DOI: 10.1126/science.1236992 , 1478 (2013); 341 Science et al. V. Angelopoulos Electromagnetic Energy Conversion at Reconnection Fronts This copy is for your personal, non-commercial use only. clicking here. colleagues, clients, or customers by , you can order high-quality copies for your If you wish to distribute this article to others here. following the guidelines can be obtained by Permission to republish or repurpose articles or portions of articles ): September 26, 2013 www.sciencemag.org (this information is current as of The following resources related to this article are available online at http://www.sciencemag.org/content/341/6153/1478.full.html version of this article at: including high-resolution figures, can be found in the online Updated information and services, http://www.sciencemag.org/content/suppl/2013/09/26/341.6153.1478.DC1.html can be found at: Supporting Online Material registered trademark of AAAS. is a Science 2013 by the American Association for the Advancement of Science; all rights reserved. The title Copyright American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the Science on September 26, 2013 www.sciencemag.org Downloaded from on September 26, 2013 www.sciencemag.org Downloaded from on September 26, 2013 www.sciencemag.org Downloaded from on September 26, 2013 www.sciencemag.org Downloaded from on September 26, 2013 www.sciencemag.org Downloaded from on September 26, 2013 www.sciencemag.org Downloaded from
et al.V. AngelopoulosElectromagnetic Energy Conversion at Reconnection Fronts
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Electromagnetic Energy Conversionat Reconnection FrontsV. Angelopoulos,1* A. Runov,1 X.-Z. Zhou,1 D. L. Turner,1 S. A. Kiehas,2 S.-S. Li,1 I. Shinohara3
Earth’s magnetotail contains magnetic energy derived from the kinetic energy of the solar wind.Conversion of that energy back to particle energy ultimately powers Earth’s auroras, heats themagnetospheric plasma, and energizes the Van Allen radiation belts. Where and how suchelectromagnetic energy conversion occurs has been unclear. Using a conjunction between eightspacecraft, we show that this conversion takes place within fronts of recently reconnected magneticflux, predominantly at 1- to 10-electron inertial length scale, intense electrical current sheets(tens to hundreds of nanoamperes per square meter). Launched continually during intervals ofgeomagnetic activity, these reconnection outflow flux fronts convert ~10 to 100 gigawattsper square Earth radius of power, consistent with local magnetic flux transport, and a few times1015 joules of magnetic energy, consistent with global magnetotail flux reduction.
Magnetic reconnection is a fundamentalprocess of electromagnetic energy con-version into kinetic energy and heat that
operates in the solar corona, astrophysical accretiondisks, active galactic nuclei, and planetarymagneto-spheres. InEarth’s space environment, reconnectionfacilitates solar wind energy input into the magne-tosphere by enabling solar wind field lines to crossthe magnetopause and be directly connected toEarth’s field lines (Fig. 1A), stretching and com-pressing them into the magnetotail lobes. Increasesin magnetotail lobe flux are evidence of the resultantmagnetic energy storage. Nightside reconnection(X in Fig. 1A) converts this stored energy into par-ticle motion, heating, or waves, moving it from themagnetosphere into the ionosphere or back to in-terplanetary space. Although energy storage andrelease often occur in distinct, easily recognizablecycles called substorms (1–4), transient magne-totail reconnection is, in fact, ubiquitous acrossall types of geomagnetic activity (5, 6).
