Cluster Observations of Energetic Electron Acceleration Within Earthward Reconnection Jet and Associated Magnetic Flux Rope

We study acceleration of energetic electrons in an earthward plasma jet due to magnetic reconnection in the Earth magnetotail for one case observed by Cluster. The case has been selected based on the presence of high fluxes of energetic electrons, Cluster being in the burst mode and Cluster separation being around 1,000 km that is optimal for studies of ion scale physics. We show that two characteristic acceleration mechanisms are operating during this event. First, significant acceleration is achieved inside the magnetic flux pile‐up of the jet, the acceleration mechanism being consistent with betatron acceleration. Second, strong energetic electron acceleration occurs in magnetic flux rope like structure forming in front of the magnetic flux pile‐up region. Energetic electrons inside the magnetic flux rope are accelerated predominantly in the field‐aligned direction and the acceleration can be due to Fermi acceleration in a contracting flux rope.

showed a difference in the acceleration on both sides of the island and identified the betatron acceleration mechanism as the dominant player (Zhong et al., 2020). Statistical studies of magnetic flux ropes have shown that only about one fourth of them show increased fluxes of energetic electrons (Borg et al., 2012). Numerical simulations have shown energetic electron production in kinetic scale flux ropes . The important role of ion-scales magnetic flux ropes for generation of energetic electrons has been shown also in large-scale simulations (Zhou et al., 2018).
The reconnection jet fronts can be one of the places of the magnetic island formation. Recent high resolution numerical simulations have shown the process of flux rope formation in front of reconnection jets, however they could not study the energetic electron properties (Lapenta et al., 2015). The experimental observations of such island formation are scarce. In this paper we present a detailed study of a single event showing high fluxes of energetic electrons generated inside kinetic-scale magnetic flux rope in front of the reconnection jet and associated magnetic pile-up region.

Observations
We have selected for deeper study one event of high suprathermal/energetic electron fluxes associated with the reconnection jet in the Earth's magnetotail based on several criteria: a) Cluster is in the magnetotail, b) the presence of strong energetic electron acceleration, c) reconnection jet associated with a magnetic flux pile-up region, d) Cluster separation is comparable to the ion scales allowing us to study microphysics of energetic electron acceleration, e) Cluster is running in Burst Mode (high telemetry mode), providing the highest resolution data from both field and particle instruments. Based on these criteria we could identify several events. For the detailed study presented in this paper we select the event around 2004-10-15 13:26 UT.
During the selected event the four Cluster spacecraft C1 to C4 are located close to the neutral sheet at [−12.5, 8.3, 0] E R GSM, see Figure 1. The Cluster separation is 1,000 km which is comparable to a characteristic local ion scale, which is the gyroradius of 10 keV proton in 10 nT field  i  1,400 km. Of particular importance for the paper is that C4 is located most tailward and C1 is located most northward.
We use measurements of magnetic field (FGM instrument), electric field (EFW), ions (CIS) and electrons (PEACE, RAPID) (Escoubet et al., 1997). It is important for our study that the particle instruments require one spacecraft spin of 4 s to produce a full 4 -sky coverage of distribution functions. At any instantaneous measurement the particle instruments measure only a cross-section of the distribution function that in the case of energetic electron instrument RAPID is a    180 22.5 slice divided in nine sectors. Therefore, depending on the direction of the ambient magnetic field, instantaneous measurement may not cover all pitch angles. During the event Cluster was in the Burst Mode (high-telemetry mode) allowing detailed and high-time resolution measurements of particles and fields. Figure 2 shows the large-scale context of the event as seen by C1. During most of the event | | B X is close to zero or is small in comparison to its expected lobe field value of 25 nT (seen as a maximum value of X B when C1 enters the lobe), see Figure 2a. Thus C1 is located inside the plasma sheet close to the neutral sheet. Similar argument applies to the other Cluster spacecraft (not shown). The plasma sheet can be also identified by the presence of several keV hot thermal electrons, see   Figure 2b, being the highest in the beginning of the interval with the peak reaching 1,500 km/s at 13:25:30 UT. Around the peak of X V we observe an increase in Z B , and the region of increased Z B (flux pile-up region) continues for a few minutes after the peak in velocity. Also, around the X V peak we observe a significant density decrease, Figure 2e. All these signatures are characteristic of earthward jets produced by the reconnection tailward of the spacecraft. Figure 2c shows the energetic electron spectrogram, by energetic we mean the electron energies are ten times and more larger than the thermal energy of electrons. Very strong increase in energetic electron fluxes is seen in association with the ion jet and magnetic flux pile-up region. The magnetic flux pile-up region and its associated energetic electron generation is the focus of this paper.
