al. 2019;Genestreti et al. 2020;Liu et al. 2022), and at its center, the electron diffusion region (EDR), enhanced energy conversion , J is the current density, V e is the electron flow velocity, E is the electric field, and B is the magnetic field (Hubbert et al. 2021;Genestreti et al. 2022).
To date, there have been only a handful of EDR encounters in the magnetotail (Torbert et al. 2018;Chen et al. 2019;Zhou et al. 2019;Lu et al. 2020b;Li et al. 2021b;Farrugia et al. 2021;Ergun et al. 2022;Pathak et al. 2022).While many such events are associated with wave activity, a subset of events appears to break into strong turbulence with intense electric field (δE) fluctuations, a deep density depletion, and accelerated (>100 keV) ions and electrons (Ergun et al. 2022).These events appear to have near-runaway behavior (Ergun et al. 2020a(Ergun et al. , 2020b)).Initially, the reconnection jets deplete the plasma sheet density, which is not fully replenished by inflow from the low-density lobes.As a result, particles each receive more of the dissipated magnetic energy (on average), leading to yet lower density.In some cases, turbulence breaks out and appears to be associated with a deeper density depletion while magnetic reconnection continues.We show Magnetospheric Multiscale (MMS) observations that may support this scenario.
In this Letter, we report an EDR in strong turbulence in a deep density depletion (∼90% from the surrounding region).The EDR is qualitatively similar to that of quasi-2D, laminar reconnection supporting Ergun et al. (2022).The EDR displays an extraordinarily large reconnection electric field (∼4 to ∼5 mV m −1 , twice that previously reported), insinuating high energy transport into the EDR via Poynting flux ( ) ).Interestingly, the aspect ratio of the EDR, a measure of reconnection rate, is roughly 0.2, which is a near-nominal value.We suggest that a large-amplitude Hall electric field (∼200 mV m −1 , 4-10 times that previously reported) and correspondingly intense particle energization may regulate energy transport out of the EDR.These observations may give us insight into what seems to be nearrunaway particle energization.This study uses data from the MMS mission, which consists of four closely spaced spacecraft.The instruments that provide the data include the fluxgate magnetometer (Russell et al. 2016), the double-probe electric field instrument (Ergun et al. 2016;Lindqvist et al. 2016;Torbert et al. 2016), and the fast plasma instrument (FPI; Pollock et al. 2016), and the Fly's Eye Energetic Particle Spectrometer (FEEPS; Blake et al. 2016).