After a pulse of transient reconnection in themagnetotail, magnetic flux transport and energyconversion are expected along the entire path ofthe flux bundle as it shrinks earthward or tailwardfrom the reconnection point (red arrows in Fig. 1A)propelled by its curvature force (7). This electro-magnetic energy conversion’s nature and agree-ment with global substorm-scale energy estimateshave been elusive, however. Energy conversionequals ∫∫JyEydtdxDyDz, where Jy is the dominanttail current; Ey is the dominant electric field (bothduskward); and x, y, and z are Geocentric SolarMagnetospheric (GSM)coordinates (8).Wheneval-uating the power conversion rate, J⋅E, electron-scaleprocessesmust be distinguished from ion-scale pro-
cesses. This can be achieved by comparing J⋅Ewith J⋅EMHD,whereE is themeasured electric fieldandEMHD is obtained from ion flowmeasurementsand the frozen-in condition (8), consistent with
ideal and Hall magnetohydrodynamics (MHD).This requires comprehensive particles and fieldsinstrumentation and high-time resolution mea-surements. In the past, there has been a lack ofmultipoint, high-time resolution, comprehensiveplasma observations that can assess the nature,intensity, spatial extent, and duration of the mosteffective conversion and transport, concurrentlywith a global monitor of the amount of energystorage and release in the magnetosphere. Here, weuse a fortuitous conjunction between the dual,lunar-orbiting mission ARTEMIS (Acceleration,Reconnection, Turbulence, and Electrodynamicsof Moon’s Interaction with the Sun) and six Earth-orbiting satellites in the magnetotail to measurelocal and global energy conversion and determinethe location and properties of the most effectiveelectromagnetic energy conversion process.
Substorm ObservationsBecause magnetic energy conversion results inplasma flows, heating, and waves and is relatedto magnetic flux transport, our event selectionwas motivated by the availability of spacecraft on
1Department of Earth, Planetary and Space Sciences and In-stitute of Geophysics and Planetary Physics, University ofCalifornia Los Angeles, 595 Charles Young Drive East, LosAngeles, CA 90095–1567, USA. 2Space Research Institute, Aus-trian Academy of Sciences, Schmiedlstrasse 6, 8042, Graz, Austria.3Institute of Space and Astronautical Science, JAXA, 3-1-1Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan.
Onset First intensification Second intensification
Fig. 1. Magnetotail configuration and geomagnetic activity analysis. (A) X-Z satellite projectionsand a sketch of the magnetotail configuration on 3 July 2012, 09:40 UT, obtained by modifying the T96model field (32). GSM coordinates are used throughout this paper unless noted; X, Y, Z point roughlysunward, duskward, and northward, respectively (8). (B) High-pass-filtered (<120-s) magnetic pulsationdata from Carson City, NV, and auroral electrojet index from Western THEMIS and ancillary stations. (C)Electron differential flux and B-field inclination at G15.
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both sides (earthward and tailward) of magneticreconnection, where such phenomena have beenobserved previously. The ARTEMIS lunar orbit-ers P1 and P2 traverse Earth’s magnetotail onceper lunar month (9, 10). Once per year, when thethree highly eccentric Earth orbiters THEMIS(Time History of Events and Macroscale Interac-tions during Substorms) P3, P4, and P5 reach theirapogee (geocentric radius of apogee, ra ~ 12 RE)at premidnight, concurrent reconnection outflowflux measurements at both sides of a reconnec-tion site can be made. During such a conjunctionon 3 July 2012 at 9 to 12 UT, a substorm occurred.
At that time, Geotail (GT, ra ~ 30 RE) (11) andGOES (Geostationary Operational EnvironmentalSatellites) 13 and 15 (G13 and G15, at ra ~ 6.6 RE)were also well positioned in the nightside mag-netosphere (Fig. 1A and fig. S1).
Ground magnetic pulsations (Fig. 1B) andabrupt changes in the auroral electrojet low (AL)index enable detailed timing (8) of substorm on-set and its two intensifications, demarcated byvertical lines in Fig. 1B. This timing is corrobo-rated by radiation belt electron injections andmagnetic field dipolarizations at G15 (Fig. 1C).The activity was centered at premidnight, exactly
where THEMIS and ARTEMIS were situated.The negative interplanetary field Bz throughoutthis time resulted in substantial magnetotail fluxloading (fig. S3). The satellite locations, the inter-planetary conditions, and the activity indices sug-gest that the observation conditions during thisinterval were appropriate for detection of mag-netic energy conversion. But where should theseenergy conversion sites be expected to residewithin these observations?