There is another smaller magnetic flux pile-up region during the second part of interval in Figure 2. There are ion flows with a localized peak of about 500 km/s around 13:34:30 UT and distinct magnetic flux pileup associated to this peak. However, there is no associated peak in energetic electron flux. It is interesting to note that the second pile-up region was included in a large statistical study  analyzing energetic electron acceleration at the dipolarization fronts, while the first one is not. The reason for this is that the second pile-up region has a very distinct and sharp front which was used as a condition for event VAIVADS ET AL.  selection in previous studies . The first pile-up region does not have such a front, but it is associated with strong energetic electron acceleration. This indicates that many pile-up regions with strong energetic electron generation may be missed by earlier studies of dipolarization fronts due to their complex front structure. We return in the discussion part to the possible reasons why the second pile-up region does not show any signs of energetic electron generation.  B GSM, (c) X V ISR2 from CIS-CODIF measurements and from  E B-velocity estimates using electric field measurement, (d) same but for Y ISR2 component, (e) energetic electron differential flux as seen by C4, (f) current estimate based on the curlometer method, (g)  j B-force based on the curlometer method.
around 13:25:15 UT C1 is observing B larger than 20 nT indicating that C1 enters into the lobe during that time period. Figure 3b shows that all spacecraft observed magnetic flux pile-up, seen as increase in the Z B . All spacecraft observe the entering into the pile-up region almost simultaneously consistent with the pile-up region passing spacecraft with a high speed. However, the exiting of the pile-up region takes much longer time and thus the boundary is moving slowly, also consistent with a low ion velocity as seen in Figure 2. We can also see that C4 is the first that sees the Z B decrease after the passage of the pile-up region. This is consistent with C4 being the most tailward spacecraft, see Figure 1. Figure 3c shows the sunward component (X-component in the ISR2 reference frame) of the  E B-drift and ion velocities. The ISR2 reference frame is individual to each of the satellites, it is close to GSE but has X and Y components in the satellite spin plane. In general the  E B-drift velocities are higher than the ion velocities, one reason being that the ion instrument measuring velocity is not able to observe all thermal ions due to their high thermal energy which exceeds the maximum energy that can be measured by the CODIF instrument. Figure 3d shows the velocity component in the dawn-dusk direction (ISR2 Y). Large flow in the dawn direction can be seen before the magnetic pile-up. During the peak sunward velocity, there are no significant dawn-dusk flows. Figure 3e shows the energetic electrons flux observed by C4 at a spin resolution. There is a general increase of energetic electron flux associated with the sunward flow seen both before and during the magnetic flux pile-up region. However, the peak fluxes are very localized and there can be large change between the measurements performed during the consecutive spacecraft spins (satellite spin is 4 s). The last two panels, Figures 3f and 3g, show the current j and the  j B force estimates based on the multi-spacecraft curlometer technique. A significant positive Y j can be seen in Figure 3f during the first half of the interval, while the current gets week during the second half where the plasma velocity is small and Z B dominates. Finally, Figure 3g shows the  j B force acting on plasma. There is a significant positive  ( ) X j B during the first half of the interval corresponding to the earthward jet. In the center of interval there is a significant negative  ( ) Z j B as the spacecraft constellation is slightly above the center of the current sheet. The negative  ( ) Y j B in the beginning of the interval is consistent with strong plasma flows in the -Y direction. To understand the details of the energization process, we are plotting the subspin resolution data. Normally it takes one spacecraft spin to measure the full 3D distribution of electrons. However, assuming that electrons are gyrotropic, we can use the instantaneous 2D measurements during the spin (subspin resolution) to obtain the electron measurements corresponding to a limited range of pitch-angles. This range will vary during the spin due to varying orientation of B relative to the 2D plane of the measurement and this variation can be clearly seen in the plot. The gray areas show regions that have not been accessible to the measurement. C1 observes the lowest fluxes because C1 is the furthest away from the center of the current sheet as can be seen from C1 seeing the largest B values in Figure  during the whole event. In the discussion we argue that this region is consistent with being a magnetic flux rope. There are several important observations related to these electrons. a) Magnetic field shows a negative-positive bipolar Z B variation near the region of the highest fluxes, the region is marked yellow in Figure 5a. b) The peak fluxes on C3 and C4 coincide with the center of bipolar Z B variation. The center of the bipolar structures where Z B crosses zero (going from negative to positive values) are marked by solid lines for C3 and C4 respectively. c) The magnitude of magnetic field shows a dip at the location of the highest fluxes at C3 and C4. d) The highest fluxes of electrons are not necessarily centered around  90 pitch angle. There even seems to be a tendency for electrons to be more field-aligned than perpendicular. e) C2 sees lower electrons fluxes, there is no dip in magnetic field magnitude and also the bipolar structure is less clear. We will discuss later that these observations are consistent with the presence of a magnetic flux rope.
