Magnetic Hump Associated with Electron Vortex at Dipolarization Front

As the plasma boundary between two distinct plasma populations, dipolarization fronts (DFs) host abundant kinetic-scale substructures that change their normal directions and thus cause their deformation. However, studies on such deformation caused by an electron vortex have been lacking. Here, we present novel observations of a subion-scale magnetic hump (MHu) associated with an oblique electron vortex at a DF through strengthening three components of the magnetic field. A radial electric field in the MHu, showing bipolar variation, is also associated with the electron vortex as it is mainly ascribed to the electron convection term. There is apparent energy conversion ( J→·E→ ∼−0.3 nw m−3) from the particles to the electromagnetic field in the MHu’s leading part, which is accompanied by inflow and outflow of electromagnetic energy (nonzero ∇·S→ ). The other regions of the DF host opposite energy conversion ( J→·E→ > 0). Broadband parallel electrostatic waves are also observed in the MHu. Our study provides insights into the kinetic-scale processes at DFs.


Introduction
Dipolarization fronts (DFs), magnetic transient structures characterized by a sharp increase of northward or southward magnetic field and a dramatic decrease of plasma density (Fu et al. 2012a;Zhou et al. 2015;Liu et al. 2021a), are usually observed accompanied by high-speed plasma flows (Nakamura et al. 2002a;Zhou et al. 2015;Liu et al. 2021a), so-called bursty bulk flows (Angelopoulos et al. 1994;Cao et al. 2006;Chen et al. 2019).They are suggested to play crucial roles in the transportation of mass, flux, and energy in the Earth's magnetosphere (Runov et al. 2009;Liu et al. 2014;Lui 2015;Wang et al. 2020) as they can propagate over long distances with the velocity of hundreds of kilometers per second (Runov et al. 2009;Ge et al. 2011) in the Earth's magnetotail.The generation of DFs is attributed to several mechanisms, including magnetic reconnection (Sitnov et al. 2009;Fu et al. 2013;Chen et al. 2023), flux rope erosion (Lu et al. 2015), spontaneous formation (Sitnov et al. 2013), flow braking (Panov et al. 2010;Birn et al. 2011), and interchange/ ballooning instabilities (Pritchett & Coroniti 2010;Lu et al. 2013).
On the magnetohydrodynamic scale, DFs, structured like saddles with a typical thickness in the order of ion inertial length, are often considered as tangential discontinuities that separate the colder and denser plasma in the ambient plasma sheet from the hotter and more dilute plasma in the high-speed plasma flows (Fu et al. 2012b;Schmid et al. 2019).The abrupt change of magnetic field on DFs would lead to an intense current perpendicular to the magnetic field in their tangential plane (Fu et al. 2012b;Yao et al. 2013), which drives strong energy conversion by combining the motional electric field (Huang et al. 2015;Khotyaintsev et al. 2017;Zhong et al. 2019;Liu et al. 2022).The DFs and their accompanied flux pile-up regions are believed to be favorable places for particle acceleration and pitch angle evolution due to the adiabatic mechanism (Wu et al. 2013;Duan et al. 2014;Dai et al. 2015;Liu & Fu 2019;Fu et al. 2020;Wei et al. 2023).