Earthward-moving reconnected flux bundlesare typically associated with 10-min time-scalebursty bulk flows (BBFs) that envelop individual1-min time-scale flow bursts and have a nominal10 RE
2 Y-Z cross-section (12, 13). Even thoughBBFs are the most efficient transporters of fluxand energy in the magnetotail, integrated BBFtransport is small compared with total transportduring substorms [see table 5 in (13) and table 1and figure C1 in (14)], perhaps because spatialaliasing prohibits detection of full BBF dura-tion or extent (13). Even if assumed continuous(and thus integrated) over substorm time scales(1.5 hours), BBF transport is smaller than substorm-scale transport of magnetic flux (0.5 to 1 GWb)by a factor of 10 and of energy (1 × 1015 to 5 ×1015 J) by a factor of 100. For the largest events(14), flux transport appears sufficient, but energytransport is still deficient by a factor of 3. Loadsof considerable magnitude (~25 pW/m3) last-ing 1 to 10 min, possibly related to BBFs, havebeen reported (15, 16). Based on 4-s resolutiontime-delay analysis from the Cluster mission, suchloads have been considered mostly stationary.When integrated over time and over their scaleestimate (3 to 8 RE) along theX direction (15), theirmaximum power is 0.9 × 1013 to 2.5 × 1013 J/RE
2,smaller by a factor of 100 than expected per RE
2
in cross-sectional area during a substorm.However, recently appreciated intense cur-
rent densities embedded within flow bursts (10 to100 nA/m2) could be potential sites of substantialelectromagnetic power conversion (17). De-fined by their rapid positive Bz excursion, thesedipolarization fronts propagate over tens of RE
from the reconnection region to the inner mag-netosphere. Correlated with negative density gra-dients of ion inertial length scale–size, intensewaves, and plasma heating, these fronts indeedhave the hallmarks of power conversion sites(18). Simulations of reconnection show that iondynamics at such fronts are uniquely capable ofsubstantial electromechanical power conversion(19). Although kinetic simulations (19, 20) differon the exact location of the dominant conversionregion, they agree that electron-scale power con-version becomes important only near the X point.Such simulations, however, are not global. Var-ious boundary conditions could explain differ-ences between simulations as well as potentialdifferences between simulations and data.
The front’s saddle-shaped current sheet (21, 22),which is at least partly supplied by the equatorial(XY ) cross-tail current, can feed into the global sub-storm field-aligned current system at high latitudes,
GT: Vx [km/s]
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Fig. 2. Magnetotail data overview. (A) Total (magnetic plus plasma) pressure. (B, C, D, G, I, and J)Energy flux spectrograms. (E andK) Magnetic field on THEMIS and ARTEMIS (Geotail’s field was unavailabledue to Earth shadow). (F, H, and L) Ion X-component flows. (M) Measured Y-component electric field.Vertical lines are transferred from Fig. 1B.
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with global consequences. Similar to its parent, non-BBF equatorial cross-tail current (23), the ion iner-tial length scale front current is often consistentwiththe Hall term in Ohm’s law (17), except when thedensity gradient within it becomes so steep thatelectron pressure gradients and electron inertiastart to dominate (22). Establishing the locations,longevity, and global evolution of these frontsthrough our multispacecraft observations couldpotentially result in adequate levels of integratedpower conversion and transport.
The same pitfalls in assessing global transportand energy conversion also apply on the tailwardside of the reconnection site, where reconnectedflux bundles ram into ambient tail plasma, form-ing proto-plasmoids (Fig. 1A). These evolve intolarge-scale plasmoids (24) and are eventually re-leased into the solar wind. Negative Bz excursionsassociated with tailward flows and density deple-tions also observed in the magnetotail were inter-preted as putative counterparts of dipolarizationfronts on the tailward side of the reconnection re-gion (25). However, the relationship between suchtailward reconnection outflow flux fronts andplasmoid formation and expulsion is unclear.More-over, the presence, nature, and similarity of physicalprocesses (flux transport, current formation, andenergy conversion) at reconnection outflow fluxfronts (or “reconnection fronts”) on the two sidesof a reconnection point have yet to be evaluated.Our multipoint measurements from the event se-lected address these questions and establish thelongevity of power conversion sites within tailward-moving plasmas for comparison with global pow-er conversion and flux transport estimates.
