Statistical properties of magnetic structures and energy dissipation during turbulent reconnection in the Earth's magnetotail
K. Bergstedt, H. Ji, J. Jara-Almonte, J. Yoo, R. E. Ergun, L.-J. Chen
mmanuscript submitted to
Geophysical Research Letters
Statistical properties of magnetic structures and energydissipation during turbulent reconnection in theEarth’s magnetotail
K. Bergstedt , , H. Ji , , J. Jara-Almonte , J. Yoo , R. E. Ergun , , L.-J.Chen May 5, 2020 Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey, USA Princeton Plasma Physics Laboratory, Princeton, New Jersey, USA Department of Astrophysical and Planetary Sciences, University of Colorado Boulder, Boulder, Colorado,USA Laboratory of Atmospheric and Space Sciences, University of Colorado Boulder, Boulder, Colorado, USA NASA, Goddard Space Flight Center, Greenbelt, Maryland, USA
Key Points: • An automated method to locate and identify plasmoids and current sheets in tur-bulent magnetotail reconnection regions has been developed • Plasmoids in a region of turbulent magnetotail reconnection have a decaying ex-ponential size distribution from sub-electron to ion scale • Plasmoids and current sheets are significant contributors to parallel particle en-ergization, but not to overall particle energization
Corresponding author: K. Bergstedt , [email protected] –1– a r X i v : . [ phy s i c s . s p ace - ph ] M a y anuscript submitted to Geophysical Research Letters
Abstract
We present the first statistical study of magnetic structures and associated energy dis-sipation observed during a single period of turbulent magnetic reconnection, by usingthe in-situ measurements of the Magnetospheric Multiscale mission in the Earth’s mag-netotail on July 26, 2017. The structures are selected by identifying a bipolar signaturein the magnetic field and categorized as plasmoids or current sheets via an automatedalgorithm which examines current density and plasma flow. The size of the plasmoidsforms a decaying exponential distribution ranging from sub-electron up to ion scales. Thepresence of substantial number of current sheets is consistent with a physical picture ofdynamic production and merging of plasmoids during turbulent reconnection. The mag-netic structures are locations of significant energy dissipation via electric field parallelto the local magnetic field, while dissipation via perpendicular electric field dominatesoutside of the structures. Significant energy also returns from particles to fields.
Plain Language Summary
Magnetic reconnection is an important mechanism for generating energetic parti-cles in space and solar environments. Turbulent magnetic reconnection causes the de-velopment of many small-scale magnetic structures, such as locally helical or loop-likemagnetic fields (plasmoids), or areas where oppositely directed magnetic fields are sand-wiched together (current sheets). The exact formation and distribution of the structures,as well as the role the structures play in particle energization and the evolution of mag-netic reconnection, is still unknown. Using data from the Magnetospheric Multiscale (MMS)mission, we developed an algorithm that is able to detect and identify the magnetic struc-tures present in a region of turbulent magnetic reconnection. The number of structureswas found to decrease with size as a decaying exponential, which is consistent with pre-vious theories. The structures contributed strongly to the energization of particles par-allel to the local magnetic field, but were not significant sites of energization overall. Over-all energization is dominated by energization perpendicular to the local field outside ofthese structures. There is also significant energy return from particles to the fields.
