Enhanced Energy Conversion by Turbulence in Collisionless Magnetic Reconnection

Magnetic reconnection and turbulence are two of the most significant mechanisms for energy dissipation in collisionless plasma. The role of turbulence in magnetic reconnection poses an outstanding problem in astrophysics and plasma physics. It is still unclear whether turbulence can modify the reconnection process by enhancing the reconnection rate or energy conversion rate. In this study, utilizing unprecedented high-resolution data obtained from the Magnetospheric Multiscale spacecraft, we provide direct evidence that turbulence plays a vital role in promoting energy conversion during reconnection. We reached this conclusion by comparing magnetotail reconnection events with similar inflow Alfvén speed and plasma β but varying amplitudes of turbulence. The disparity in energy conversion was attributed to the strength of turbulence. Stronger turbulence generates more coherent structures with smaller spatial scales, which are pivotal contributors to energy conversion during reconnection. However, we find that turbulence has negligible impact on particle heating, but it does affect the ion bulk kinetic energy in these two events. These findings significantly advance our understanding of the relationship between turbulence and reconnection in astrophysical plasmas.


Introduction
Magnetic reconnection is a prevalent process for releasing energy in various explosive spaces and astrophysical phenomena.Magnetic energy is rapidly converted into plasma kinetic and thermal energy during reconnection (Parker 1957;Sonnerup 1984;Schindler et al. 1988;Zhou et al. 2019).Reconnection is not limited to large-scale current sheets, such as the Earth's magnetotail neutral sheet and magnetopause current sheet, but also occurs in small-scale current sheets resulted from chaotic magnetic field lines in turbulence, which is a multiscale energy cascade process that regulates the transfer of energy, mass, and momentum (Retinò et al. 2007;Sahraoui et al. 2010;He et al. 2019;Phan et al. 2018;Xu et al. 2023).Turbulence plays a crucial role in controlling energy dissipation in plasma.
Reconnection and turbulence are intimately correlated, and their interplay/coupling has been the subject of extensive research in recent decades.Reconnection has been discovered in turbulent bow shock and highly turbulent magnetosheath downstream of the bow shock and solar wind, as reported in various studies (Retinò et al. 2007;Yordanova et al. 2016;Vörös et al. 2017;Phan et al. 2018;Wang et al. 2023;Zhong et al. 2022).On the other hand, reconnection also drives turbulence, leading to turbulent reconnection as observed in the Earth's magnetosphere (Eastwood et al. 2009;Huang et al. 2012;Osman et al. 2015;Fu et al. 2017;Zhong et al. 2018;Zhou et al. 2021;Li et al. 2022).One well-known mechanism for generating turbulence in reconnection is the repeated formation of kinetic-scale magnetic flux ropes in filamentary currents and their interactions (Che et al. 2011;Daughton et al. 2011;Wang et al. 2016Wang et al. , 2023)).In turbulent reconnection, magnetic field lines are entangled and induce considerable variations in the out-of-plane direction, in contrast with laminar reconnection, where the reconnection layer is structured and quasi-2D.A large number of energetic particles is produced in turbulent reconnection (Ergun et al. 2018(Ergun et al. , 2020a(Ergun et al. , 2020b)).Recent studies have highlighted that secondary reconnection is formed in the turbulent outflow, contributing substantially to the overall energy release (Lapenta et al. 2015;Zhou et al. 2021;Yi et al. 2023).
The role of turbulence in reconnection is an important scientific question in plasma physics and astrophysics.Lazarian & Vishniac (1999) proposed a turbulent reconnection model (known as the LV99 model) to explain fast reconnection in presence of turbulence.They suggest that wandering field lines could open the exhaust angle, leading to fast reconnection (Matthaeus & Lamkin 1986;Lazarian & Vishniac 1999;Vishniac et al. 2012;Lazarian et al. 2020).Recent magnetohydrodynamic (MHD) simulations show that external forces driving turbulence facilitate the conversion of magnetic energy into plasma kinetic energy, thereby increasing the reconnection rate (Sun et al. 2022), while 2D particle-in-cell (PIC) simulation of reconnection with imposed turbulent force found that turbulence enhances the energy conversion rate but does not obviously increase the reconnection rate (Lu et al. 2023).Conversely, 3D PIC simulations demonstrate that the reconnection rate and total energy conversion rate in turbulent reconnection (turbulence driven by reconnection) closely resemble those in laminar reconnection by 2D simulations (Daughton et al. 2014).Until now, the role of turbulence in reconnection remains a controversial and open question.This paper provides direct observational evidence that turbulence enhances energy conversion in reconnection by using Magnetospheric Multiscale (MMS) spacecraft observations in the terrestrial magnetotail.
This study utilized various instruments on board MMS.The Flux Gate Magnetometer instrument and the Electric Double Probes provide the magnetic field and electric field data with a time resolution of 128 and 8192 samples per second in burst mode, respectively (Ergun et al. 2016;Lindqvist et al. 2016;Russell et al. 2016;Torbert et al. 2016); the Fast Plasma Investigation (FPI) supplies the plasma moments with a time resolution of 0.03 s for electrons and 0.15 s for ions in the burst mode (Pollock et al. 2016); The Fly's Eye Electron Proton Spectrometer and Energetic Ion Spectrometer were used to measure the energetic electron and ion data, respectively, with time resolutions of 0.3 and 20 s (Blake et al. 2016;Mauk et al. 2016).

