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Profiles of electron temperature and B-z along Earth’smagnetotail

A. V. Artemyev, A. A. Petrukovich, R. Nakamura, L.M. Zelenyi

To cite this version:A. V. Artemyev, A. A. Petrukovich, R. Nakamura, L.M. Zelenyi. Profiles of electron temperatureand B-z along Earth’s magnetotail. Annales Geophysicae, European Geosciences Union, 2013, 31,pp.1109-1114. �10.5194/angeo-31-1109-2013�. �insu-01256271�

Ann. Geophys., 31, 1109–1114, 2013www.ann-geophys.net/31/1109/2013/doi:10.5194/angeo-31-1109-2013© Author(s) 2013. CC Attribution 3.0 License.

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Profiles of electron temperature andBz along Earth’s magnetotail

A. V. Artemyev1,2, A. A. Petrukovich1, R. Nakamura3, and L. M. Zelenyi1

1Space Research Institute, RAS, Moscow, Russian Federation2UMR7328, LPC2E/CNRS – University of Orleans, Orleans, France3Space Research Institute, Austrian Academy of Sciences, Graz, Austria

Correspondence to:A. V. Artemyev (ante0226@gmail.com)

Received: 18 February 2013 – Revised: 26 May 2013 – Accepted: 27 May 2013 – Published: 25 June 2013

Abstract. We study the electron temperature distribution andthe structure of the current sheet along the magnetotail us-ing simultaneous observations from THEMIS spacecraft. Weperform a statistical study of 40 crossings of the current sheetwhen the three spacecraft THB, THC, and THD were dis-tributed along the tail in the vicinity of midnight with co-ordinatesXB ∈ [−30RE,−20RE], XC ∈ [−20RE,−15RE],andXD ∼ −10RE. We obtain profiles of the average electrontemperature〈Te〉 and the average magnetic field〈Bz〉 alongthe tail. Electron temperature and〈Bz〉 increase towards theEarth with almost the same rates (i.e., ratio〈Te〉/〈Bz〉 ≈

2 keV/7 nT is approximately constant along the tail). We alsouse statistics of 102 crossings of the current sheet from THBand THC to estimate dependence ofTe andBz distributionson geomagnetic activity. The ratio〈Te〉/〈Bz〉 depends on geo-magnetic activity only slightly. Additionally we demonstratethat anisotropy of the electron temperature〈T‖/T⊥〉 ≈ 1.1 isalmost constant along the tail forX ∈ [−30RE,−10RE].

Keywords. Magnetospheric physics (magnetotail; plasmaconvection; plasma sheet)

1 Introduction

The current sheet (CS) of the near-Earth magnetotail(−10RE < X < −30RE, whereRE is the Earth radius) canbe approximately considered as a 2-D structure with themain gradient along the normal direction (alongZ) and theweak gradient along x-direction (GSM coordinate system isused). Configuration of the magnetotail CS controls the rateof charged particle acceleration and following injection intothe inner magnetosphere (see recent reviews byBaumjohannet al., 2007; Sergeev et al., 2012, and references therein).With the multi-spacecraft Cluster mission, transverse (along

Z) structure of the CS was studied in detail (especially at thedistancesX ∼ −20RE, where Cluster collected main statis-tics; seeRunov et al., 2006; Artemyev et al., 2011b). Al-though the distribution of the magnetic field along the tailplays an important role in particle (mainly electron) acceler-ation, it is less investigated.

Electrons are magnetized in the magnetotail, and their mo-tion is controlled by the global gradients of the magneticfield. One of the most effective mechanisms of electron en-ergization is adiabatic heating in the course of the earth-ward convection (Lyons, 1984; Zelenyi et al., 1990). Thismechanism predicts monotonic growth of electron tempera-ture withBz(X) (i.e., withX). However, recent observationsand the numerical modeling suggest that a substantial rolein electron energization could be played by various transientprocesses (seeAsano et al., 2010; Fu et al., 2011; Ashour-Abdalla et al., 2011; Fu et al., 2012; Birn et al., 2012, andreferences therein). To compare impacts of adiabatic heating(throughout the paper, we use this term for global betatronacceleration) and transient acceleration to the electron ener-gization, one needs to study gradient∂/∂X of the electrontemperature and magnetic fieldBz along the magnetotail.