As the plasma boundary between two distinct plasma populations, DFs and their adjacent regions should host abundant kinetic-scale processes.There sometimes exist kinetic-scale magnetic dips prior to the DFs (Yao et al. 2013), attributed to dawnward current carried by either reflected ions (Zhou et al. 2014) or electrons (Huang et al. 2022).DFs and their adjacent regions are closely associated with various types of plasma waves, such as whistler waves (Hwang et al. 2014;Viberg et al. 2014;Chen et al. 2021Chen et al. , 2022)), lower hybrid drift waves (Zhou et al. 2009;Divin et al. 2015;Chen et al. 2021), and high-frequency electrostatic waves (Zhou et al. 2009;Zhang & Angelopoulos 2014;Yang et al. 2017;Chen et al. 2022), which can heat and accelerate electrons, and result in energy conversion (Huang et al. 2015;Khotyaintsev et al. 2017;Liu et al. 2023).DFs are sometimes unstable to the interchange instability, which can produce finger-like/bubble magnetic structures together with electron jets around them and an alternating duskward and dawnward electric field (Pritchett & Coroniti 2010;Yu et al. 2022).Lower-hybrid drift instabilities are commonly observed at DFs due to gradients of magnetic field and plasma density (e.g., Zhou et al. 2009;Divin et al. 2015), which can also produce rippled magnetic structures (Divin et al. 2015;Pan et al. 2018).DFs are deformed by such finger-like/rippled substructures, whose normal direction diverges from the initial normal direction of DFs.Such electron-scale finger-like/rippled structures are capable of accelerating electrons to a higher energy than that accelerated by typical smooth DFs (Bai et al. 2022).In addition to such an electron-scale substructure at DFs, a recent study has confirmed the existence of an electron-scale front, at which a strong electron jet and structured electric field drive intense energy conversion, while ions cannot respond (Chen et al. 2023).Even at DFs with a typical thickness in the order of ion inertial length, electron jets play crucial roles in energy conversion, as demonstrated by recent studies that show that strong energy conversion is primarily attributed to currents driven by electron jets (e.g., Liu et al. 2018;Zhou et al. 2019) rather than ions, as suggested in other studies (e.g., Khotyaintsev et al. 2017).Currents driven by electron jets can change the magnetic structure of DFs as well.Zhou et al. (2019) illustrated that two dawnward electron jets along a DF boost the northward magnetic field at its leading part while decreasing it at its trailing part.Jiang et al. (2020) reported that an electron vortex decreases the local northward magnetic field and causes an electron-scale plateau.However, the change in profile of DFs caused by electron jets does not seem to be significant, where the normal direction does not diverge and significant substructures similar to finger-like/rippled substructures produced by instabilities do not develop, but only a strengthening or weakening of their northward magnetic field.Liu et al. (2021a) performed a statistical study and found that only a few cases of electron vorticity ( ´ V e ) can generate intense magnetic field perturbations.However, they did not investigate these cases in detail.Therefore, it is unknown whether there are special electron jets that can induce significant substructures and cause DF deformation.
In this study, utilizing high-resolution data from the magnetospheric multiscale (MMS) mission (Burch et al. 2016), we provide observational evidence of a subion-scale magnetic hump (MHu) associated with an oblique electron vortex at a DF through strengthening the magnetic field in all three components.A bipolar electric field in the MHu is also associated with the electron vortex.The energy is transferred from particles to the electromagnetic field in the MHu, while other regions of the DF host opposite energy conversion.

Observations
In this study, the data used are taken by the following instruments: the direct current-coupled magnetic field (128 samples) by the Fluxgate Magnetometer (Russell et al. 2016); the alternating current-coupled magnetic field (8,192 samples) by the Search-Coil Magnetometer (Le Contel et al. 2016); the 3D electric field (8,192 samples) by the Axial Double Probe (Ergun et al. 2016) and the Spin-plane Double Probe (Lindqvist et al. 2016); and the 3D plasma data (30 ms for electrons and 150 ms for ions) from the Fast Plasma Investigation (Pollock et al. 2016).All data are measured by MMS operating in burst mode and are presented in geocentric solar magnetospheric (GSM) coordinates unless noted otherwise.
The event of interest was observed during the interval between 08:05:25 UT (Universal Time) and 08:05:55 UT on 2018 September 11, when the four MMS satellites with an interseparation of ∼50 km were located at [−14.54, 7.94, 0.07] RE (the Earth radius).Figure 1 presents an overview of the event.Since measurements from all four satellites are similar, only measurements from MMS1 are presented.During the whole interval, the MMS were located in the central current sheet according to the spectrum of differential energy flux of ions and electrons (Figures 1(a) and (b)).A DF, manifested by an abrupt increase of magnetic B z component from ∼−1 nT to ∼19 nT (Figure 1(c)) and a dramatic decrease of number density from ∼0.62 cm −3 to ∼0.30 cm −3 (Figure 1(d)), was observed between 08:05:38 UT and 08:05:42 UT, before which a magnetic dip was observed as well (Figure 1(d); Yao et al. 2013).There existed an apparent magnetic substructure around 08:05:39.80UT at the DF (Figure 1(c)), where all three magnetic components were strengthened, especially the B y component, which exceeded the B z component.The existence of a significant duskward magnetic field component at a DF with a northward magnetic field indicates a picture like hump (Figure 2(d)).Thus, the magnetic substructure is referred to as an MHu in the following text.The B z component shows a similar profile to that of DFs with a rippled substructure caused by instabilities and a plateau caused by an electron vortex, as presented in previous observations (Pan et al. 2018;Jiang et al. 2020), while the other two components show different features.Since the existence of the MHu possibly alters the normal direction of the DF, we analyzed the normal direction and velocity of the substructure and other regions separately.We focused on the MHu marked by yellow shadow (08:05:39.28-08:05:40.40UT) and the trailing part of the DF marked by gray shadow (08:05:40.40-08:05:42.00UT).
