The structure of a perturbed magnetic reconnection electron diffusion region G. Cozzani, * Yu. V. Khotyaintsev, D. B. Graham, and M. Andr´ e Swedish Institute of Space Physics, Uppsala, Sweden J. Egedal Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA A. Vaivads Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden A. Alexandrova and O. Le Contel Laboratoire de Physique des Plasmas, CNRS, Sorbonne Universit´ e, Universit´ e Paris-Saclay, Observatoire de Paris, ´ Ecole Polytechnique Institut Polytechnique de Paris, Palaiseau, France R. Nakamura Space Research Institute, Austrian Academy of Sciences, Graz, Austria S. A. Fuselier and J. L. Burch Southwest Research Institute, San Antonio, Texas, USA C. T. Russell University of California, Los Angeles, California, USA (Dated: March 24, 2021) We report in situ observations of an electron diffusion region (EDR) and adjacent separatrix region. We observe significant magnetic field oscillations near the lower hybrid frequency which propagate perpendicularly to the reconnection plane. We also find that the strong electron-scale gradients close to the EDR exhibit significant oscillations at a similar frequency. Such oscillations are not expected for a crossing of a steady 2D EDR, and can be explained by a complex motion of the reconnection plane induced by current sheet kinking propagating in the out-of-reconnection-plane direction. Thus all three spatial dimensions have to be taken into account to explain the observed perturbed EDR crossing. Magnetic reconnection is a fundamental plasma pro- cess that yields to the topological reconfiguration of the magnetic field and the concurrent energization and accel- eration of plasma species [1]. Reconnection is found in a variety of environments in space and astrophysical plas- mas [2] and dedicated laboratory experiments [3, 4]. A crucial constituent of the collisionless reconnection pro- cess is the electron diffusion region (EDR), where the demagnetization of both ions and electrons enables the magnetic field topology change. As a result, the processes that take place in the EDR affect the system up to its global MHD scales. Despite their central role, these pro- cesses are still largely unknown. In particular, the con- tribution of plasma waves and instabilities to the EDR dynamics as well as to the overall reconnection process remain unclear [5, 6]. Waves and instabilities operat- ing in the center of the current sheet could affect the two-dimensional, steady and laminar reconnection pic- ture. For guide-field reconnection, in particular, the role of streaming instabilities leading to turbulence develop- ment at the reconnection site has been discussed in simu- lation studies [7, 8] and electrostatic turbulence promot- ing electron heating is observed at a magnetopause EDR [9]. Among the instabilities that can develop in current lay- ers, the lower hybrid drift instability (LHDI) has been ex- tensively studied since it can potentially provide anoma- lous resistivity sustaining the reconnection electric field [10]. Some early observational work supported this idea [11]. However, spacecraft observations at the magne- topause [12–14] and magnetotail [15, 16] suggest that electrostatic LHDI modes could not supply the necessary resistivity, consistent with the fact that these modes de- velop at the edges of the current sheet but are stabilized in the center [17]. On the other hand, eigen-mode anal- ysis and kinetic simulations of ion-scale Harris current sheets [18, 19] suggest that electromagnetic LHDI modes can penetrate in to the center of the current layer. Such modes are characterised by lower growth rates and longer wavelength compared to the electrostatic modes. Elec- tromagnetic fluctuations in the lower-hybrid frequency range were observed within a reconnecting current sheet in the MRX laboratory experiment [20] but in situ obser- vations of electromagnetic LHDI modes within the EDR are still lacking. Indeed, before the launch of the Magnetospheric Multi- arXiv:2103.12527v1 [physics.plasm-ph] 23 Mar 2021
Transcript
The structure of a perturbed magnetic reconnection electron diffusion region
G. Cozzani,∗ Yu. V. Khotyaintsev, D. B. Graham, and M. AndreSwedish Institute of Space Physics, Uppsala, Sweden
J. EgedalDepartment of Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA
A. VaivadsDepartment of Space and Plasma Physics, School of Electrical Engineering and Computer Science,
KTH Royal Institute of Technology, Stockholm, Sweden
A. Alexandrova and O. Le ContelLaboratoire de Physique des Plasmas, CNRS, Sorbonne Universite, Universite Paris-Saclay,
Observatoire de Paris, Ecole Polytechnique Institut Polytechnique de Paris, Palaiseau, France
R. NakamuraSpace Research Institute, Austrian Academy of Sciences, Graz, Austria
S. A. Fuselier and J. L. BurchSouthwest Research Institute, San Antonio, Texas, USA
C. T. RussellUniversity of California, Los Angeles, California, USA
(Dated: March 24, 2021)
We report in situ observations of an electron diffusion region (EDR) and adjacent separatrixregion. We observe significant magnetic field oscillations near the lower hybrid frequency whichpropagate perpendicularly to the reconnection plane. We also find that the strong electron-scalegradients close to the EDR exhibit significant oscillations at a similar frequency. Such oscillationsare not expected for a crossing of a steady 2D EDR, and can be explained by a complex motion of thereconnection plane induced by current sheet kinking propagating in the out-of-reconnection-planedirection. Thus all three spatial dimensions have to be taken into account to explain the observedperturbed EDR crossing.