Magnetic reconnection is a process by which the topology of the magnetic field withina plasma is altered, allowing for the rapid conversion of magnetic energy into kinetic en-ergy (Parker, 1957). It is responsible for the penetration of solar wind plasma into themagnetosphere (Russell & Elphic, 1978), and plays an important role in powering so-lar flares and coronal mass ejections (Sweet, 1969; Lin & Forbes, 2000). When reconnect-ing current sheets are sufficiently stretched to have large aspect ratios, plasmoids are ex-pected to form via the tearing mode instability (N. Loureiro et al., 2007), leading to themulti-scale evolution of fast reconnection (e.g. Shibata & Tanuma, 2001; Bhattachar-jee et al., 2009) across space and astrophysics including Earth’s magnetotail (Ji & Daughton,2011). In the latter case, plasmoids have been observed via the ISEE-3 and GEOTAILsatellites over an extended period of time (Baker et al., 1984; Jr et al., 1984; Richard-son et al., 1987; Moldwin & Hughes, 1992; Nagai et al., 1994; Ieda et al., 1998; Slavinet al., 2003) and more recently by the CLUSTER mission on the ion scales (e.g. Chenet al., 2008; Chen et al., 2012). Plasmoids are also routinely seen in kinetic simulations(e.g. Daughton et al., 2006; Drake et al., 2006). Therefore, a thorough analysis of thestructures present in a reconnecting current sheet can shed light on the dynamics of fastreconnection, which in turn affect the global dynamics of the magnetosphere.An important feature of magnetic reconnection is the dissipation of magnetic en-ergy to plasma particle energy through J · E where J and E are current density andelectric field, respectively. There is an ongoing debate about whether the component of J · E along or across the local magnetic field, expressed as J (cid:107) E (cid:107) and J ⊥ · E ⊥ , respec- –2–anuscript submitted to Geophysical Research Letters tively, is the primary source of particle energization (e.g. Drake & Swisdak, 2014; Ya-mada et al., 2018; Fox et al., 2018; Pucci et al., 2018). Furthermore, whether the dis-sipation within the localized reconnection structures is significant (e.g. Egedal et al., 2012)or can be ignored (e.g. Drake et al., 2019) in a large system is still unclear. From thesame MMS data used in this Letter, Ergun et al. (2018) found that the main positivecontributor to the overall J · E was J ⊥ · E ⊥ at frequencies at or below the ion cyclotronfrequency, but did not examine the spatial correlation between energy dissipation andmagnetic structures. Therefore, a detailed statistical study of magnetic dissipation, in-cluding the decomposition into parallel and perpendicular components within and out-side of the magnetic structures can provide insight on these ongoing debates.Many analytic and numerical studies have characterized possible size distributionsof secondary islands in various regimes (Uzdensky et al., 2010; Fermo et al., 2010, 2011;N. F. Loureiro et al., 2012; Y.-M. Huang & Bhattacharjee, 2012; Takamoto, 2013; Guoet al., 2013; Lingam & Comisso, 2018; Petropoulou et al., 2018). Many of these stud-ies have used Magnetohydrodynamic (MHD) models that are not generally applicableto kinetic scale plasmoids. However, the model developed by Fermo et al. (2010) is sta-tistical in nature, and therefore can potentially be applied in a multiscale fashion. It pos-tulates that plasmoids start small, then grow in size both by expansion and by plasmoidmerging, leading to a smooth energy spectrum via an inverse-cascade (Nakamura et al.,2016). A characteristic of the model of Fermo et al. (2010) is that for sufficiently largesize (represented as a characteristic length scale), the number of plasmoids present ina reconnecting current sheet decreases exponentially with increasing plasmoid size. Stud-ies have determined plasmoid size scalings in experimental plasmas (Dorfman et al., 2014;Olson et al., 2016), in solar plasmas via ex-situ methods (Guo et al., 2013), and in spaceplasmas via in-situ methods (Fermo et al., 2011; Vogt et al., 2014; Akhavan-Tafti et al.,2018). In-situ studies provide more detailed information on each plasmoid, but no in-situ study thus far has utilized structures present in only a single turbulently reconnect-ing region. Plasma conditions varied considerably between each observation and intro-duced unquantified uncertainties to the observed scaling. An analysis of the distributionof structures within a single turbulently reconnecting current sheet is desirable and nec-essary for accurately quantifying the plasmoid size scaling.The most common type of plasmoid observed in the magnetosphere is the flux rope,which is a helical magnetic field structure with a strong core field and an enhancementof the total magnetic field. Flux ropes have been extensively studied in space, and mod-els of cylindrical force-free (Elphic & Russell, 1983) and non-force-free (Lundquist, 1950;Lepping et al., 1990) flux ropes are widely used. Flux ropes have been observed with com-plex internal structures (Stawarz et al., 2018), including enclosed waves (Wang et al.,2016). Various other plasmoids have been observed