Observations
MMS recorded nearly 30 magnetotail reconnection events between 2017 and 2020, encompassing a broad range of inflow Alfvén speed ä [400, 3000] km s −1 and plasma beta ä [0.01, 3].Since energy conversion and particle acceleration during reconnection depend on inflow parameters such as the inflow Alfvén speed V A,in and plasma beta β in (Phan et al. 2013(Phan et al. , 2014;;Lu et al. 2019;Yi et al. 2019), we single out two turbulent reconnection events that have similar V A,in , β in and guide field strength but with distinct magnitudes of turbulent field for comparison.This procedure helps to highlight the effects of turbulence on reconnection.In the magnetotail, the ambient level of turbulence is relatively weak compared to that in the solar wind and magnetosheath.Hence, turbulent reconnection in this paper means that reconnection is primarily initialed in a laminar current sheet, then drives turbulence and evolves into turbulent state.
Figure 1 provides an overview of the MMS1 observations from 15:40 UT to 15:58 UT on 2017 July 6.This event was observed by MMS near [−24.1, 1.3, 4.5] R E (Earth radius) in the magnetotail.MMS observed a clear reversal of ion bulk flow from tailward to earthward, accompanied by a change of the magnetic field B z from negative to positive, indicating that the spacecraft encountered a tailward retreating X-line.Although the magnetic field B x was mostly negative during this period, it frequently approached zero.The plasma β is almost greater than 0.5 between 15:42 and 15:52 UT, suggesting that MMS was inside the magnetotail plasma sheet.Additionally, Hall electromagnetic fields, typical evidence for the ion diffusion region, were detected around 15:46 UT (Rogers et al. 2019).Figure 1(f) shows that energetic electrons and ions with energies up to 100 keV were observed in this reconnection region.A few energetic electron flux bursts were observed in the tailward flow, while the flux exhibits consistent enhancement in the earthward flow.The inflow region is identified between 15:51:10 and 15:51:18 UT when the outflow is absent and a large stable |B X | notably decreased in density and electron flux were observed by MMS (shown in Figure 1).
As seen in Figure 1(a), the magnetic field exhibits considerable fluctuations.The power spectrum of the magnetic field follows a power-law spectrum, with a slope close to −1.67 in the inertial range, from 0.01 to 0.1 Hz, which is consistent with previously reported power-law spectra in plasma turbulence (e.g., Leamon et al. 1998;Sahraoui et al. 2009Sahraoui et al. , 2013;;Huang et al. 2012Huang et al. , 2017Huang et al. , 2014;;Hadid et al. 2015;Breuillard et al. 2016;Ergun et al. 2018;Zhou et al. 2021).Figure 1(b) displays the disturbed magnetic field dB, which is the high-pass filtered magnetic field above 0.05 Hz.Here, 〈|dB|〉 is used to quantify the fluctuation level of the observed turbulence, which is calculated as , where B PSD x y z , ,