So far, estimates of the gradient∂/∂X in the magnetotailhave been obtained by using three independent approaches:(1) small-scale gradients of the near-Earth dipolarized CScan be estimated using direct measurements of Cluster mis-sion in 2007–2009 (Nakamura et al., 2009) or THEMIS mis-sion in the case of specific spacecraft configuration (Saitoet al., 2010; Panov et al., 2012); (2) statistical investigationcan give average profiles of the main CS parameters (Bzcomponent, plasma pressure and plasma density) along thetail (see statistics collected by AMPTE/IRM, Geotail andTHEMIS spacecraft inKan and Baumjohann, 1990; Wanget al., 2012); and (3) thermal electrons could be used as

Published by Copernicus Publications on behalf of the European Geosciences Union.

1110 A. V. Artemyev et al.:Te(x) and Bz(x) profiles in the magnetotail

Fig. 1. Example ofBx component of the magnetic field measuredby four spacecraft. Also spacecraft positions are shown.

tracers of the magnetotail structure (Artemyev et al., 2011c).The distribution of electron temperature along the magne-totail was studied only using statistical investigation (e.g.,Wang et al., 2012). Each of these methods has principal dis-advantages for the determination of the gradient∂/∂X in themagnetotail: (1) direct calculation of∂/∂X is possible onlyfor relatively strong gradients in the dipolarized CS; (2) aver-age profiles cannot give snapshot-like information about themagnetotail structure (the latter is important because majortail parameters vary in a wide range on timescales from min-utes to hours); and (3) to use electrons as tracers, one needsrealistic models of the electron heating and detailed informa-tion about the transverse structure of CS.

Therefore, existing approaches cannot be used for investi-gation of the relation betweenTe(X) andBz(X) profiles and,as a result, cannot help us study the role of electron adiabaticheating for general electron energization in the magnetotail.To obtain distribution of CS parameters along the magneto-tail, the only reliable way is to organize simultaneous ob-servations at substantially different x-coordinates. In this pa-per we use the statistics of simultaneous observations of thinCSs from several THEMIS spacecraft to study the relationbetweenTe(X) andBz(X) distributions.

2 Dataset

In this study we use two datasets, which consist of THEMISand Cluster observations, respectively. THEMIS data provideus with simultaneous observations of the magnetotail CS atdifferent x-coordinates, while the Cluster dataset containsobservations in the magnetotail for 2001–2009 from the C2

spacecraft and gives average values ofTe for several rangesof X. Due to small separation of Cluster spacecraft, we can-not use Cluster measurements for simultaneous observationsof CS at different x-coordinates. The Cluster dataset includesmeasurements only with|Bx| < 10 nT and|Y | < 5RE (thisis essentially the same dataset as the one used byArtemyevet al., 2011a).

The THEMIS statistics includes 102 events, when twospacecraft THB and THC crossed the magnetotail CS within30 min (we consider 2008 and 2009). For 40 events from thislist, THD also crossed the magnetotail CS within the sametime interval. Thus, we have substatistics of 40 events withsimultaneous observations at three different x-coordinates.All 102 events can be attributed to CSs with the duration ofcrossing varying from tens of seconds (for THB) up to tensof minutes (for THD). We cannot estimate thickness of ob-served CSs directly and use a criterion of rapid crossing forTHB to select mainly thin CSs. For this dataset we use themagnetic field (Auster et al., 2008) and the electron measure-ments (McFadden et al., 2008). All data are obtained fromthe CDAWeb database (http://cdaweb.gsfc.nasa.gov/). For allcrossings|Y | coordinate is smaller than|X| (i.e., all crossingsoccur approximately around the midnight).

A typical example of an event from THEMIS statistics isshown in Fig.1. Grey color denotes CS crossings by the fourspacecraft. THB spacecraft crossed CS; then THC and THE(as well as THD) crossedBx = 0 in agreement with the distri-bution of z-coordinates of spacecraft. Synchronous crossingscorrespond to the vertical flapping motions of the CS (see thedetailed study of CS flapping observed by several THEMISspacecraft inRunov et al., 2009).