in the magnetotail current sheet thatdo not have the typical cylindrical structure, including flattened flux ropes (Sun et al.,2019) and plasmoids which have loop-like field lines rather than helical (Zhang et al., 2013).These non-ideal plasmoids are indicative of the dynamic nature of magnetic reconnec-tion. In a turbulent region, plasmoids may experience external forces which could slowor prevent their evolution into ideal cylindrical states. Therefore, for a turbulently re-connecting current sheet, in order to get a comprehensive survey of the plasmoids present,it is necessary to search for plasmoids that do not necessarily fit the ideal cylindrical fluxrope model.Another question for a statistical survey of plasmoids is whether to identify the plas-moids ‘by eye’, or to attempt an automated detection method. Automated methods aremore rigorously defined and repeatable, and thus are less susceptible to human sourcesof bias. For example, methods have been developed to automatically detect flux ropesin satellite data (Smith et al., 2017; S. Huang et al., 2018). These methods are repeat-able, rigorous, and calculate valuable parameters such as the spacecraft’s distance of clos-est approach to the center of the flux rope and the flux rope’s radius. However, both meth- –3–anuscript submitted to
Geophysical Research Letters ods are based on cylindrical flux rope models, force-free (Lundquist, 1950) and non-force-free (Elphic & Russell, 1983) respectively. These methods will not be suitable in a dy-namic turbulent reconnection region which is likely to have large numbers of plasmoidswhich do not fit cylindrical flux rope models and unlikely to have obvious quiescent mag-netic field backgrounds to compare the magnetic field fluctuations against. Therefore,an automated method has been developed to detect non-ideal plasmoids, as well as cur-rent sheets resulting from two different physical processes. This method has been usedto probe the structure, dynamics, and dissipation of a turbulently reconnecting currentsheet observed in the magnetotail.
MMS observed a period of turbulent reconnection on July 26, 2017 at 07:16:53 UT,and all four satellites collected about 17 minutes of data at their burst data rates. Theelectron energization and dissipation during this period was previously studied, and itwas found that the main contributor to the overall net positive dissipation was due to J ⊥ · E ⊥ at or below the ion cyclotron frequency ( ∼ J (cid:107) E (cid:107) , and that J (cid:107) E (cid:107) was associated with electrons withenergies up to 100 keV. Whether this finding can be generalized to the structures reportedhere was investigated. For this work, magnetic field data from the Fluxgate Magnetome-ter (FGM), which has a burst data rate of 128 Hz, is used (Russell et al., 2016). Elec-tric field measurements from the axial and spin-plane double probes at a data rate of 8192Hz (Ergun et al., 2016; Lindqvist et al., 2016; Torbert et al., 2016), and electron and ionmoments from the Fast Plasma Instrument (FPI) are also used. FPI data is availableat burst data resolution of 30 ms and 150 ms for electrons and ions respectively (Pollocket al., 2016). In parts of the turbulent reconnection region, the electron density dropsbelow 0.01 cm − , which means that the electron moments data will have large uncer-tainties during those time intervals. We elected not to use the electron moments datain these time intervals.In order to categorize the structures as plasmoids or current sheets, idealized mod-els of the structures and their orientations within the magnetotail current sheet were used,as shown in Figure 1. The magnetotail current sheet is generally in the X-Y GSM plane,with the current primarily in the +Y ( J y >
0) direction when sufficiently near the Y=0plane. Plasmoids will generally be oriented with their invariant directions (e.g. the coredirection of a flux rope) in the Y direction, and thus the currents within them will onaverage be in the +Y direction. We similarly assume that “pull current sheets” —currentsheets between plasmoids that are not currently merging— will maintain the same gen-eral orientation of the quiescent plasma sheet, and thus be approximately in the X-Y plane,with the current on average in the +Y direction. In contrast, “push current sheets”, whichare current sheets formed by two plasmoids pushing into each other and potentially merg-ing via reconnection, will be generally oriented in the Y-Z plane. The current directionis opposite that of our model plasmoids, pull current sheets, and the quiescent magne-tosphere, so we expect currents within push current sheets to have components in the-Y direction ( J y < < B z signature. In contrast, a pull cur- –4–anuscript submitted to Geophysical Research Letters (a) (b) (c)
X GSM
Z GSM
X GSM Z GSM X GSM Z GSM
Plasmoids Pull current sheets Push current sheets
Vx positive (negative) Vx postive (negative) Vx positive (negative) Jy GSM positive Jy GSM positive Jy GSM negative Bz bipolar increasing (decreasing) Bz bipolar decreasing (increasing) Bz bipolar decreasing (increasing)
Figure 1.