~(
) is the magnetic field power spectral density (PSD) with a frequency greater than 0.05 Hz, df is the frequency bandwidth, and 〈〉 represents the time average.In this event, 〈|dB|〉 is approximately 2.2 nT, and the relative amplitude of the fluctuation 〈|dB|/|B 0 |〉 is about 0.5, where B 0 is the low-pass filtered magnetic field below 0.05 Hz (shown in Table 1).Here, we employ high-pass and low-pass filtering on the magnetic field to extract disturbances generated by turbulent reconnection and to retain the reconnected laminar current sheet without interference from disturbances.We also calculated the root mean square of dB and B 0 to quantify the amplitude of turbulence.We find that the calculated turbulence levels are different by different methods.Nevertheless, a consistent observation is that the ratio of turbulence levels between a strong turbulent reconnection (STR) and weak turbulent reconnection (WTR) consistently hovers around 2 to 3.
MMS recorded another reconnection event on 2017 July 12 (Figures 2(a)-(j)), during which two consecutive flow reversals from tailward to earthward were observed.Similar to the aforementioned event, the flow reversals coincided with the polarity changes of B z from negative to positive.This suggests the possibility of either passing two sequentially tailward retreating X-lines or the oscillation of a single X-line along the Sun-Earth line in the magnetotail (Zhou et al. 2019).The inflow region is between 14:22:30 and 14:25:08 UT. Figure 2(k) shows that the magnetic field power spectrum presents a slope of −1.76 in the inertial range, close to the Kolmogorov index.The fluctuation level 〈|dB|〉 is 0.65 nT and 〈|dB|/|B 0 |〉 is 0.14.These observations confirm that both events are turbulent reconnection events, with varying degrees of turbulence strength.Energetic electrons and ions with energies up to 100 keV were also observed in this event, similar to the previous one.
It is worth noting that 〈|dB|〉 of 2.2 ranks 2nd and 〈|dB|〉 of 0.65 ranks 24th among the 29 surveyed reconnection events.As a result, we refer to the first reconnection event as an STR and the second one as a WTR henceforth.The fluctuating magnetic energy in the STR is almost 1 order of magnitude larger than that in the WTR.Moreover, we have also examined 〈|dB|〉 and the power-law index of the magnetic power spectrum in the central plasma sheet before the onset of reconnection.We find that 〈|dB|〉 in the prereconnection plasma sheet is small (less than 0.25 nT in both events; see Figure A1 of the Appendix), and the magnetic power spectrum in the plasma sheet preceding reconnection exhibits a spectral index of −3.4 and −2.6 within the inertial range in the STR and WTR, respectively (see Figure A2 of the Appendix).The different slopes between the prereconnection plasma sheet and reconnection outflow region, along with a quiet plasma sheet prior to reconnection, indicate that turbulence observed during reconnection is not a result of preexisting turbulence in the plasma sheet but rather is driven by reconnection.