At ARTEMIS, total pressure peaks (Fig. 2A,at ~09:52 and ~10:46 UT) accompanied by bi-polar Bz signatures and tailward flows (Fig. 2, Kto L) (also see expanded views in figs. S5, K to L,and S6, K to L) indicate plasmoid passage, which isevidence of near-Earth reconnection. The plasmoidswere followed by multiple bipolar Bz variationsindicative of smaller plasmoids at P1 at 10:04to 10:14 UT (after the first intensification) andat both P1 and P2 at 10:46 to 11:20 UT (after thesecond intensification), suggesting multiple in-stances of reconnection following each intensifica-tion. Integrating in situ flux transport measurementsaround plasmoid traversals is a poor measure ofglobal flux transport because the spacecraft oftenenter the tail lobe after plasmoid passage. The lowdensity, increased Debye length, and increasedspacecraft potential magnitude at the lobe precludein situ flux transport measurements there, consistentwith our expectation of spatial aliasing in evaluatingtailward transport. ARTEMIS’s location in the dis-tant tail, however, enables previously unavailablemeasurements of global flux transport, and itsconversion rate and duration, for accurate com-parisons with locally measured transport.
Lobe Flux: Storage and ConversionUsing P2’s total pressure inside the magneto-pause and the solar wind dynamic pressure out-side it allowed us (8) to determine and integrate
X [R
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Fig. 3. Magnetotail flux transport and power conversion. (A) Solar wind magnetotail flux loading(red) (fig. S3E) and instantaneous magnetotail lobe flux, F (black) (figs. S7 and S8). (B) Cumulativeflux transport past ARTEMIS and THEMIS, per unit of Y distance, estimated from the measured electricfield. (C) Location and timing of reconnection impulses derived from time delays of waves and particlesmeasured at P1 to P5 and GT as tabulated in table S1 [also see (8) and figs. S9 to S13]. Reconnectionsites progress from near-Earth to ARTEMIS in two cycles; during each cycle, the sites remain earthwardof 60 RE. (D and E) Eight-minute detail of flux transport per unit of Y distance and energy conversionper unit Y-Z area observed past P2 and P3 after the second intensification. Dashed lines are zero levels.Red and blue in (E) are the cumulative power conversion due to the measured electric field or the MHDapproximation. Black is the nominal cross-tail current, 0.5 nA/m2, times the MHD electric field, forcomparison with the contribution from reconnection fronts. Note the different scales for P3 (left) and P2(right). (F) Detail (25-s) of Ey, Bz during front passage by P2. (G) Tailward-moving power conversiondensity JyEy at P2 in the MHD approximation (blue) and using the measured Ey (red); (also see fig. S15for context). (H and I) Five-second detail of the same quantities at P3, as in (F) and (G), for P2 (also seefig. S16 for context). Durations in (F) to (I) were chosen to enable sufficient resolution of the electron-scale structures.
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the (presumed) monotonically decreasing mag-netopause flaring angle, a, to obtain the tail ra-dius, RT, at P2. We used a variant of a techniquethat has been validated against simulations andobservations (26). During our event, RT variedbetween 35 and 38 RE (8).
Next, using RT and the magnetotail lobe fieldinferred from the total pressure at P2, we ob-tained the lobe flux, F, and compared it with thesolar wind input (Fig. 3A). The sharpF increasesand decreases demarcated by short vertical linesin the panel are not global; they correspond toplasmoid or BBF passage at P2, when intenselocal curvature or inertial forces invalidate ourimplicit approximation of a planar, quasistaticplasma sheet. If they are ignored,F agrees wellwith the solar wind input before the first substormintensification, supporting our finding that lobereconnection did not accompany the first plasmoidexpulsion. For half an hour after the first inten-sification, however, substantial reduction in lobeflux relative to the solar wind input was observed,suggesting that lobe reconnection sufficient tobalance the solar wind input was taking place.