Magnetic reconnection is a fundamental plasma pro-cess that yields to the topological reconfiguration of themagnetic field and the concurrent energization and accel-eration of plasma species [1]. Reconnection is found in avariety of environments in space and astrophysical plas-mas [2] and dedicated laboratory experiments [3, 4]. Acrucial constituent of the collisionless reconnection pro-cess is the electron diffusion region (EDR), where thedemagnetization of both ions and electrons enables themagnetic field topology change. As a result, the processesthat take place in the EDR affect the system up to itsglobal MHD scales. Despite their central role, these pro-cesses are still largely unknown. In particular, the con-tribution of plasma waves and instabilities to the EDRdynamics as well as to the overall reconnection processremain unclear [5, 6]. Waves and instabilities operat-ing in the center of the current sheet could affect thetwo-dimensional, steady and laminar reconnection pic-ture. For guide-field reconnection, in particular, the roleof streaming instabilities leading to turbulence develop-ment at the reconnection site has been discussed in simu-lation studies [7, 8] and electrostatic turbulence promot-ing electron heating is observed at a magnetopause EDR
[9].Among the instabilities that can develop in current lay-
ers, the lower hybrid drift instability (LHDI) has been ex-tensively studied since it can potentially provide anoma-lous resistivity sustaining the reconnection electric field[10]. Some early observational work supported this idea[11]. However, spacecraft observations at the magne-topause [12–14] and magnetotail [15, 16] suggest thatelectrostatic LHDI modes could not supply the necessaryresistivity, consistent with the fact that these modes de-velop at the edges of the current sheet but are stabilizedin the center [17]. On the other hand, eigen-mode anal-ysis and kinetic simulations of ion-scale Harris currentsheets [18, 19] suggest that electromagnetic LHDI modescan penetrate in to the center of the current layer. Suchmodes are characterised by lower growth rates and longerwavelength compared to the electrostatic modes. Elec-tromagnetic fluctuations in the lower-hybrid frequencyrange were observed within a reconnecting current sheetin the MRX laboratory experiment [20] but in situ obser-vations of electromagnetic LHDI modes within the EDRare still lacking.
Indeed, before the launch of the Magnetospheric Multi-
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scale (MMS) mission [21], observational evidence of theseinstabilities occurring at the EDR were prevented by thelower resolution of the available particle measurementsand by the limited knowledge of the EDR and relatedelectron-scale processes. Electrostatic lower hybrid driftwaves (LHDW) in the EDR have been investigated onlyrecently [22].
In this Letter, we report MMS observations of a mag-netotail electron diffusion region and adjacent separatrixregion characterised by unexpected electric field, electronvelocity and magnetic field oscillations. We compare 2Dfully kinetic simulations and four-spacecraft observationsto investigate the mechanism responsible for the observedoscillations.