Observation
On 2019 September 6, MMS encounters a region in the Earth's magnetotail with active magnetic reconnection, strong turbulence, and intense ion acceleration (Figure 1).At the beginning of Figure 1 (04:10 UT), the tailward ion flow velocity (V i , Figure 1(h), blue trace) reaches ∼−700 km s −1 , which is a significant fraction of the local Alfvén speed and plasma density n ∼ 0.028 cm −3 .We use electron density, as it is more reliable than that derived from ion distributions, which can be affected by penetrating radiation; see Torbert et al. 2018 andGershman et al. 2019).After the first encounter with fast ion flow, MMS observes several more tailward (negative blue trace) ion jets.The excursions of V i back to near-zero velocity when |B| is high (e.g., at ∼04:20:00 UT; |B| is in Figure 1(a), black trace) are likely due to MMS leaving the plasma sheet (the jet) and approaching the lobe.There are three ion jet reversals (Figure 1(h), negative-to-positive excursions in the blue trace) marked by vertical lines at ∼04:31:30 UT, ∼04:39:00 UT, and at ∼04:45:30 UT, indicating possible magnetic reconnection sites.
We focus on the second ion jet reversal.MMS, located at [−21.9, 6.4, 1.6] Earth radii (R E ) in geocentric solar ecliptic (GSE) coordinates, is surrounded by strong turbulence evidenced by fluctuations in B and E (Figures 1(a) and (b)).
Figure 2 shows the spectra of B and E that indicate developing turbulence.The B spectrum has a shallow index (−1.25) in the inertial region that breaks near the ion cyclotron frequency ( f ci ) to −2.74.The E spectrum has a shallow index just above f ci , which is similar to previous observations (Ergun et al. 2015(Ergun et al. , 2022)).
In the same region, the density becomes extremely low (Figure 1(c)) while both electrons and ions are intensely energized (Figures 1(d)-(g)).We hypothesize that the turbulence is triggered by active magnetic reconnection (Franci et al. 2017;Kowal et al. 2017;Ergun et al. 2020a;Lu et al. 2020a;Ergun et al. 2022).Interestingly, the reconnection site at the center of the turbulence is not short-lived; instead, the ion jets exiting the reconnection site are seen for several minutes (hundreds of ion gyroperiods) and, as we show later, the reconnection itself seems to be boosted.
Figure 3 highlights a shorter interval centered around an EDR marked as "V i reversal 2" in Figure 1 featuring the thin current sheet crossing, high-speed electron jets, increased positive energy conversion ( ¢ J E • ), and large E N .The components are plotted in a local LMN coordinate system, where L is along the annihilating B, N is perpendicular to the current sheet, and M = N × L. This EDR encounter offers a rare opportunity to study magnetic reconnection embedded in strong turbulence.
Turbulence, however, adds difficulty in establishing the LMN system, which is vital for determining EDR characteristics.Here, we follow a process outlined in Qi et al. (2023).The N direction is derived from the maximum variance of E and from the maximum directional derivative of B and E. N is derived repeatedly using low-pass filters of 1, 2, and 4 Hz, employing time periods centered on the EDR (∼04:38:58.5) of 2, 4, and 8 s, and isolating the most active components of B and E. The 36 derived values are in good agreement with a standard deviation of less than 5°.L, initially derived from the maximum variance in B, is forced to be orthogonal to N (a 10°correction) since N is robustly derived.L is further rotated about the N (1°.5)axis so that the guide field ( B M ) has nearly identical values on the four MMS spacecraft as they cross the current sheet.We arrive at L = [0.999,−0.017, −0.031], M = [0.026,0.953, 0.301], and N = [0.005,−0.301, 0.953] in GSE.
The reconnecting magnetic component (B L ) is initially positive at about 10 nT (red trace in Figure 3(a)) and then reverses sign to −7 nT.At the same time, the M component (B M ) exhibits a quadrupolar Hall magnetic field pattern (green trace in Figure 3(a)) with a guide field of ∼0.8 nT.The flapping motion of the magnetotail current sheet causes periodic fluctuations of B L after 04:39.Before and after the current sheet where B L reverses, an extremely high-amplitude E appears (Figure 3(b)) with the normal component, E N , dominating.E N is consistent with the Hall electric field.The peak value of ∼200 mV m −1 is over 5 times that reported in previous magnetotail EDRs (Torbert et al. 2018;Chen et al. 2019;Li et al. 2021b;Farrugia et al. 2021).
The largest component of the electron velocity is along M (Figure 3(d), green trace) and is consistent with an electrondominated current in the EDR (Figure 3(e)).The electron flow velocity peaks at ∼2.6 × 10 4 km s −1 , which is roughly the electron thermal speed of 2.4 × 10 4 km s −1 (Te ∼3.3 keV) suggesting a near-Buneman limit to the electron current (Buneman 1958).The L component of electron velocity V e,L (red trace) has a negative-to-positive reversal slightly before the B L reversal.After switching to positive, the V e,L remains positive for a few more seconds until ∼04:39:04 UT.The negative V e,L excursion is likely an unusually high flow entering the EDR as part of the Hall current.• .The overall energy conversion (black trace) is positive at the EDR and dominated by the perpendicular contribution (blue trace) indicating the conversion of electromagnetic energy into plasma kinetic energy, which is expected.The parallel contribution (red trace) stands out at the negative V e,L inflow into the x-line.The peak value of ¢ J E • exceeds 3 nW m −3 .This value translates to ¢ J E n • ∼700 keV s −1 per electronproton pair, which is a remarkably rapid energy conversion rate compared to that reported in other magnetotail EDRs, where ¢ J E • ∼ 0.2-0.6 nW m −3 and n is similar or larger.Figure 4 shows B L , B M , E N , and V e along the spacecraft trajectories in the L − N plane.The position of MMS1 in N is derived from Ampere's law.Starting from J M ∼ ∂B L /∂N − ∂B N /∂L, ΔN can be written as Pathak et al. 2022 andQi et al. 2023 for details).B N (Figure 3(a)) has a small and nearly constant slope suggesting a smooth progression in L so ∂B N /∂L is a small correction.N is set to zero where MMS1 B L reverses (Figure 4(a)).L is set to zero at the location where the Hall magnetic fields change sign from negative to positive (B M with guide field subtracted; Figure 4(b)).We assume a constant L velocity of 200 km s −1 (Torbert et al. 2018;Ergun et al. 2022).The MMS2, MMS3, and MMS4 are known (fixed) relative to MMS1.
As shown in Figure 4, even though this EDR is embedded in turbulence, its characteristics are similar to those in quasiplanar, 2D reconnection.In panel (a), all four spacecraft observe the first B L reversal at N = 0 as expected when crossing the current sheet.Later, due to the flapping motion of the current sheet, MMS again crosses the current sheet and B L again reverses near N = 0.This consistency supports our choice