To better characterize this magnetic structure in Figures 5e-5h, we plot various quantities computed using 4-point measurements by Cluster. Figure 5e shows the average magnetic field. It can be seen that during the time of the bipolar Z B variation there is also a strong Y B component. Such a Y B component is consistent with core field of magnetic flux rope as we will show in the discussion part. Figure 5f shows the current, the peak in Y j is coinciding with the region of highest energetic electron fluxes. Figure 5g shows  j B force. During the whole interval    positive signature in  ( ) X j B . Finally, Figure 5h shows the current parallel to the average magnetic field j ‖ , and we can see a strong peak in j ‖ coinciding with the location of high energetic electron fluxes.

Discussion
Based on the observations presented above we can make the overall interpretation of the event. During the time interval 13:25--13:26 we see a high-speed earthward jet that reaches velocities above 1,000 km/s in ion data and more than 2000 km/s in  E B-drift velocity. This jet is consistent with being an earthward reconnection jet. One reason why the ion velocity shows values lower than the  E B-drift velocity is that a significant fraction of thermal ions have energies above the energy range of the CODIF instrument which is used to estimate the ion velocity. During about 2 min following the peak of the jet velocity we observe a region where Z B is dominating, with the Z B values of the order of 10 nT. We interpret this as the magnetic flux pile-up region driven by the jet. However, during the last part of the Z B -dominated region X V decreases to small values and even reverses the sign. This suggests that spacecraft are on the dipolar field lines close to the jet braking region. Thus the spacecraft are located in the right region to observe the incoming magnetic pile-up region driven by the reconnection jet, how it brakes due to the near Earth dipolar-like field and how the jet driven magnetic pile-up becomes part of the near Earth dipolar field. Additional support for this hypothesis comes from the Y j observations, see Figure 3. In the beginning of the interval Y j is strong and positive both before and in the beginning of the magnetic flux pile-up region. This is consistent with spacecraft located in the thin current sheet in the beginning of the interval followed by reconnection jet driven magnetic flux pile-up. As the jet brakes and its velocity decreases to zero also Y j value goes to zero consistent with spacecraft being on dipolar field lines. Finally, on the exit boundary of dipolar like field region Y j is negative as expected when being on the outer region of dipolar field lines. Thus, we are observing the whole chain consisting of the onset of fast reconnection jet, followed by jet braking and spacecraft location being close to the dipolar field lines where the jet brakes.
During the interval of jet we observe significantly increased energetic (40-400 keV) electron fluxes. The Cluster separation of 1,000 km comparable to characteristic ions scales allows for detailed exploration of energetic electron acceleration. We observe that there are several mechanisms in play providing the acceleration. In the pile-up region the dominant acceleration is occurring at close to  90 pitch angles, with the highest fluxes observed at 13:25:30 UT simultaneous with the detection of the highest jet velocities. Thus, this region is most probably a magnetic flux pile-up region driven by the reconnection jet and what we observe is the betatron acceleration as has been reported in earlier studies (Fu et al., 2011;Khotyaintsev et al., 2011). However, high fluxes of energetic electrons are also observed in the turbulent region in front of the pile-up region, as can be clearly seen in Figures 4 and 5. Closer inspection of data in Figure 5 shows that this turbulent region contains the highest electron fluxes during the whole event (observed during a short time interval around 13:25:20 UT).
Multi-spacecraft observations allow us to clearly identify the structure of the region with the highest electron fluxes at 13:25:20 UT. The magnetic field observations are consistent with it being a flux-rope-like structure: a negative-positive Z B variation for earthward moving structure, converging  j B force, strong parallel current in the center of the structure and a significant core field Y B . The characteristic cross-section of the flux rope is of the order of the spacecraft separation (ion scales). This is observed both in the X-direction and Z-direction. In the X-direction the two spacecraft separated in X-direction, C2 and C4, simultaneously observe peak values of Z B of opposite sign consistent with C2-C4 separation being comparable to the flux rope size. In the Z-direction, C1 is separated by 1,000 km from the other three spacecraft, and while C1 sees lobe field values the other three spacecraft are still near the center of the current sheet; this is also consistent with the flux-rope scale being comparable to the spacecraft separation. Figure 6 summarizes in a simplified sketch the characteristic separation of spacecraft in comparison to the thickness of the current sheet and the size of magnetic island and illustrates how the spacecraft cross the flux rope.