Energy Conversion
First, we investigate the impact of turbulence on the energy conversion rate (J • E) during reconnection.The electric current density J is estimated at the tetrahedron barycenter using the curlometer technique based on the four spacecraft's measured magnetic fields (Dunlop et al. 2002).The electric field E has been averaged over the four spacecraft.Figure 3(a) compares the probability density distribution (PDF) of J • E in the two events.It can be observed that the PDF of J • E in both events is signed indefinitely, implying that energy exchange in turbulent reconnection goes both ways.The PDF of J • E in the STR is much broader than that in the WTR, which indicates that the local energy exchange in the STR is greater than that in the WTR.Furthermore, the average J • E in the STR is nearly 10 times greater than that in the WTR (shown in Table 1).Note that the 〈J • E〉 varies depending on the chosen time intervals for averaging; however, there is always a fiveto tenfold difference between the two values if the selected interval covers the major flow reversal.Figure 3 where n in , V A,in , and B in are the inflow plasma density, ion-Alfvén speed, and magnetic field, respectively.The normalized J • E is also larger in the STR although the PDF is less broad compared to that in Figure 3(a) because B 0 is smaller in the WTR than in the STR. Figure 3(c) exhibits the PDF of J • E/n normalized by n in , which represents the energy gain of a particle pair (one ion and one electron) per unit time.It is noticeable that the PDF of J • E/n has a heavier tail and wider distribution in the STR.The average J • E/n in STR is still greater than that in WTR.Thus, it can be safely concluded that turbulence promotes energy exchange between electromagnetic fields and plasma and also the net energy conversion from fields to plasma.
To gain a better understanding of the factors contributing to the larger energy exchange in the STR compared to the WTR, we express J • E as |J||E| cosθ, where θ is the angle between J and E, and we examine which variable is responsible for the evident difference in J • E. Figure 4(a) illustrates that the PDFs of θ maximize at approximately 90°and gradually decrease toward 0°and 180°, implying that the electric field E tends to be perpendicular to the electric current J and that the difference of J • E between the two events is not caused by the angle between J and E. As illustrated in Figures 4(b) and (c), regardless of STR or WTR, large J • E mainly corresponds to large current density and electric field.Both current density |J| and electric field |E| are greater in the STR than in the WTR.
Figures 5(a) and (b) provide a comparison of J ⊥ • E ⊥ and J || • E || in these two events.The broader PDF of J ⊥ • E ⊥ compared to J || • E || suggests that energy exchange primarily occurs through the perpendicular channel rather than the parallel channel.The generalized Ohm's law allows J • E to be decomposed into where E MHD is the MHD electric field, V MHD is the bulk velocity defined as ) , and E ni is the nonideal electric field, including the electric field contributed by the divergence of the electron pressure tensor and the electron inertial term.Note that the Hall term does not contribute to energy conversion because J • (J × B) = 0.
To evaluate E MHD and E ni accurately, it is important that the ion/electron bulk velocity is measured as accurately as possible.Here we compare the electric current derived by the curlometer technique (denoted as J c ) and that directly calculated from the plasma density and velocity (denoted as J p ) to validate the accuracy of the ion/electron bulk velocity.We find that the correlation between J c and J p is good for the STR event, with a correlation coefficient larger than 0.8, while it is poor in the other event, with the correlation coefficient less than 0.5, which implies that the particle data of the WTR event are not very accurate; hence, we compared J • E MHD and J • E ni for the STR only.Figure 5(c) compares the contribution of the MHD term and nonideal term to J • E for the STR.The analysis indicates that the nonideal term is the main contributor to J • E.