Left- cartoon model of the structure categories. Right- example of a structurefrom data. For (a) a tailward-moving plasmoid, (b) a tailward-moving pull current sheet, (c) atailward-moving push current sheet. The red vertical bar denotes the zero crossing and the bluebars denote the beginning and end of the structure. The magnetic field data was smoothed by a6-point Hamming window for better estimation of the structure durations.Table: A summary of the selection criteria for the three structure categories.–5–anuscript submitted to
Geophysical Research Letters rent sheet will look like a first positive, then negative bipolar signature. If instead thestructure is moving in the -X (tail-ward) direction, a plasmoid will appear as a first pos-itive, the negative bipolar signature, while pull current sheets will appear as first neg-ative, then positive bipolar signatures. Push current sheets will appear as positive-then-negative bipolar signatures if travelling in the +X direction, and negative-then-positivesignatures if travelling in the -X direction. This leaves one category of structure with-out a known physical interpretation (structures with J y < B z structure in the data can be categorized as a plasmoid, a pull current sheetor a push current sheet via three considerations: 1) the direction of the bipolar signa-ture (negative-to-positive or positive-to-negative), 2) the direction of the X componentof the structure’s velocity, and 3) the direction of the Y component of the current den-sity. Examples of these three types of structures are shown on the right side of Figure1, and a summary of the selection criteria is in the table at the bottom of that Figure.Structure candidates were first selected by identifying their bipolar B z signaturein MMS1. In order to avoid some of the high-frequency transient turbulent magnetic fieldfluctuations, the data was first smoothed with a six-point Hamming window. Upon find-ing potential structure candidates, their sizes were determined by finding the nearest lo-cal minimum in the negative part of the bipolar signature, and the nearest local max-ima in the positive part of the bipolar signature. The number of comparison points fordetermining a local extrema was variable, but for the primary data 10 points to each sidewere used. At this point, if the other MMS satellites did not also observe a bipolar B z signature within the structure candidate, the structure candidate was discarded. Themagnetic field data for the structure was then synced to a common timeline via a four-point Bartlett window (Harvey & Schwartz, 1998), and the lower resolution ion and elec-tron moments data was synced to the same timeline via a cubic spline interpolation. Theelectric field data was synced to a common timeline via a linear interpolation to avoidartificial oscillations.In order to calculate the structures’ velocities and current densities, multi-spacecrafttechniques were used. The current density was calculated via the curlometer technique(Robert et al., 1998; Dunlop et al., 2002). The structure velocity was calculated in a two-step process. First, the dimensionality, invariant directions, and natural coordinates ofthe structure were calculated using the Minimum Directional Derivative (MDD) tech-nique (Shi et al., 2005), using the linear approximation of the magnetic field spatial gra-dient tensor from the barycentric coordinate approach (Chanteur, 1998). Then the Spatio-Temporal difference (STD) method was applied to determine the velocity of the struc-ture in its non-invariant directions (Shi et al., 2006). The STD method cannot be usedto determine the structure’s velocity in its invariant directions (e.g. the core directionof an ideal flux rope), but motion in these directions by definition does not cause a largechange of the magnetic field strength or direction. Therefore the velocity in the non-invariantdirections is sufficient to determine the structures general motion in the X direction forcategorization purposes.There are some additional limitations to the multi-spacecraft techniques used. Forone, they are only reliable when all four spacecraft of the tetrahedron are within the samestructure. The spacecraft spacing was ∼ ∼ –6–anuscript submitted to Geophysical Research Letters from MDD and STD. The techniques also have some advantages; namely, they can beused at every data point in the time cadence, unlike other techniques that determine nat-ural coordinates for structures such as minimum-variance analysis which can be used ondata from a single spacecraft (Sonnerup & Cahill Jr., 1967; Sonnerup & Scheible, 1998).This also allowed us to evaluate the time-stationarity of the data by observing how theresults from MDD and STD change with time throughout the structure.