There have been studies showing presence of high fluxes of energetic electrons in kinetic-scale magnetic islands in the thin current sheet close to the reconnection onset Retinò et al., 2008). Both studies show that the highest electron fluxes where detected in the center of magnetic island, while the island was embedded into a thin reconnecting current sheet. When it was possible to measure pitch angle VAIVADS ET AL. 10.1029/2021JA029545 8 of 13 distribution, it was concluded that main acceleration is of energetic electrons at perpendicular direction to the magnetic field. The study by Retinò et al. (2008) also analyzed the pitch-angle distribution and found the highest fluxes for electrons close to 90 pitch angles suggesting that they can be energized by the betatron mechanism. Similarly, there is a case study using the MMS observations of energetic electrons inside an ion-scale magnetic island with perpendicular acceleration of electrons (Zhong et al., 2020). Here, we show that magnetic islands can also form in front of the magnetic pile-up region driven by the reconnection jet. In addition, we show that other acceleration mechanisms than betatron acceleration can be at play in the center of the magnetic island. This is related to the fact that we observe the dominant acceleration in the field-aligned direction, and not in the perpendicular direction as expected for the betatron mechanism.
There can be several possible electron acceleration mechanisms inside the flux rope. One is the direct acceleration by the parallel electric field (Pritchett, 2006). The presence of the strong parallel current in the center of the flux rope suggest that there should be also strong parallel fields forming leading to acceleration of electrons in the anti-parallel direction. The presence of parallel fields inside the flux ropes is indirectly supported by observations of electron holes inside the ropes (Khotyaintsev et al., 2010). There is some indication in data, see Figure 5, that C4 which looks in the anti-parallel direction detects the highest fluxes, however, there are too few data points to make a solid conclusion. It is also seen, that C3 that is looking predominantly in the parallel direction also sees increased electron fluxes. Thus there should be additional acceleration mechanisms in play, such as wave-particle interaction or Fermi acceleration in contracting flux rope (Drake et al., 2006). Possible importance of the Fermi acceleration in magnetic flux ropes has been demonstrated also in recent 2D numerical simulations of magnetic reconnection (Arnold et al., 2021). Those simulations show that in case of not too large guide field, which is the case for the magnetotail reconnection, magnetic flux ropes can provide efficient acceleration of energetic electrons. Such a Fermi acceleration mechanism could work also in our case. First, the size of the cross-section of magnetic flux rope most probably is decreasing because flux rope should be gone once the jet pile-up region hits the near Earth dipolar field. Thus the decrease of the cross-section effectively leads to contraction of field lines with a following Fermi acceleration. Second, in 3D the flux rope should have a finite length in the direction along the core of the flux rope, corresponding to out-of-plane direction in 2D plots of a magnetic island. In such a case the initial build-up of the flux-rope's core field efficiently corresponds to shortening the length of the field line between the ends of the flux rope. If there are trapped electrons inside the flux rope then this shortening of the field lines will again effectively lead to Fermi acceleration. Thus, both mechanisms separately or in combination can lead to Fermi acceleration inside the flux rope that we observe.
The few detailed case studies of electron acceleration inside flux ropes clearly show that more than one acceleration mechanism can be at play and more studies are needed to understand the relative importance of all those mechanisms. In addition, an important question remain of the relative importance of energetic electron acceleration mechanisms due to acceleration inside the magnetic pile-up region and the turbulent region in front of the jet, including magnetic flux ropes. In our study, the energetic electrons inside the flux rope are observed for a much shorter time and smaller volume angle than the energetic electrons in the pile-  up region. This suggest that the main pile-up region is still the largest source of energetic electrons. However, the energetic electrons in the flux rope move more parallel to magnetic field and thus can easier escape the region than electrons in the pile-up region which are more perpendicular and therefore more trapped. Thus, there can still be a significant contribution from the flux-rope to the overall energetic electron generation, but more studies are needed to really distinguish the relative contribution of different energization processes.