Based on the minimum variance analysis (MVA) on the magnetic field between 08:05:39.28UT and 08:05:40.28UT, the normal direction of the MHu, namely the minimum variable direction, was obtained as [0.97, 0.25, 0].Here, the ratio of the median eigenvalue to the minimum eigenvalue is as large as 240, confirming that the results are reliable.Based on the timing analysis, the normal velocity of the MHu was determined as 247 × [0.97, 0.20, 0.12] km s −1 .The normal direction of the trailing part was determined by MVA on the magnetic field during 08:05:40.40-08:05:42.40UT as [0.84 0.53 0.10] with the ratio of the median eigenvalue to the minimum eigenvalue as large as 23.The normal velocity of the trailing part was determined as 410 × [0.80, 0.60, 0.05] km s −1 .The normal directions obtained by these two methods are consistent and corroborate each other's reliability.The angles between the normal directions of these two regions are 25°, suggesting the deformation of the DF.The projection of the normal velocity of the trailing part on the normal direction of the MHu is ∼370 km s −1 , indicating that the trailing part moved faster than the former MHu.Thus, the DF may be growing with an ongoing accumulation of magnetic flux.By multiplying the duration of the MHu (1.12 s), the scale of the substructure is determined as ∼276 km or equivalently ∼0.89 is the ion inertial length (n ∼0.54 cm −3 is the average number density in the MHu).
A number density dip was simultaneously observed in the MHu (Figures 1(d) and (f)) due to pressure equilibrium (Figure 1(g)).The MHu was also together with an electric field of bipolar variation (Figure 1(h)), particularly the E z component up to ∼ ±20 mV m −1 .This is possibly attributed to the electron flow velocity of bipolar variation (Figure 1(i)), which will be demonstrated later.As can be seen, the V ey component exhibits negative-to-positive variation up to ∼ ±1000 km s −1 , while the V ez component exhibits positive-to-negative variation up to ∼ ±1500 km s −1 .Such bipolar variation of electron flow velocity is possibly ascribed to the encounter of an electron vortex.Different from the electron flow, the ion flow velocity shows no significant variations and is much slower than the   The B z component can be fitted by a hyperbolic tangent function (Fu et al. 2012a).The cyan curves and magenta curves in Figures 3(a , y z ) caused by the current driven by the electron vortex.To verify the speculation, we compared the average current density calculated by using electron moments (J emav = −enV e ) to the current density calculated by using the magnetic field perturbations ) and the hypothetical magnetic field ( = J cfit m  ´¾  B h 0 ), respectively.The J cMH and J cfit are calculated by the Curlometer method.The J cfit differs greatly from J emav , while the J cMH is consistent with the J emav , which supports that the magnetic field perturbation is attributed to the electron jet.Therefore, the MHu is indeed sustained by the electron vortex at the DF, which is illustrated in Figure 2(d).When the MMS crossed the MHu with enhancements of all three magnetic components, an electron vortex with V ey of negative-to-positive variation and V ez of positive-to-negative variation was detected.Such a picture is consistent with the observations.Now, we focus on the properties of the MHu.In the MHu, the X component of the electron convection term (- ´ V B e x ) exhibits a bipolar variation that varies in a similar fashion to the measured E x component and is roughly equal to the measured E x component (Figure 4(b)), suggesting that the electric field is primarily attributed to a combined contribution from the V ey and V ez components of bipolar variation (Figure 1(i)).Considering a cylindrical coordinate system, one can find that the electron vortex in the azimuthal direction and the magnetic field in the axial direction result in the electric field in the radial direction.Since the MMS crossed the MHu mainly along the X GSM direction, the radial electric field shows bipolar variation in the X GSM component.There also exists a decouple between electrons and the magnetic field as the measured electric field and electron