MMS encountered an EDR on August 10, 2018 at12:18:33 UTC when it was located in the Earth’s magne-totail at [−15.2, 4.6, 3.1]GSM RE (in Geocentric SolarMagnetospheric system). The indicative signatures ofan EDR [23–25] – including super-Alvenic electron jets,enhanced electron agyrotropy, intense energy conversionand crescent-shaped electron distribution functions – areobserved [26]. During this event, MMS stays mostly inthe plasma sheet (B ∼ 7 nT and n ∼ 0.17 cm−3). Aweak guide field Bg ∼ 2 nT ∼ 0.13Binflow is present(Binflow is the inflow magnetic field computed in the in-terval 12:21:20-12:21:40 [26]). The mean inter-spacecraftseparation ∼ 20 km is comparable to the electron inertiallength de ∼ 13 km. As a first step, we determine the ap-propriate LMN coordinate system and establish the MMStrajectory relative to the EDR by adopting methods re-ported in Refs.[27, 28]. For this we use a 2D-3V kineticPIC simulation performed with the VPIC code [29] whichmimics the MMS event in terms of guide field (simulationrun featuring upstream βe,∞ = 0.09 and Bg = 0.1 [30]).The realistic ion-to-electron mass ratio mi/me = 1836allows us to establish a one-to-one correspondence be-tween the dimensionless units of the simulation and thephysical units of MMS data.
Fig.1 shows an overview of the EDR crossing. Allthe quantities are shown in the LMN coordinate system(L = [0.96, −0.15, −0.22], M = [0.17, 0.98, 0.03], N =[0.22, −0.07, 0.97] in GSM, obtained via an optimisa-tion approach aided by simulation data [27]). The MMStrajectory relative to the EDR is shown in Fig.1(j). Thetrajectory is reconstructed in interval A–F (12:18:28.9-12:18:36.5) of Fig.1. The part of trajectory correspond-ing to interval 12:18:28.9-12:18:34.8 is reconstructed byadapting the method of Ref.[28] to include the electronvelocity ve,M and the electron temperature anisotropy.For the part of the trajectory corresponding to interval12:18:34.8-12:18:36.5, we use the method of Ref.[27] (in-cluding EN and BL) which allows us to reproduce theobserved electric field oscillations.
MMS is initially located south and tailward of thereconnection site, corresponding to BL < 0 (Fig.1(a)),BN < 0 (Fig.1(c)) and Vi,L < 0 (not shown). Then,
MMS crosses the diffusion region diagonally so that BL
and BN change from negative to positive. MMS sam-ples mainly the positive lobes of the Hall quadrupolarfield (BM > Bg, Fig.1(b)). Figure 1(h) shows the elec-tron temperature anisotropy Te,||/Te,⊥, where paralleland perpendicular refer to the local magnetic field direc-tion. The Te,||/Te,⊥ peak observed at 12:18:30.5 indicatesthat MMS performed a brief excursion into the inflow re-gion, where Te,||/Te,⊥ is expected to increase [31, 32],before approaching the inner EDR (interval C–D) [33].Interestingly, during the current sheet crossing (intervalB–E), MMS observes significant magnetic field oscilla-tions δB (Fig.1(i)) reaching ∼ 20% of the upstream mag-netic field in the plasma sheet (∼ 7 nT ). Applying thetiming method [34] on the sharp BL variation in inter-val 12:18:32.0 - 12:18:33.3 we estimate the current layerwidth to be dcs ∼ 2 de, in agreement with Ref.[26]. Thisimplies that MMS crossed an electron scale current sheet.
While the typical signatures of an EDR encounter areobserved overall, the multi-spacecraft analysis of elec-tric and velocity fields along the spacecraft trajectoryallows us to identify signatures which are distinctive ofthis event. Figure 1(f) shows the normal component ofthe electric field, EN , exhibiting a bipolar behavior (pos-itive on the -N side and negative on the +N side of theneutral line) consistent with Hall dynamics. While thedifferent spacecraft see similar EN in the interval A–D(12:18:28.9 - 12:18:33.4), significant differences betweenthe spacecraft are observed in interval D–F (12:18:33.4- 12:18:36.5). Indeed, while MMS2 and MMS4 observeEN < 0, MMS1 measures EN ∼ 0 and even EN > 0. Thelargest difference is observed between spacecraft with thelargest separation in the N direction (MMS1 and MMS2,Fig.1(k)) while spacecraft which are close to each other inthe N direction and separated both in L direction observenearly identical signals. MMS2-MMS4 is the spacecraftpair with the largest separation in the M direction (1.1 de,not shown) but the observations from the two spacecraftare nearly identical. We conclude that the observed dif-ferences at the scale of the tetrahedron are related todifferent positions primarily in the N direction.