For each CS crossing from THEMIS dataset, we use theaverage values of〈Te〉, 〈T‖/T⊥〉, and 〈Bz〉 component ofthe magnetic field computed in the central region of CS(|Bx| < 10 nT), whereTe = (T‖ + 2T⊥)/3, andT‖ and T⊥

represent diagonal components of the electron temperaturetensor (smaller than|Bx| < 10 nT region of averaging some-times leads to only a few points of electron data).

3 Distribution of CS parameters along the tail

We start with the statistics of 40 crossings of the magneto-tail CS by three THEMIS spacecraft. For each event we havethree values of〈Te〉 and〈Bz〉 measured at corresponding co-ordinatesX. Four examples of〈Te〉 and 〈Bz〉 distributionsalong the tail are shown in Fig.2. One can see that the pro-files 〈Te〉(X) almost coincide with the profiles〈Bz〉(X).

The profiles〈Te〉 and 〈Bz〉 along the tail for the wholeTHEMIS dataset are shown in Fig.3a and c. There is a gen-eral increase of the magnetic field and the electron tempera-ture withX (i.e., in the earthward direction). At the large dis-tance where THB crossed the CS (X ∼ −25RE), the value ofBz is very small (Bz ∼ 1 nT). Therefore, any deformations ofthe CS could result in substantial errors in estimation ofBz,

Ann. Geophys., 31, 1109–1114, 2013 www.ann-geophys.net/31/1109/2013/

A. V. Artemyev et al.: Te(x) and Bz(x) profiles in the magnetotail 1111

Fig. 2.Profiles of the average electron temperature〈Te〉 (shown by solid lines) and the magnetic field〈Bz〉 (shown by dotted lines) along thetail.

Fig. 3. 〈Te〉, 〈Bz〉 and〈T‖/T⊥〉 distributions in the magnetotail for 40 events, when THB, THC, and THD crossed the CS. Panels(a), (c), and(f) show all profiles of〈Te〉 and〈Bz〉 from our database. In panels(b), (d), and(g), we present average values of corresponding quantities withstandard deviations. Panel(e)shows average values of electron temperature anisotropy. Various symbols (red, green, and blue diamonds) areused for data collected by THB, THC, and THD (THE) spacecraft. Black crosses show averaged data from Cluster C2 statistics. In panels(f)and(g), color curves show approximations〈Te〉/〈Bz〉 ≈ 2keV/7nT (red curve) and〈Te〉/(〈Bz〉+1nT) ≈ 1.7keV/8nT (blue curve). See textfor details.

when the normal direction to the CS is tilted in the(X,Z)

plane. This effect is clearly seen in Fig.3f, where profiles〈Te〉 as function of〈Bz〉 are shown.〈Te〉 mainly varies from200 to 500 eV up to 1.5–2 keV, while〈Bz〉 changes withinthe range 2–10 nT. However, there are several observationsof small 〈Bz〉 with relatively large〈Te〉 shown by the greycircle in Fig. 3f. As a result, we cannot use the relation〈Te〉/〈Bz〉 ≈ const for the individual CS crossings.

To obtain a more reliable presentation describing profiles〈Te〉 and〈Bz〉, we average our statistics for four intervals of

X ∈ [−10,−25]RE (see Fig.3b, d). Although averaging re-sults in a loss of information regarding the peculiarities ofindividual cases, this operation is more accurate than collec-tion of Cluster statistics because it takes into account onlymonotonic profiles of〈Te〉 and〈Bz〉 along the tail. For〈Bz〉

we obtain the following approximation based on the aver-aging at four intervals ofX: 〈Bz〉 ≈ 7nT· (−1−X/5RE)−1.The corresponding approximation of the electron tempera-ture is 〈Te〉 ≈ 2keV· (−1− X/5RE)−1. These two approx-imations give the empirical proportionality〈Te〉/〈Bz〉 ≈

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1112 A. V. Artemyev et al.:Te(x) and Bz(x) profiles in the magnetotail

Table 1. Ratios of electron temperature and magnetic field. Num-bers of events for three Kp range are 42, 43, and 17.