There were 288 structures observed, and a summary of them is shown in Figure2. Of these, 94 were plasmoids, 99 were pull current sheets, and 51 were push currentsheets. 34 structures could not be categorized due to low certainty in the overall direc-tion of the X component of the velocity or the Y component of the current density. 10had sufficient certainty to be categorized, but did not match any of the given categories.These accounted for ∼
3% of the identified structures, so we conclude that the categoriesdevised were adequate to describe the majority of sufficiently certain cases. Statisticswere then performed on each of the structure types separately.An attempt was made to fit the observed plasmoids to force-free and non-force-freeflux rope models in order to accurately measure the plasmoids’ radii; however, the fitswere of inconclusive. Therefore, each structure’s size was approximated by the productof the normal velocity of the structure and the duration of the structure. By this method,the majority of the structures were < d e in size, electron-scale. The size distributionhistograms of plasmoids and pull current sheets are shown in Figure 2. The size datafor plasmoids and pull current sheets were fit using maximum likelihood estimation (MLE),which does not require binning the data and is therefore more robust. Kolmogorov-Smirnovtesting of the fits (Chakravarti et al., 1967) found consistency with an exponential dis-tribution but not with a power law. The push current sheets did not have a definitivefit (not shown). This decaying exponential is consistent with the prediction of Fermo etal. 2010 for sufficiently large scale size. This is the first in-situ confirmation of Fermoet al.’s prediction from observations taken from a single turbulently reconnecting region.Due to the turbulent nature of the magnetic field, we did not calculate the over-all guide field of the reconnecting region. The guide field during magnetotail reconnec-tion can change significantly on the timescale of less than a minute, so this event maynot have a consistent overall guide field (Chen et al., 2019). Instead, we calculated thecore fields of the observed plasmoids by finding the magnetic field strength along the mostinvariant direction determined from MDD analysis. This most-invariant direction wasgenerally primarily aligned with the GSM Y direction, so the distribution of the core fieldsof the plasmoids will be indicative of the total guide field of the region. Figure 2 showsthe distribution of observed core fields of the satellites, with positive core fields beingaligned with the +Y GSM direction and negative core fields aligned with the -Y GSMdirection. There are more plasmoids with positive core fields than negative ones, indi-cating a possible slight positive guide field. However, the core fields are not overwhelm-ingly in the +Y direction, indicating that the guide field was not strong, or was chang-ing over the course of the event. In the case of stronger guide field, it would be possi-ble to follow the procedure outlined by Nakamura et al. (2016) to use band-pass filter-ing to identify electron-scale flux ropes. However, for weak guide field the structures iden-tified in this fashion may be the product of instabilities other than the tearing instabil-ity, and therefore the technique is not appropriate for this data. –7–anuscript submitted to Geophysical Research Letters (a) (b) (c) (d) (e) (f)
Figure 2. (a) Summary bar chart of structure types counted. (b) Histogram of the averagedcore fields of the observed plasmoids. (c) Histogram of plasmoid sizes. (d) Probability-Probabilityplot of the exponential and power law fits for the plasmoid size data. (e) Histogram of pull cur-rent sheet sizes. (f) Probability-Probability plot of the exponential and power law fits for thepull current sheet size data. Error bars are from Poisson uncertainties. The errors on the fitparameters were computed by n = 100 bootstrap using (Pedregosa et al., 2011). Kolmogorov-Smirnov tests (Chakravarti et al., 1967) were performed on the exponential and power law fits,which accepted the exponential fit and rejected the power law fit. The probability-probabilityplots for the power law fits were done using a truncated power law distribution, as our selectionmechanism is only sensitive to structures of a particular size range.–8–anuscript submitted to Geophysical Research Letters (a) (d) (b) (e) (c) (f)