Discussion
To better understand the observed high-energy particle flux enhancements (Figures 1(d)-( ).However, isolating E M is challenging due to the high-amplitude E N (blue trace, Figure 3(b)) and turbulent fluctuations.Following the methods discussed by Genestreti et al. (2018) and Ergun et al. (2022), the average E M is calculated from each MMS spacecraft using time intervals from 8 to 256 s in factors of 2 surrounding the EDR.This method varies LMN to eliminate E M -E N and E M -B L correlations.E M , estimated over an 8 s interval, is ∼4.1 mV m −1 (standard deviation of 1.3 mV m −1 ).The 256 s interval yields ∼5.0 mV m −1 ± 2.4 mV m −1 .These values are about a factor of 2 higher than previously observed (Genestreti et al. 2018;Ergun et al. 2022), supporting rapid energy conversion and the high velocity of the electron jets (Figure 3(d), red trace and Figure 4(d)), which reach 10 4 km s −1 .Following the equation (Hesse et al. 1999): with DV L =10 4 km s −1 , ΔL = 150 km (Figure 4), and T e = 3.3 keV (measured), E M is predicted to be ∼6.3 mV m −1 , supporting the estimation.
The large E M suggests unusually high energy flow (Poynting flux S) into the EDR.In the magnetotail, magnetic energy stored in the lobe supplies the energy (Poynting flux) for reconnection in the plasma sheet.The lobes have sufficient stored energy to support reconnection for many tens of minutes.For the EDR we are reporting here, at N=125 km, B L =7 nT, the energy flowing into the reconnecting current sheet from north and south, á ñ One possibility to explain the large energy flow is by a high reconnection rate (commonly defined as inflow speed divided by the Alfvén speed).For a reconnection rate local to the EDR, the best approach is to estimate the aspect ratio of the diffusion region by the gradient of the magnetic field following the equation (Hesse et al. 2009;Heuer et al. 2022): Interestingly, the aspect ratio at the x-line is about 0.  reconnection rate (opening angle) alone seemingly does not explain the high energy conversion or magnetic flux transport, which suggests a different mechanism is at play.In a quasi-steady state EDR, S in is balanced by a combination of energy conversion in the EDR (J • E) and Poynting flux leaving the EDR (S out ≈ −E N B M /μ 0 ).J • E has high positive peak values but strong fluctuations.The standard deviation of J • E exceeds the average value when MMS is in the EDR, so it is unclear if J • E is sufficient to balance S in .On the other hand, observations suggest that the contribution from S out can be significant.The measured S out (versus N) is displayed in Figure 5 .This crude estimate suggests that a substantial fraction of S entering the EDR by the ±N faces appears to exit the ±L faces.The high-amplitude E N , which supports S out , may be a regulator allowing the EDR to remain at a normal aspect ratio while supporting rapid magnetic flux annihilation and energy transport.
The observations open several questions on the interplay between reconnection and turbulence, and the role of the density depletion.(Ergun et al. 2020a(Ergun et al. , 2020b)).Before reconnection onset, the plasma pressure in the plasma sheet balances the magnetic pressure in the lobes.MMS briefly visited the lobes several times before and after the EDR (e.g., Figure 1(d) at ∼04:42:00 marked on the plot) measuring plasma density between 0.01 and 0.02 cm −3 .After reconnection onset, the plasma density near the x-line depletes because, as mentioned earlier, inflow from the lobes does not necessarily replenish the plasma at the same rate that the ion jets expel it.As reconnection continues, the same amount of magnetic energy enters the region with fewer particles to absorb the energy.On average, each particle must absorb more energy leading to further density depletion, which, in turn, causes higher particle energization.This process is more likely to occur when the density in the lobe is low, as observed here.
The role of turbulence is less clear.One hypothesis is that if particles cannot receive the energy with a laminar process, turbulence breaks out, which may further energize particles, lower the plasma density, and enable the positive feedback (Ergun et al. 2020a).The specific plasma modes, for example, the tearing mode (e.g., Bhattacharjee et al. 2009) or drift waves including lower-hybrid drift instability (e.g., Daughton et al. 2004), cannot yet be identified with such few events.This second step of the hypothesized, near-runaway energization is an outcome of the initial energization enabled by the low lobe density.Whether turbulence is a necessary addition to the positive feedback needs further investigation.However, we note this near-runaway effect may be further amplified if the magnetic field annihilation rate increases in a low-density region as suggested by the observations.Reconnection processes in the L-N plane in this event are intensified but remain similar to those occurring in 2D reconnection.The ion jets suggest that the reconnection endures for several minutes, despite the turbulence.However, the 3D aspect of reconnection needs to be explored.The extension of the x-line is finite (Li et al. 2023).In the event reported here, we cannot determine how far the rapid energy conversion rate extends along the x-line due to the small spacecraft separation.The x-line extent in the Earth's magnetotail is estimated to be between 2 and 3 R E (Nakamura et al. 2004), but the large S in may be localized.If highly localized, the magnetic field annihilation rate may strongly vary along the x-line, creating a 3D inflow pattern, and causing patchy magnetic reconnection.It is also unclear if the intense particle energization affects the growth or extent of the x-line.