Kp 〈BTCz /BTB

z 〉 〈T TCe /T TB

e 〉 〈1Te〉/〈1Bz〉

≤ 1+ 1.4± 0.2 1.8± 0.05 350/1.9 ≈ 185 eV/nT2 1.75± 0.05 1.7± 0.1 500/2.1 ≈ 240 eV/nT≥ 3− 1.9± 0.1 1.8± 0.1 600/2.9 ≈ 205 eV/nT

2keV/7nT (exact value is 1.9(±0.5)keV/7.4(±1.2)nT).Due to the above-mentioned problems with small〈Bz〉 mea-sured by THB, the obtained temperature growth is weakerthan observed growth of〈Bz〉. Thus, the approximation〈Te〉/〈Bz〉 ≈ 2keV/7nT slightly overestimates growth of〈Te〉. To correct the approximation of〈Bz〉, we need to intro-duce one additional free parameter responsible for constantshift: 〈Bz〉 ≈ −1nT+8nT· (−1.3−X/4.5RE)−0.7. The cor-responding approximation of〈Te〉 profile is 〈Te〉 ≈ 1.7keV·

(−1.3−X/4.5RE)−0.7 (exact value of〈Te〉/(〈Bz〉+ 1nT) is1.7(±0.3)keV/8.1(±0.7)nT).

We plot profiles〈Te〉 as function of〈Bz〉 in Fig. 3f, wherered and blue curves show both our approximations. Onecan see that both approximations describe observations welland actually are not that different (corresponding correla-tion coefficients are 0.62 and 0.7). Proportionality〈Te〉 ≈

(1.7keV/8nT) ·(〈Bz〉+1nT) approximates data slightly bet-ter than〈Te〉/〈Bz〉 ≈ 2keV/7nT (see Fig.3g, where we com-bine the profiles from Fig.3b, d and show〈Te〉 as function of〈Bz〉). Moreover, both approximations of〈Bz〉 coincide withAMPTE/IRM statistics presented byKan and Baumjohann(1990) (not shown here).

We also compare measurements of electron temperaturefrom the THEMIS mission with the Cluster dataset. Fig-ure 3d shows Cluster C2 data of the electron temperaturecollected in the central region of the magnetotail CS. Clustermeasurements demonstrate the growth of〈Te〉 with X (i.e.,in the earthward direction) as well. However, the absolutevalues of the temperature are larger than data obtained byTHEMIS. This discrepancy could be explained by differentsolar activity for the seasons, when Cluster and THEMIS op-erated in the magnetotail. Smallness of the THEMIS statis-tics also can be responsible for this effect.

The profile of the average electron anisotropyT‖/T⊥

shown in Fig.3e demonstrates thatT‖/T⊥ is almost con-stant along the tail andT‖/T⊥ ≈ 1.1 (this is a typical valueof electron anisotropy; seeSergeev et al., 2001; Artemyevet al., 2011b). The same results are derived from the Clusterstatistics (see large crosses in Fig.3e). Therefore, the combi-nation of〈Te〉 ∼ 〈Bz〉 and〈T‖/T⊥〉 ≈ const leads to the sur-prising conclusion that the parallel component of the tem-perature increases with the same rate as the perpendicularone (∼ 〈Bz〉). However, we should note that the variance ofT‖/T⊥ is large. Thus, we only can conclude that temperature

ratio is T‖/T⊥ ∈ (1,1.2) without strong variation along themagnetotail.

We use full THEMIS statistics of 102 events when THBand THC crossed the magnetotail CS within short time in-terval. The large amount of two-point events allows us todivide these events in three groups depending on geomag-netic activity (Kp≤ 1+, Kp = 2, and Kp≥ 3−). We do notconsider the same statistics forX > −15RE because of thesmall of number of events when THB/THC and THD crossedthe magnetotail CS within 30 min. For each range of Kp, weobtain average ratios〈BTC

z /BTBz 〉 and〈T TC

e /T TBe 〉 (Table1).

For small Kp, the increase ofBz is weaker than for Kp≥ 2.The ratio of temperatures is〈T TC

e /T TBe 〉 ∼ 1.8 independent

of Kp.We calculate1Te = T TC

e − T TBe and 1Bz = BTC

z − BTBz

(distance between THB and THC is about∼ 6RE for eventsfrom our statistics). In this case, the approximationTe =

const0Bz+const1 gives1Te/1Bz = const0. For small Kp≤1, the temperature difference〈1Te〉 is smaller than forKp ≥ 2. The ratio 〈1Te〉/〈1Bz〉 is similar to the value2keV/7nT∼ 290eV/nT obtained forX ∈ [−10,−30]REwith three-point statistics. For Kp≤ 1 this ratio is one andhalf times smaller. However, this can be the effect of smallstatistics. Therefore, dependencies of ratios〈Te〉/〈Bz〉 and〈T TC

e /T TBe 〉 on geomagnetic activity seem to be weak.