convection term do not cancel each other out (Figures 4(b)-(d)).Since the current is predominantly carried by the electrons, the current density calculated by using the Curlometer method shows a profile similar to the electron velocity (Figure 4(e)), such as the J y and J z components of bipolar variation.Since the electron convection term cannot completely cancel out the measured electric field (Figures 4(b)-(d)), the electron velocity is not strictly perpendicular to the electric field, which will lead to energy conversion ( •   J E ).In the MHu, the strongest conversion occurs in its leading part, where the perpendicular energy conversion is dominant (Figure 4(f)).The negative energy conversion, stronger than the average value at DFs reported in a statistical study (Zhong et al. 2019), reaches ∼−0.3 nw m −3 , which indicates energy converted from the particles to the electromagnetic field.Since the current was predominantly carried by electrons, the energy conversion was dominantly driven by electrons.The divergence of the Poynting flux density ( •   S ) (Figure 4(g)) oscillates between ∼−1.5 nw m −3 and ∼1 nw m −3 in the MHu's leading part (before 08:05:39.80UT), while it is almost zero in the MHu's trailing part.In a word, there is apparent energy conversion from the particles to the electromagnetic field in the MHu's leading part, which is accompanied by inflow and outflow of electromagnetic energy.At the junction region between the MHu and the DF's trailing part (∼08:05:40.48UT), the electromagnetic field energy is transported into the region ( •   S < 0) and converted to particles S , which indicates the increase of electromagnetic field energy in this junction region, according to Poynting's law:

Conclusion and Discussion
In our study, we have presented observations of a subionscale MHu associated with an oblique electron vortex at a DF through strengthening the magnetic field in all three components.A radial electric field, showing bipolar variation, is also associated with the electron vortex as it is mainly ascribed to the electron convection term.There is apparent energy conversion ( •   J E ∼−0.3 nw m −3 ) from the particles to the electromagnetic field in the MHu's leading part, which is accompanied by inflow and outflow of electromagnetic energy (nonzero The other regions of the DF host opposite energy conversion ( •   J E > 0).Such energy conversion is primarily driven by electrons.Broadband parallel electrostatic waves are also observed in the MHu.Our study provides a new insight into the kinetic-scale substructures and physics at DFs.
Recently, some observational studies have illustrated that electron jets can modify the structure of DFs (Liu et al. 2018;Zhou et al. 2019;Jiang et al. 2020;Liu et al. 2021a).However, the change in profile of DFs caused by electron jets does not seem to be significant, where significant substructures similar to rippled substructures produced by instabilities do not develop, but only a strengthening or weakening of their northward magnetic field.Such changes cannot cause the deformation of DFs.A statistical study by Liu et al. (2021a) also argues that vorticity-induced magnetic field perturbations are not significant at DFs.In our study, for the first time, we demonstrate that an MHu is sustained by an electron vortex, leading to the deformation of the DF, where the normal direction of the MHu diverges from the initial normal direction of the DF.
One may consider the inverse process, where the change of magnetic field induces an electric field vortex and thus drives electron flows.In such a picture, the electron velocity is antiparallel to the electric field, which is inconsistent with the observations.In the observations, the electric field is mainly attributed to the electron convection term (- 4(b)), namely that the electron velocity is mainly perpendicular to the electric field.Therefore, such an inverse process cannot explain the observations.One may also consider that such a magnetic structure is attributed to the interaction between two DFs.However, the B y component is stronger than the B z component (Figure 1(e)) in the hump, inconsistent with the definition of DFs.