Coherent Structures and Current Filaments
Numerous studies have demonstrated the significance of kinetic-scale intermittent structures and current filaments in energy conversion during turbulent reconnection (Ergun et al. 2020a;Huang et al. 2022;Zhou et al. 2021).Therefore, we investigate the relationship between the coherent structure (CS)/current filament (CF) and energy conversion in this study.Here, the multispacecraft partial variance of increments (PVI) method is employed to identify the CS (Greco et al. 2008(Greco et al. , 2009;;Chasapis et al. 2018).The PVI index is calculated as where B(t) is a time series of the magnetic field, and the pair i, j = 1, 2, 3, 4 indicates the different MMS spacecraft.For each time instant, the PVI index is determined as the average value of PVI ij over the six pairs of the different spacecraft (Chasapis et al. 2018).To identify the CS, the peak value of PVI index should exceed the threshold value 〈PVI〉 + σ PVI , where σ PVI is the standard deviation of the PVI index in the whole interval (Greco et al. 2008).The boundary of each CS is defined as the rms of the PVI index (Califano et al. 2020;Man et al. 2022).  is the inflow plasma β, where P B is the magnetic pressure; n e is the plasma density; T i and T e are the ion and electron temperature, respectively; and K B is the Boltzmann constant.The energetic electron rate (EER) is defined as the ratio of the differential energy flux between the energetic electrons (47-550 keV) and thermal electrons (50 eV-25 keV), while the energetic ion rate (EIR) is defined as the ratio between the energetic ions (45-200 keV) flux and thermal ions (250 eV-25 keV).B g represents the guide field strength.
Figure 2. The same format as Figure 1, except for the turbulent reconnection event observed on 2017 July 12 (the WTR event).Due to incomplete burst mode data coverage for the entire period in this event, we used survey mode data to conduct the spectral analysis, with a maximum frequency of 4 Hz, as shown in (k).
Finally, we identified 191 CSs in the STR and 116 CSs in the WTR based on the CS definition.The corresponding occurrence rates of CS in the STR and WTR events are approximately 19.1 and 9.3 minute −1 .In addition, we evaluated the number of CFs.A CF is required to have a peak current density larger than 2J rms , where J rms is the rms of the current density in the entire time interval.The boundary of the CF is determined by the value of J rms (Califano et al. 2020;Man et al. 2022).Our findings reveal 104 CFs in the STR and 58 CFs in the WTR (see Table 2).The corresponding occurrence rates are approximately 10.4 minute −1 and 4.6 minute −1 , respectively.These results suggest that stronger turbulence induces more intermittent structures in reconnection, and the ratio of the occurrence rate of CF between the two events is consistent with that of the CS.
Figure 6 displays the proportion of data points within the CSs conditioned on the binned (J • E)/(J • E) rms in the two events.Approximately, 12% and 28% of the total data points in the WTR and STR, respectively, are contained in the CSs.Among data points with J • E > 4(J • E) rms , about 72% (38%) of them are located in the CSs in the STR (WTR).About 78% (64%) of the data points with J • E < − 4(J • E) rms are located in the CSs in the STR (WTR).It is noteworthy that there is an obvious asymmetry in the profile of the WTR, with the  proportion corresponding to the positive J • E being remarkably lower than that corresponding to negative J • E. The reason behind this asymmetry remains unclear and warrants further investigation.Since the PVI method may not detect all the CSs in the reconnection, such as vortices (Sundkvist et al. 2005;Roberts et al. 2016;Hou et al. 2021), the contribution of CSs to the intense J • E may be even higher than estimated here.

Spatial Scale of Magnetic Fields and CF Thickness
We performed further analysis on the variation of the spatial scale of the magnetic field L dB as a function of J • E. The spatial scale of the magnetic fields is determined using the expression as L dB = |B|/(|∇B|), where |∇B| denotes the norm of the Jacobian matrix of the magnetic field, i.e., Elements in the Jacobian matrix are estimated within the MMS tetrahedron by assuming a linear magnetic gradient within the tetrahedron (Shen et al. 2003).
Figure 7(a) shows the L dB conditioned on (|J • E|)/(J • E) rms .We find that the average L dB is typically smaller in the STR than that in the WTR and the average L dB is below 1 d i,in (d i,in is the inflow ion inertial length) in both events.Moreover, the average L dB gradually decreases with the increment of J • E in both events.Figure 7(b) compares the PDF of the L dB within the CS between the two events.The PDF of L dB in the STR shifts toward to smaller scale compared to that in the WTR.Additionally, the L dB corresponding to the peak PDF in the STR is also smaller than that in the WTR, which is in accordance with Figure 7(a).These findings indicate that L dB within the CS in the STR is typically smaller than that in the WTR.The average L dB within the CS is 0.4 d i,in and 0.73 d i,in in the STR and WTR, respectively.
Figure 7(c) presents the proportion of CFs with different CF thicknesses.The CF thickness is determined by multiplying the CF normal speed by the duration.To estimate the normal speed of the CS, a timing analysis on the magnetic field is performed (Russell et al. 1983).To obtain reliable results, it is required that the cross-correlation coefficient of the magnetic field among the four spacecraft be greater than 0.9 (refer to Man et al. 2022 for details).The CF thickness has been normalized by d i,in .We can see that most CFs have thicknesses around 0-0.6 d i,in , However, the proportion of CFs with thickness greater than 1.0 d i,in in the WTR is higher than that in STR, implying that there are more sub-ion scale CFs in the STR than in the WTR.The average thickness of the CF in the WTR is 1 d i,in , which is larger than the average thickness of CF in the STR, approximately 0.5 d i,in (refer to Table 2).This result agrees well with the distribution of the spatial scale L dB shown in Figures 7(a) and (b).