The difference between EN measured at MMS1 andMMS2 (which are only 1.1 de apart along the N direc-tion) reaches a maximum value of ∼ 30 mV/m (e.g. at12:18:35.01). This indicates the presence of strong gra-dients at the electron scales. Analogously to the differ-ences in EN , also significant differences are observed inve,L (Fig.1(e)), reaching 2000 km/s, and in the param-eter E′ = E + ve × B (Fig.1(g)) which quantifies thedemagnetization of the electrons. E′N 6= 0 for the major-ity of interval A–F, indicating that the electrons are notfrozen-in to the magnetic field. These differences furtherconfirm the presence of strong gradients on spatial scales∼ de.
Hence, during this EDR encounter we identify strongelectron scale gradients and electron demagnetization.
FIG. 1. Top: Four spacecraft (a)BL, (b)BM and (c)BN mea-sured by FGM [35]; (d) ve,M and (e) ve,L from FPI [36]; (f)EN from EDP [37, 38]; (g) N component of E′ = E+ve×B;(h) Te,||/Te,⊥; (i) magnitude of magnetic field fluctuations(computed filtering FGM data with 0.5 Hz < f < 64 Hz).The green shaded interval indicates the inner EDR. Bottom:(j) 2D PIC simulation data of Te,||/Te,⊥ with the recon-structed MMS trajectory crossing the EDR. The magneticflux contour lines are superposed; (k) spacecraft position rel-ative to MMS1 in the LN plane.
However, the most intriguing feature of this EDR cross-ing is the presence of large fluctuations in EN , ve,L alongthe separatrix (region D–F) and of δB in the center of thecurrent sheet (interval B–E). Such oscillations are not ex-pected for a smooth crossing of a laminar EDR, and theirpresence indicates that the EDR crossing is perturbed bysome process. We investigate these oscillations in detailin order to identify this process.
Figure 2 focuses on the separatrix region characterisedby the strong gradients. Both ve,L and EN (Fig.2(b)–(c))show very different profiles at each of the spacecraft. No-tably, MMS2 and MMS4 observe a strongly fluctuatingand mostly negative EN while the EN is mostly positivefor MMS1 and the fluctuations are not as prominent.Indeed, the observed difference between EN measured
by MMS1 and MMS2 (∆EN = EN,MMS2 − EN,MMS1,Fig.2(d)) and analogously between ve,L measured byMMS1 and MMS2 (∆ve,L = ve,L,MMS2 − ve,L,MMS1)show large variations. Such large variations in the ob-served gradients can be either caused by kinking of thecurrent sheet as a whole or by temporal variations of thegradients at electron scales, or by a combination of thetwo.
Figures 2(e)–(f) show 2D PIC simulation data of EN
and ve,L in the LN plane. The location of MMS corre-sponding to the E-labeled line in Fig.2(a)–(d) is shownin the LN plane. The simulation data (Fig. 2(e)–(f))exhibit large differences in EN and ve,L at the differentspacecraft locations, thus electron scale gradients as theones identified in the in situ observations are also presentin the simulation data. However, considering the laminarcharacter of the simulation data, if one were to considera smooth MMS trajectory across a steady-state 2D re-connection plane (see e.g. [25, 27]), one would expectthe difference between EN and ve,L observed at differentspacecraft to be rather constant and the related gradientsto be uniform along the separatrix. This is in strikingcontrast with the large variations in the gradients ob-served by MMS. The 2D simulation can be matched tothe in situ data only if we use a rather complex trajec-tory, as shown in Fig. 2(e)–(f)). This trajectory is overalltangential to the separatrix, yet it exhibits several back-and-forth motions which are necessary to reproduce theoscillating ∆EN and ∆ve,L observed in situ.