Outside Structures Within Structures Outside Structures Within Structures
Figure 3. (a) Breakdown of the net contribution to J (cid:107) E (cid:107) and J ⊥ · E ⊥ from the structures,compared to the regions outside the structures. (b) Comparison of the positive and negativecontributions to J (cid:107) E (cid:107) . Outside circle is contributions from outside the structures, inside circleis contributions from the structures. (c) Comparison of the positive and negative contributionsto J ⊥ · E ⊥ . Outside circle is contributions from outside the structures, inside circle is contri-butions from the structures. (d-f) Histogram comparing the averaged contributions of magneticstructures to J (cid:107) E (cid:107) and J ⊥ · E ⊥ for (d) plasmoids, (e) pull current sheets and (f) push currentsheets. –9–anuscript submitted to Geophysical Research Letters
To determine the dissipation mechanisms of the structures, we compared the J (cid:107) E (cid:107) and J ⊥ · E ⊥ contributions from the structures and from outside the structures, sum-marized in the pie chart in Figure 3. The structures covered ∼
10% of the total time du-ration of the region, but they contributed ∼
40% of the total J (cid:107) E (cid:107) and only ∼
3% of thetotal J ⊥ · E ⊥ . These electron-to-ion-scale structures are major contributors to the J (cid:107) E (cid:107) in the region, which is consistent with Ergun et al. (2018)’s identification of a flux-rope-like structure associated with large J (cid:107) E (cid:107) and highly energized electrons of >
100 keV.However, the breakdown between positive and negative contributions to J · E shows morecomplexity. As shown in Figure 3, the regions both inside and outside of the structureshave significant positive and negative contributions to J (cid:107) E (cid:107) and J ⊥ · E ⊥ . The struc-tures have a larger ratio of positive to negative for J (cid:107) E (cid:107) , leading to their significant con-tribution to net J (cid:107) E (cid:107) >
0. In contrast, the region outside of the structures has a largerratio of postive to negative for J ⊥ · E ⊥ , leading to a much smaller contribution fromthe structures, which are closer to parity. This breakdown shows that both within andoutside of the structures there is ongoing energy conversion from fields to particles andvice versa, whereas the net energy exchange favors particle energization.The histograms of the averaged J (cid:107) E (cid:107) and J ⊥ · E ⊥ are shown for the three ma-jor structure types in Figure 3, and they confirm that the structures are sources of bothpositive and negative J · E . The average perpendicular components have a larger spreadthan the parallel components by a factor of ∼
2, indicating that J ⊥ · E ⊥ has the largerimpact on overall J · E , whether positive or negative. The histograms for the plasmoidsshow a bias towards positive J · E , both for the parallel and perpendicular components,indicating these structures are on average sites of some particle acceleration. There aresome notable outliers, but they do not significantly impact the structures’ average con-tributions.Overall, J ⊥ · E ⊥ contributes ∼
90% of the total J · E , whereas J (cid:107) E (cid:107) only accountsfor ∼ ∼
85% of the total average J · E comes from J ⊥ · E ⊥ outside of the struc-tures. Therefore, the structures have a small contribution to the overall J · E , thoughsome may serve as injection sites with large J (cid:107) E (cid:107) which provide rapid energization tosmall populations of electrons, while the J ⊥ · E ⊥ between structures provides the largestnet energization, such as proposed in Comisso and Sironi (2019). This result supportsthe use of codes which simulate particle energization during magnetic reconnection onlarger-than-kinetic scales, such as the one detailed in Drake et al. (2019), but some han-dling of electron injection source terms may still be necessary. We utilized models of the expected magnetic signatures of plasmoids, pull currentsheets, and push current sheets to automate the detection and