Discussions and Conclusions
Table 1 presents a comparison of the energetic ions and electrons produced in the STR and WTR.It is shown that the STR generated slightly more energetic ions and electrons than the WTR.Specifically, the maximum energetic electron rate (EER), defined as the ratio between the differential energy flux of energetic electrons (>47 keV) and the thermal electrons (50 eV-25 keV), is approximately twice as high in the STR compared to the WTR.Similarly, the maximum energetic electron flux is also greater in the STR.Additionally, both the energetic ion flux and energetic ion rate (EIR) are 2 times higher in the STR than in the WTR.However, the difference in the energetic particle fluxes and EER/EIR between the two events is minor.Hence, it can be concluded that the strength of turbulence does not significantly affect the production of energetic particles in reconnection.
In addition, there was no prominent difference in the degree of ion/electron bulk heating between the two events.The average electron temperatures in the outflow region 〈T e,out 〉 is ∼1515 eV in the STR and ∼1910 eV in the WTR.Here, the outflow region is defined as the region where the outflow speed is greater than 0.2 V A,in .The average electron temperatures in the inflow region 〈T e,in 〉 is ∼970 eV (1250 eV) in the STR (WTR).Hence, the average electron heating was ΔT e ∼546 and 666 eV in two reconnection events, respectively.Notably, these values agree remarkably with the empirical formula m V 0.017 i A,in 2 ∼ 570 eV ∼ ΔT e proposed in Phan et al. (2013).In terms of ion temperatures, the average inflow ion temperatures 〉 is ∼1942 eV (∼1980 eV) in the STR (WTR), and the increase of the ion temperature in the outflow region ΔT i is ∼2356 eV (∼2414 eV) in STR (WTR).The observed ion heating ΔT i is about 0.07 m V i A,in 2 , which is half of the empirical value of m V 0.13 i A,in 2 reported by Phan et al. (2014), namely, ΔT i /T i,in = 0.14/β i,in .A caveat needs to be given that the ion temperature may be underestimated in the outflow region since high energy ions are beyond the energy Note.The second and third columns represent the number of CSs and their occurrence rate; the fourth and fifth columns represent the number of CFs and their occurrence rate.The sixth column represents the average CF thickness.Here, the CF thickness is normalized by d i,in .
Figure 6.The proportion of data points within CSs conditioned on the binned J • E/(J • E) rms , where (J • E) rms is the rms of J • E in the corresponding event.
(J • E) rms is about 0.01 nW m −3 and 0.07 nW m −3 in the WTR and STR, respectively.coverage of the FPI used in this study to measure the ion temperature.
To gain insights into the partition of the released magnetic energy in turbulent reconnection, we roughly assessed the energy balance for the two events.Assuming that the converted magnetic energy during reconnection is totally absorbed by the plasma from the inflow region, we obtain the following relation based on the principle of energy conservation: where is the averaged energy conversion rate (see Table 1); L x , L y , and L z represent the length of the effective reconnection region (ERR), which generally refers to the reconnection region where effective energy conversion takes place, in the x-, y-, and z-directions, respectively; V z denotes the inflow speed; n in is the inflow plasma number density; and ΔW i and ΔW e is the average energy gain per ion and electron, respectively.Here we have and thermal energy 1.5k B n in 〈ΔT i,e 〉 for the inflow plasma are listed in Table 3.By substituting typical inflow speed of V z ∼ 0.1 V A,in into Equation (2), we find that L z ∼ 1 d i,in in the STR and L z ∼ 5 d i,in in the WTR.The estimated thicknesses of the ERR are reasonable (e.g., Nakamura et al. 2006).Notably, the relative thicker ERR in the WTR is also consistent with our analysis on L dB and CF thickness.It becomes evident from Table 3 that the magnetic energy conversion enhanced in the STR is mainly manifested as increased ion bulk kinetic energy compared to that in the WTR.The increased ion bulk kinetic energy in the STR is probably due to the stronger magnetic tension force in the STR than in the WTR.Magnetic tension depends on magnetic field intensity and gradients, which are larger in the STR.Moreover, the role of magnetic tension in reconnection is to produce a net acceleration of the plasma, which involves mainly the ions.It is also possible that what MMS observed is premature turbulence in the fast flows.With the development of turbulent reconnection, the instabilities and turbulence can eventually transform bulk kinetic energy into thermal energy.