In order to identify the process responsible for thecomplex EDR crossing, we analyze the observed fluctua-tions of magnetic field δB (see Fig.1(i)). Fig.3(a) showsthat the δB fluctuations, with similar amplitude in allthree components, are present in the center of the currentsheet, where the current density peaks (Fig.3(b), yellowshaded interval 12:18:30.3 - 12:18:36.5). Figure 3(c) and3(d) show the wavelet power spectra of the electric andmagnetic fields observed by MMS1. Both the magneticand electric powers clearly drop for frequencies f > fLH
(fLH ≈√fcifc,e is the lower hybrid frequency) and in
the inner EDR the waves have f ∼ fLH . The parameterEB
1vph
(Fig.3(e)), where vph is the phase speed of the ob-
served waves (see Fig.3(g)), is used to quantify the elec-trostatic and electromagnetic component of the waves.Theoretically, the parameter E
B1
vph→∞ for purely elec-
trostatic waves. Averaging this parameter in the yel-low shaded interval of Fig.3 and in the frequency range1 Hz < f < 5 Hz, we obtain a mean value of E
B1
vph∼ 15
which is much smaller than the typical value of EB
1vph
in
the quasi electrostatic case. For example, EB
1vph∼ 400
(for 0.3 < f/fLH < 0.8) for the quasi-electrostatic fluc-tuations reported in Ref.[40]. Thus, the fluctuations inthe center of the reconnecting current sheet are charac-terised by a significant electromagnetic component.
To better characterize these fluctuations, we compute
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FIG. 2. Four spacecraft MMS observations: (a) BL; (b) ve,L;(c) EN ; (d) ∆EN = EN,MMS2 − EN,MMS1 and ∆ve,L =ve,L,MMS2 − ve,L,MMS1. PIC simulation: (e) contour plotof ve,L; (f) contour plot of EN . The black and blues linesrepresent the MMS1 and MMS4 trajectories.
the dispersion relation from the phase differences of δBN
between spacecraft pairs, using multi-spacecraft interfer-ometry [39, 40]. Figure 3(g) shows that the normalizedpower P (f, k)/Pmax peaks at f ∼ 1.4 Hz (black dashedline) which is close to fLH at the current sheet cen-ter (12:18:32.8). The wave number at the P (f, k)/Pmax
peak is kρe ∼ 0.3 (ρe ∼ 24 km is the electron gyrora-dius) which corresponds to phase speed vph = 660 km/sand wavelength λ ∼ 500 km. Figure 3(h)–(i) shows thatthe wave vector k is directed mainly along the M di-rection, i.e. it is anti-aligned with the direction of thecurrent and perpendicular to the reconnection plane LN.The average direction of propagation of the fluctuationsis k = [0.12, −0.92, 0.38] in LMN coordinates and itis mainly perpendicular to the magnetic field direction(θk = arccos k·B
|k||B| ∼ 70◦, not shown). Similar results
are obtained if a different component of δB is consideredfor the analysis. These signatures are consistent withlower hybrid drift fluctuations propagating in the out-of-reconnection-plane direction.
FIG. 3. Top: (a) Three components of δB. Offsets of 2.3nT and 4.3 nT are added to δBM and δBN respectively;(b) three components of J calculated from particle moments;(c) Spectrum of B wave power; (d) spectrum of the E wave
power; (e) spectrum of log10
(EB
1vph
); (f) βe. The black line
indicates fLH . Bottom: Normalized power of magnetic fieldfluctuations δBN versus (g) |k|ρe and frequency; (h) kLρeand kMρe (0.5 Hz < f < 2.5 Hz); (i) kMρe and |kN |ρe(0.5 Hz < f < 2.5 Hz);. The dashed line in panel (g) corre-sponds to f = 1.4 Hz.