Such a magnetic substructure, electron flows, and electric field structure, formed self-consistently, can also be produced by plasma instabilities, such as mirror mode instability (Wang et al. 2016;Liu et al. 2021b), ballooning/interchange instability (Nakamura et al. 2002b;Pritchett & Coroniti 2010;Vapirev et al. 2013;Panov et al. 2020), and lower-hybrid drift instability (Divin et al. 2015;Pan et al. 2018).The MHu may not be attributed to mirror mode instability, as we find that  is generally lower than zero in the MHu (not shown) and thus the mirror mode remains stable.The substructures produced by the ballooning/interchange and the lower-hybrid drift instabilities show a similar profile, as demonstrated in previous simulation studies (Nakamura et al. 2002b;Pritchett & Coroniti 2010;Vapirev et al. 2013;Divin et al. 2015;Panov et al. 2020Panov et al. , 2022)).As illustrated by simulations (e.g., Figures 4 and 5 in Pritchett & Coroniti 2010, Figures 3 and 4 in Divin et al. 2015, and Figures 1 and 2 in Vapirev et al. 2013), finger-like substructures appear at intervals along the dawn-dusk direction (the Y GSM direction) on the equatorial plane (the X GSM − Y GSM plane), while there is no substructure along the northward direction (the Z GSM direction) on the meridian plane (the X GSM − Z GSM plane), which looks like a fence.In other words, these substructures look like bulgy DFs with a smaller scale along the dawn-dusk direction (the Y GSM direction), in which the magnetic field is dominantly northward.Thus, the self-consistent plasma flows along the edges of these substructures are mainly on the equatorial plane (the X GSM − Y GSM plane) (see Figure 6 in Pritchett & Coroniti 2010).However, the self-consistent electron vortex in our observation is oblique with both significant V ey and V ez of bipolar variation (Figures 1(i 10g in Divin et al. 2015, andFigure 1a in Panov et al. 2020) shows a similar profile to our observation (Figure 1(e)), there seems to be no B x or B y component peak/dip coincident with the B z peak in the simulations.The picture similar to our observation with simultaneous peaks/dips in all three magnetic field components seems to have been absent in the simulations even in the later stage when the substructures gradually erode away from the DFs (e.g., Movie S1 in Panov et al. 2022), as the magnetic field is dominantly northward in these substructures once they were generated.However, if these plasma instabilities develop in a local region at DFs rather than along the whole DFs, they may produce a picture similar to our observation.

Figure 1 .
Figure 1.Overview of an MHu at a DF on 2018 September 11.(a) Ion differential energy flux, (b) electron differential energy flux, (c) magnetic field, and (d) electron (black) and ion (red) number density.(e-l)A zoomed-in view of (e) the magnetic field, (f) electron and number density, (g) magnetic pressure (blue), plasma thermal pressure (red), and total pressure (black), (h) electric field, (i) electron velocity, (j) ion velocity, (k) electron temperature, and (l) ion temperature.
Figure 3 demonstrates the formation of the MHu associated with the electron vortex.As shown in Figures 3(a)-(d), the magnetic field B x and B y components exhibit no significant variation in the trailing part of the DF.Thus, we assume the original state of the DF and that the B x and B y components are constant across the DF.

Figure 2 .
Figure 2. Encounter of an electron vortex.(a-c) Electron flow vectors V exz , V exy , and V eyz on the X − Z, X − Y, and Y − Z plane, respectively.The MHu velocity has been subtracted from the measured electron flow velocity.(d) Cartoon to illustrate the formation of the MHu by the electron vortex.The red ellipse denotes the electron vortex, with the black arrowed curve denoting the flow direction.The 3D arrowed line denotes the MMS trajectory.
)-(d) denote the original B x and B y components obtained by averaging the measured B x and B y components during the interval 08:05:40.50-08:05:41.00UT.The black curves in Figures 3(a)-(d) denote the original B z component fitted by hyperbolic tangent functions.The difference value between the measured magnetic field (

Figure 3 .
Figure 3.The MHu sustained by the electron vortex by using Ampere's law.(a-d) The measured magnetic field ( [ ]  = B B B B , , x y z ) and the hypothetical initial magnetic field of the DF ( [ ] ¾  = B B B B , , h xav yav zfit ) from (a) mms1, (b) mms2, (c) mms3, and (d) mms4.(e) The X component, (f) Y component, and (g) Z component of current density obtained from electron moments (J emav = − enV e , red), the hypothetical initial magnetic field ( m =  ´¾  J B h cfit 0 , black), and the magnetic field perturbation ( ( ) m =  ´¾  J d B

Figure 4 .
Figure 4. Properties of the MHu.(a) Magnetic field, (b-d) X component, Y component, and Z component of the measured electric field and the electron convection term, (e) current density from the Curlometer method, (f) energy conversion, and (g) divergence of the Poynting flux.(h-j) The power spectrum of (h) the magnetic field, (i) the perpendicular electric field, and (j) the parallel electric field.
) and 2(a)-(d)), not confined to the X GSM − Y GSM plane, as in the simulations.Although the magnetic field B z component in the simulations (e.g., Figure 9(a) in Pritchett & Coroniti 2010, Figure