Magnetic reconnection not only converts magnetic energy to bulk kinetic energy, which may then be further converted to thermal energy, but also directly transfers magnetic energy to thermal energy.In turbulent reconnection, bulk kinetic energy cascades from large scale to small scale, ultimately dissipating at the smallest scale (the dissipation range), in the form of disordered thermal energy.Various mechanisms may account for the dissipation, such as wave-particle interactions (Khotyaintsev et al. 2019) or secondary reconnection (Zhou et al. 2021).Nevertheless, reconnection persistently drives bulk flow, the energy of which is partially converted to thermal energy.Thus, an equilibrium might be achieved between the bulk kinetic energy and thermal energy.The partition of magnetic energy between plasma bulk kinetic energy and thermal energy during reconnection is still an outstanding question and remains a subject for future research.
In the following, we provide some hints of why J • E is typically larger in the STR than in the WTR. Figure 4 demonstrates that the intense J • E generally occurs in regions with large |J| and |E|.We have shown that the CF thickness and the local scale of magnetic fields are larger in the WTR than in the STR.It is reasonable to expect that a smaller spatial scale corresponds to a larger current density as J ∼ B/L according to Ampere's law, where L is the spatial scale of the magnetic fields.Furthermore, it is shown that J • E ni dominates over J • E MHD .Since either the divergence of the electron pressure tensor or electron inertial term, both of which vary inversely with spatial scale, contribute to E ni , it is also greater in regions with smaller L. On the other hand, it is possible that turbulence produced in STR can break the thicker CF into multiple thinner CFs.While these thinner CFs may individually occupy a smaller volume compared to the thicker CFs, the higher quantity of CFs in the STR may ensure that the total volume constituted by the CFs in the STR is not significantly smaller than that in the WTR.Therefore, the integrated J • E is also larger in the STR.
In summary, we have conducted an analysis of turbulence amplitude on energy conversion in magnetotail reconnections with similar inflow conditions.The most prominent result is that the reconnection with stronger turbulence exhibits a higher energy exchange/conversion rate than the reconnection with weaker turbulence, i.e., turbulence tends to enhance the energy conversion during reconnection.Stronger turbulence generates more coherent structures with smaller spatial scales, which contribute significantly to energy conversion during reconnection.Furthermore, turbulence impacts the ion bulk kinetic energy and exerts a minor positive influence on the generation of energetic particles.This study contributes to a more comprehensive understanding on the role of reconnectiondriven turbulence in reconnection.These results hold significant potential for advancing our comprehension of the nonlinear interplay between reconnection and turbulence in a broader astrophysical context.
It is worth noting that the turbulence strength varies under similar inflow conditions.To understand why the two reconnection events produce turbulence with different amplitudes, we did a preliminary statistical analysis based on the 30 Note.The second and third columns represent the average electron and ion temperature enhancement; the fourth and fifth columns represent the average electron and ion bulk kinetic energy in the outflow region.The sixth and seventh columns represent increments of the electron and ion thermal energy.n in is the plasma density in the inflow region.
magnetotail reconnection events observed by MMS between 2017 and 2020.We find a clear correlation between the magnetic field disturbance in the outflow (dB t ) and V A,in , and β in .The inflow disturbance (dB in ) also exhibits a positive correlation with dB t (not shown here).For instance, the inflow disturbance (dB in ) in WTR and STR is approximately 0.2 and 1.6 nT, respectively.Therefore, we speculate that reconnections with similar inflow conditions producing distinct strengths of turbulence may be caused by the different fluctuation levels the inflow region.Nevertheless, the correlation between dB in and dB t does not necessarily imply a causal relationship.
Fluctuations in the outflow region may leak into the inflow region, stirring the inflow region (e.g., Lapenta 2008).These inflow fluctuations, in turn, impact the reconnection, creating a cyclic process that ultimately contributes to the formation of different turbulence.The effect of inflow parameters on the reconnection-driven turbulence falls beyond the scope of this paper and is worth further investigating.