The δB fluctuations in the current sheet center andthe electric and velocity field fluctuations at the separa-trix have similar time scales which are comparable to thelower hybrid frequency (Fig. 3(c)–(d) and 2(d)). Thissimilarity suggests that they are related to each other.As shown in Fig.2, we can match the observed oscillat-ing ∆EN and ∆ve,L to the steady-state 2D reconnectionstructure if we employ a complex motion of the 2D re-connection plane. Both such complex motion and theδB fluctuations in the center of the current sheet canbe produced by kinking of the current sheet propagatingin the out-of-reconnection-plane direction (see a qualita-tive representation in Fig.4). On the other hand, giventhe electron-scale inter-spacecraft separation which doesnot allow the sampling of the larger scales, we cannotestablish whether the oscillations shown in Fig.2(b)–(d)are indeed produced exclusively by the rigid motion ofthe reconnection plane, or if a more complex behaviorincluding time evolution is present.
FIG. 4. Schematic representation of the kinking of theelectron scale current sheet propagating in the out-of-reconnection-plane direction (not to scale).
are related to one of the various drift instabilities thatare eigen-oscillations resulting in current sheet kinking[18, 19]. Several modes that have been considered as dis-tinguished in the past actually belong to the same class ofinstabilities ranging from the electrostatic lower hybriddrift instability LHDI (fast growing, short-wavelengthmode with kρe ∼ 1) localized at the edges of the cur-rent sheet [17] to the electromagnetic, longer-wavelengthmodes with k
√ρiρe ∼ 1 located close to the current
sheet center which arise in later phases of the instabil-ity [18, 19, 42–44]. In the event reported here, MMSobserved electromagnetic fluctuations with kρe ∼ 0.3(which is somewhat smaller than the typical kρe ∼ 0.5−1observed for LHDW at the magnetopause [14, 41]) andk√ρiρe ∼ 2.7 located within the EDR (ρe and
√ρiρe are
averaged over the yellow shaded interval of Fig.3). Thesefluctuations are rather similar to the electromagnetic cur-rent sheet modes described in Ref.[18, 19]. Electromag-netic fluctuations in a reconnecting current sheet havebeen observed at the magnetic reconnection experiment(MRX) [20], and it was suggested that the fluctuationswere generated by the Modified Two Stream Instability(MTSI) [45, 46] which can occur at higher βe observedin the current sheet center (see Fig.3(e)).
Nonetheless, the comparison between our observationsand the analytical/simulation studies [18, 19] or labora-tory/spacecraft observations [20, 47] focusing on currentsheet instabilities is constrained by the fact that the cur-rent sheet thickness in these studies is dcs ∼ di whileour event presents a very thin current sheet dcs ∼ 2 de =0.05 di. Also, the plasma considered in previous stud-ies is usually homogeneous [48] or reconnection is notpresent [18, 19] or it is asymmetric [49]. Independentlyof the specific instability operating in the current sheet,when the direction of propagation is perpendicular to thereconnection plane the out-of-plane direction cannot betreated as an invariant axis of the system. Thus, a 3Ddescription is required to understand the dynamics of theprocess.
In conclusion, we report MMS observations of a per-
turbed EDR crossing. We observe oscillations of theelectron-scale gradients at the separatrix and magneticfield fluctuations in the center of the current sheet. Thesefeatures are not expected for a simple crossing of asteady-state 2D EDR. We find an overall good agreementbetween the observations and 2D PIC simulations of re-connection, but we can only match the observed oscilla-tions to the 2D model if we consider a complex motion ofthe spacecraft in the fixed 2D reconnection plane. We at-tribute such complex motion to a kinking of the currentsheet which is propagating in the out-of-reconnection-plane direction. Despite the overall quasi-2D geometryof the event, these results suggest that we need to takeinto account the three-dimensionality of the system tofully understand the observed EDR crossing. Further insitu data analysis and three-dimensional kinetic simula-tions enabling the out-of-plane dynamics are needed toestablish the role of current sheet instabilities in affectingthe EDR structure.
We thank the entire MMS team and instruments PIsfor data access and support. MMS data are available atthe MMS data center. We gratefully thank W. Daughtonfor running the simulations. This work was supported bythe Swedish Research Council, Grants No. 2016-05507and 2018-03569, and the Swedish National Space Agency,Grants No. 128/17 and 144/18.
G.C. dedicates this work to the memory of FedericoTonielli.
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