categorization of 288 mag-netic structures within a 17-minute turbulent reconnection region. The majority of thesehad sizes between the electron and ion skin depths, making this the first statistical sur-vey of mainly electron-scale structures within the same current sheet. It is possible tochange the parameters of the detection algorithm to find systematically larger structures,but the focus of this work was on the smaller-scale ones, which may potentially be em-bedded within larger structures.The estimated size distribution of the plasmoids was found to fit a decaying expo-nential, which is consistent with Fermo et al. (2010)’s statistical model of plasmoid dis-tribution, growth, and merging. The presence of push current sheets consistent with plas-moid merging provides further evidence of the importance of merging plasmoid dynam-ics to the overall structure of the reconnecting current sheet. The bulk motion of the struc-tures supports the analysis of Ergun et al. (2018), who observed a large-scale reconnec- –10–anuscript submitted to
Geophysical Research Letters tion region with turbulent outflows. We also noticed that structure sizes were positivelycorrelated with the structure speeds (not shown). However, the resolution limit of themagnetic field data prevents detection of small, fast-moving structures. Additionally, struc-ture speed is used to calculate size, so there could be some artificial correlation.The region was shown to have significant energy conversion from fields to parti-cles and vice versa, but net J · E was positive for particle energization at the expenseof the field energy. On average the structures were significant contributors to the net J (cid:107) E (cid:107) of the region, contributing ∼
40% of the net J (cid:107) E (cid:107) . In contrast, 97% of the J ⊥ · E ⊥ con-tribution was from the regions between the structures, meaning that these larger regionswere the main contributor to the overall positive J · E , which was comprised of 85% J ⊥ · E ⊥ from outside of the structures. This is consistent with a model of the structures asinjection sites, with strong localized J (cid:107) E (cid:107) able to quickly accelerate electrons, which thencan be slowly accelerated along with ions in the larger-scale regions of net positive J ⊥ · E ⊥ . This indicates that the majority of the particle acceleration from these turbulentreconnection regions can be modeled using larger-scale physics, with the smaller-scale J (cid:107) E (cid:107) injection sites largely ignored, or modeled as source terms of energetic electrons.Therefore, codes which are focused on capturing the larger-scale dynamics of reconnec-tion regions (such as Drake et al. 2019), perhaps with added electron injection, shouldaccurately describe the bulk of the particle energization in the reconnection region.Fitting the plasmoids to mathematical models would yield more details about theirstructure. We found that the observed plasmoids did not fit the constraints of force-freeor non-force free cylindrical models, but more general models were not tried. The useof other methods for ascertaining magnetic field topology, such as the first-order Tay-lor expansion method outlined in (Fu et al., 2015), would also provide greater insight intothe structure of this turbulently reconnecting region.It would be valuable to repeat the analysis of this paper using a different plasmoiddetection algorithm, such as the method detailed in Nakamura et al. 2016, which requiresstrong guide field. A machine learning algorithm could possibly be more comprehensivethan our algorithm, which has inflexible cutoffs for structure detection. This work didnot explore whether the observed current sheets were reconnecting or not. If a nuancedautomated method was developed to detect evidence of ongoing reconnection, additionalinformation about the dynamics of the reconnection region could be obtained. Acknowledgments
This work was supported by the U.S. Department of Energys Office of Fusion EnergySciences under Contract No. DE-AC0209CH11466 and by NASA under Grant No. NNH15AB29I.The data used is available from the MMS Science Data center (https://lasp.colorado.edu/mms/sdc/public/).
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