Figure 1 .
Figure 1.Observations of a turbulent reconnection by MMS on 2017 July 6 (referred to as the star turbulent reconnection event).From the top to bottom are (a) three components of the magnetic field and magnetic field strength; (b) high-pass filtered magnetic field above 0.05 Hz; (c) electron number density; (d) three components of the ion bulk velocity and (e) the electric field; (f) energetic and (g) thermal electron differential energy flux; (h) energetic and (i) thermal ion differential energy flux; (j) plasma β; and (k) trace of the power spectral density (PSD) of the magnetic field.The magenta straight lines represent linear fits of the PSD.The black and green vertical dashed lines indicate the ion cyclotron frequency ( f ci ) and low hybrid frequency ( f lh ), respectively.Due to the small spacing among the four spacecraft, the observations from all four spacecraft are similar; therefore, only MMS2 observations are presented here.The red vertical line represents the selected inflow region.

Figure 3 .
Figure 3. PDFs of (a) the energy exchange rate (J • E); (b) the normalized (J • E) by qn in V A,in 2 B in ; and (c) (J • E)/n.The red and blue curves represent the STR event (2017 July 6) and the WTR event (2017 July 12), respectively.

Figure 4 .Figure
Figure 4. PDFs of (a) the angle θ between electric current J and electric field in E. (b) and (c) show the scatterplot of |J • E| as a function of current intensity |J| and electric field intensity |E| in the STR and WTR, respectively.Both the color and size of the dots represent the value of |J • E|, with larger sizes representing higher values.

Figure 7 .
Figure 7. (a) Average value of the L dB conditioned on (|J • E|)/(J • E) rms in the two turbulent reconnection events.The vertical bars in panel (a) represent the standard error of the mean; (b) PDF of the L dB within CSs; (c) PDF of the normalized CF thickness.Here, L dB and the CF thickness are normalized by d i,in .
The left-hand side of Equation (2) represents the total released magnetic energy in the ERR during the time interval δt, while the right-hand side of Equation (2) represents the total energy gain of the inflowing particles into the ERR during δt.The estimated increment of the bulk

Figure A1 .
Figure A1.The overview of the STR event.From top to bottom are (a) three components of the magnetic field and magnetic field strength; (b) magnetic field strength; (c) electron number density; (d) three components of the ion bulk velocity and (e) electron bulk velocity; and (f) plasma β.

Table 1
Key Parameters Are Provided to Describe the Two Reconnection Events Observed by MMS on 2017 July 6 and 2017 July 12 The parameter 〈dB〉 refers to the averaged amplitude of the high-pass filtered magnetic field above 0.05 Hz, representing the magnetic field fluctuation.The relative amplitude of the fluctuations is expressed by 〈|dB|/|B 0 |〉, where B 0 is the low-pass filtered magnetic field below 0.05 Hz.V

Table 2
Statistics of the CS and CF in the Two Events

Table 3
The Estimated Increment of the Bulk Kinetic Energy and Thermal Energy for the Inflow Plasma in WTR and STR