Summary
In summary, this study details an Earth's magnetotail EDR crossing within a region of strong turbulence.The ion outflow jets suggest ongoing magnetic reconnection lasting for minutes.Colocated with turbulence and reconnection, energetic ion and electron fluxes increase while plasma density decreases significantly.This particle energization and density depletion are accompanied by high Hall and reconnection electric fields, as well as rapid energy conversion.This intense energization and density depletion seem due to a low lobe plasma density and possibly amplified by the interaction between reconnection and turbulence to a near-runaway effect, rather than a fast reconnection rate.
This EDR crossing event offers us an opportunity to explore the connection between reconnection and turbulence at small scales through in situ observations, raising questions about how these plasma processes interact.This interaction is expected not only in Earth's magnetotail but universally, wherever plasma turbulence and magnetic reconnection occur, such as in the solar corona, solar wind, planetary magnetospheres, supernova remnants, and other astrophysical plasmas.

Figure 1 .
Figure 1.The context of the EDR crossing event on 2019 September 6.(a) and (b) Magnetic and electric field components in GSE coordinates.(c) Electron density.(d) Omnidirectional electron flux from 60 to 500 keV.(e) Differential electron energy flux from 6 eV to 25 keV.(f) Omnidirectional ion flux from 70 to 600 keV.(g) Differential ion energy flux from 3 eV to 25 keV.(h) Ion flow velocity in GSE.(i) A schematic of the earth's magnetotail and an approximate MMS trajectory.The L direction is close to GSE x-direction, N is close to GSE z, and the M is close to the GSE y.

Figure
Figure 3(f) displays the energy conversion rate ¢ J E• .The overall energy conversion (black trace) is positive at the EDR and dominated by the perpendicular contribution (blue trace) indicating the conversion of electromagnetic energy into plasma kinetic energy, which is expected.The parallel contribution (red trace) stands out at the negative V e,L inflow into the x-line.The peak value of ¢ J E• exceeds 3 nW m −3 .This value translates to ¢ J E n • ∼700 keV s −1 per electronproton pair, which is a remarkably rapid energy conversion rate compared to that reported in other magnetotail EDRs, where ¢ J E • ∼ 0.2-0.6 nW m −3 and n is similar or larger.Figure4shows B L , B M , E N , and V e along the spacecraft trajectories in the L − N plane.The position of MMS1 in N is derived from Ampere's law.Starting from J M ∼ ∂B L /∂N − ∂B N /∂L, ΔN can be written as D ~D of LMN coordinates and the calculation of N locations.Panel (b) shows B M − B g .The quadrupolar variations reveal the Hall magnetic field.Near the upper and lower edges of the current sheet, the E N designates a strong Hall electric field (panel (c)).In panel (d), we plot the MMS3 electron velocity vectors projected in the L − N plane along the MMS trajectory with a schematic background showing the regions of reconnection.Above the x-line, the long, thick, deep blue arrows are a sign of the fast electron inflow mentioned earlier.To the right of the xline at the center of the current sheet, the long, thick, deep red arrows demonstrate the electron outflow jet.

Figure 2 .
Figure 2. The B and E power spectral density.

3.
The EDR crossing by MMS3.(a) and (b) B and E in LMN.(c) Electron density.(d) V e in LMN.(e) Current density in LMN.(f) The energy conversion rate, ¢ J E• .The yellow shadow marks the EDR region.

Figure 4 .
Figure 4. (a)-(c) The measured B L , B M , and E N over the estimated path across the EDR.The gold area represents the EDR.(d) V e,LN , the measured electron flow velocity projected in the L-N plane.The arrowʼs color and length indicate the speed and direction.The arrows around the peak speed are set to be thicker to highlight the jet.The purple line is the estimated path.And the background is a cartoon of an ideal reconnection region with the magnetic field lines (gray lines with arrows), EDR (gold area), positive (blue area), and negative (green) Hall magnetic field regions.