Finally, we discuss the second pile-up region that we mentioned discussing Figure 2 and on which we zoom in Figure 7. The magnetic flux pile-up as seen in Figure 7a has very sharp and clear Z B increase, there is a significant up to 500 km/s earthward X V component, see Figure 7b, and as such this event has passed the criteria for earlier dipolarization front studies. However, in comparison to the first pile-up region, this event shows very low flux levels of high energy electrons, see Figures 7c and 7e. The thermal electron population shown in Figure 7d shows that spacecraft are in the plasma sheet, with relatively small changes in the properties of the electron population. Also density observations in Figure 2e show that density varies inside the jet and the pile-up region but stays close to the surrounding values which is in contrast to the first pile-up region that shows very low densities. One possible explanation might be that the electrons in this second flux pile-up region were initially accelerated at a reconnection site different from the one associated to the first pile-up region and associated to different plasma sheet source electrons. However, we find this unlikely since the two pile-up regions are observed with about 10 min time differences during which the overall plasma sheet conditions around the reconnection site should have not changed substantially. Instead, our interpretation is that the second pile-up region is associated to a local flow enhancement and is not the reconnection jet itself. The flow enhancement can still be caused by a reconnection jet and jet braking further away from the spacecraft. This interpretation is supported by the Y V and  j B force observations, see Figures 7b and 7g. The Y V is larger than the X V and the  j B force in Y direction, consistent with the pile-up region pushing the plasma in front of it in the Y direction. This sideways motion can be generated by an incoming jet as it brakes or interacts with another reconnection jet ahead of it, and it pushes surrounding plasma sideways. Such scenario was recently suggested by observations of two consecutive reconnection jets, where the trailing jet had a Y V much larger than X V while for the leading jet the largest velocity was X V (Catapano et al., 2021). Inside the second pile-up region there is some energetic electron energization in perpendicular direction, see Figure 7e, that is most probably caused by the betatron acceleration. However, following the arguments above, it is likely that such energetic electrons come from the pile-up of the local plasma sheet plasma which has lower fluxes of energetic electrons compared to those with the reconnection jet itself. For this reason, the overall fluxes of energetic electrons stay small and this second pile-up region is less important for energetic electron generation compared to the case where the piling-up plasma comes directly from the reconnection site with preexisting high flux levels of energetic electrons, which is the case for the first pile-up region. The highest fluxes of energetic electrons in the magnetic flux pile-up and jet braking regions would then be expected for jets produced by lobe reconnection, as has been suggested also earlier in for example, Vaivads et al. (2011). Although less important for electron acceleration, the boundary in front of the second pile-up region shows strong parallel current, see Figure 7h, suggesting that this kind of pile-up regions can be important for field aligned coupling to the ionosphere.

Summary and Conclusions
We present a detailed case study of energetic electron acceleration observed in the region where an earthward reconnection jet reaching up to 2,000 km/s brakes close to the near-Earth dipolar-like field. We use data from Cluster spacecraft separated by 1,000 km that is comparable to the characteristic ion scales (gyroradius of thermal ions). Such separation scale is well suited for applying multi-spacecraft methods to estimates current and  j B force on characteristic ion kinetic scales in the region. We show that the energetic electrons are accelerated both in the magnetic flux pile-up region of the jet mainly through betatron acceleration, as well as in a turbulent region in front of the jet. Inside the turbulent region we can clearly identify a magnetic flux rope or magnetic island-like structure that shows the highest fluxes of energetic electrons during the whole event. The highest acceleration region coincides with the center of the flux rope where we also observe the largest current during the event, including the largest field-aligned current. The energetic electrons inside the flux rope have the highest fluxes in the field-aligned directions consistent with being accelerated by either parallel electric field or Fermi acceleration due to contraction of the magnetic VAIVADS ET AL.  in GSM, (b) plasma velocity in GSM, (c) high energy electron differential number flux, (d) electron differential number flux, (e) pitch angle spectrogram of energetic electrons measured by the RAPID channel of 60 keV at subspin resolution, the areas marked in gray correspond to pitch angles not accessible for measurement during that moment of the spin, the magnetic field magnitude is overplotted with a black line (the y-axis range corresponds to 0-25 nT). (f) current in GSM based on curlometer method, (g)  j B-force in GSM, (h) current parallel to the ambient magnetic field. pile-up region observed during the same interval but showing much lower fluxes of energetic electrons. The second pile-up region is most probably formed due to local flow enhancement in the plasma sheet and does not contain plasma coming directly from the reconnection site. We conclude that for highest electron energization it is important that the pile-up region is forming from plasma coming from the reconnection site with preexisting high levels of energetic electrons.

Data Availability Statement
Cluster data are downloaded from Cluster Science Archive https://csa.esac.esa.int/csa-web/.