4 Conclusions

In conclusion, we have shown the following: (1) electrontemperature in the vicinity of the neutral plane increaseswith 〈Bz〉 almost linearly, and (2) anisotropy of the elec-tron temperature is almost constant along the tail forX ∈

[−25RE,−10RE]. Here, we note that our results can be ob-tained only owing to simultaneous observations of the mag-netotail current sheet from several spacecraft in differentX.

These two effects provide some difficulties for the sim-ple explanation of electron energization via the adiabaticmechanism as well as via models of the transient acceler-ation. Profiles of magnetic field along the magnetotail donot contain any artificially (transient) large values of〈Bz〉.Therefore, we observe in our statistics the averaged profilesof Bz(X) corresponding to the quiet magnetotail configura-tion. If transient processes had substantial impact on the elec-tron energization, electron temperature would not correlatewith averaged〈Bz〉 profiles in the magnetotail. Moreover, inthis case〈Te〉 in the near-Earth region (X ∼ −15RE) wouldbe larger than a value obtained from a simple approxima-tion 〈Te〉/〈Bz〉 ≈ const with〈Te〉 measured atX ∼ −25RE.In contrast, the approximation〈Te〉/〈Bz〉 ∼ const slightlyoverestimates growth of〈Te〉, and real energization is evenweaker than the increase of〈Bz〉. Thus, we can concludethat there is no evidence (direct or indirect) of a substantialrole of any transient process (like reconnection and/or dipo-larization) in additional energization of the thermal electron

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A. V. Artemyev et al.: Te(x) and Bz(x) profiles in the magnetotail 1113

population. Strictly speaking, this conclusion can only be ap-plied to quiet time conditions when the averaged〈Bz〉 pro-file is monotonous along the magnetotail. However, transientmechanisms still can be important for acceleration of high-energy electrons (seeAsano et al., 2010; Fu et al., 2011;Ashour-Abdalla et al., 2011; Fu et al., 2012; Birn et al., 2012,and references therein).

Although the relation〈Te〉/〈Bz〉 = const can be consideredas evidence of the adiabatic heating, we also cannot use thismodel to describe the observed electron energization. Adia-batic heating predicts a variation of the electron temperatureanisotropy.T⊥ increases linearly with〈Bz〉 according to thebetatron mechanism, while the rate ofT‖ growth provided byFermi mechanism is smaller:T‖ ∼ 〈Bz〉

2/5 (seeLyons, 1984;Zelenyi et al., 1990; Artemyev et al., 2011c, and referencestherein). Therefore, in the simplified model of the magneto-tail, one should obtain the decrease of the anisotropyT‖/T⊥

with the increase of〈Bz〉 (seeArtemyev et al., 2012).

Acknowledgements.We acknowledge NASA contract NAS5-02099 and V. Angelopoulos for use of data from the THEMISMission. We would like to thank the following people specifi-cally: C. W. Carlson and J. P. McFadden for use of ESA data,K. H. Glassmeier, U. Auster and W. Baumjohann for the use ofFGM data provided under the lead of the Technical Universityof Braunschweig and with financial support through the GermanMinistry for Economy and Technology and the German AerospaceCenter (DLR) under contract 50 OC 0302. We would like to thankV. A. Sergeev and V. S. Semenov for useful discussions. Thework of L. M. Zelenyi, A. V. Artemyev and A. A. Petrukovichwas supported by the RF Presidential Program for State Supportof Leading Scientific Schools (project no. NSh-623.2012.2.), theRussian Foundation for Basic Research (projects nos. 10-05-91001, 10-02-93114). The work of R. Nakamura was supportedby Austrian Science Fund (FWF) I429-N16. Work was alsosupported by the European Union Seventh Framework Programme[FP7/2007-2013] under grant agreement no. 269198 – Geoplasmas(Marie Curie International Research Staff Exchange Scheme).

Guest Editor M. Balikhin thanks two anonymous referees fortheir help in evaluating this paper.

The publication of this articleis financed by CNRS-INSU.

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