The most notable lobe flux reduction duringthe three-hour interval of interest occurred within30 min after the second substorm intensification(10:42 UT), when F decreased ~0.5 GWb (by afactor of two). By 11:35 UT,F began to increaseagain, signifying a new cycle of lobe magneticflux and energy loading from the solar wind. Cu-mulative flux transport past P1 to P5 (Fig. 3B),which occurred in short-lived bursts, differed con-siderably at the five satellites. We attribute this tospatial aliasing, as activity moves away from thespacecraft, or as the spacecraft moves into thelobes where particles and electric field are barelymeasureable. Becausemagnetic flux is conserved,however, the increasing difference between solarwind input and F (Fig. 3A) is proof of ongoingmagnetotail transport; the recurrence of plasmoidsand BBFs suggests that such transport occurscontinually over substorm time scales (severaltens of minutes).
Reconnection Site LocationsDuring a substorm, magnetic reconnection in themagnetotail is not stationary but has been ob-served to progress downtail in a series of im-pulsive, localized activations (27). In our event,this motion needs to be understood to permitintegration of J⋅E over a volume that contains theX point. Reconnection locations can be deter-mined by timing emittedMHDwave pulses (28),energy dispersion of accelerated particles (29, 30),or flow reversals. By using such standard meth-ods (8), we found (Fig. 3C and table S1) thatreconnection started near X ~ –23 RE at substormonset and progressed tailward of ARTEMIS by10:32 UT. Thereafter, the current sheet thinnedglobally, as evidenced by the increased Bx dif-ference between P1 and P2 and between P5 andP4 (Fig. 2, E and K). Subsequently, a new recon-nection site formed near Earth (X5, X ~ –23 RE)and initiated a new sequence of tailward-moving
activations (X6 and X7). Thus, in the ~30 minafter the second intensification, the reconnectionsite remained earthward of ARTEMIS, suggest-ing that a reasonable approximation of the mag-netotail at that time is a cylinder bounded by X = 0and –60 RE, where energy flows out along TXonly from the high-beta plasma sheet, mostly asparticle energy recently converted frommagneticenergy. Because reconnection remained in thiscylinder, all magnetic energy conversion occurredinside it.
Reconnection FrontsWithin the plasmoids observed here and else-where at a similar distance (24), tailward recon-nection fronts usher low-density, hotter, presumablyrecently reconnected plasma (Fig. 2, I to L) (alsosee greater detail in figs. S5, I to L, and S6, I toL). These structures may be proto-plasmoids,formed by interaction of newly reconnected fluxbundles with ambient plasma, as observed recent-ly in simulations (31). The sharp interface be-tween ambient and recently reconnected plasma(e.g., 10:45 UT) contains an intense westwardcross-tail current. Using the 12-s time delay ofthe Bz minimum from P2 to P1 produces a speedof ~600 km/s, consistent with the in situ mea-sured ion velocity, 400 to 800 km/s (Fig. 2H andfigs. S11H and S12H). The similarity of the frontat P1 and P2 also indicates that it lasts muchlonger than the ~2-s observation period at eachsatellite; its speed suggests that it emanated fromthe X5 reconnection site (Fig. 3C and table S1)several minutes earlier.
The observed 20 nT Bz decrease over 2-s re-sults in estimates of 13 nA/m2 and 1200 km forthe front’s average current density and thickness(~2 to 3 ion inertial lengths; ~1 to 2 ion gyroradii).The order-of-magnitude density drop; ion heat-ing; and intense Ey (~13 mV/m), which deviatesvery little from the MHD approximation near thepeak |Bz| and just behind the front; and an Ex atthe front consistent with a Hall current (fig. S14,A to G) are also classical dipolarization frontsignatures (17), except that they have a reverseBz. Again, as for dipolarization fronts, this tail-ward reconnection front’s speed, estimated frommultiple spacecraft observations, agrees fairly wellwith the ion flow, Vx, validating our approxima-tion dx ~ –Vxdt for converting temporal to spatialderivatives, at least near the front.
The main terms in J⋅E during front motion areJyEy~ (–∂Bz/∂x)Ey/m0+JctEy,where Jct = (∂Bx/∂z)/m0is the equatorial cross-tail non-BBF current (~0.5nA/m2), which is at least 10 times smaller than thefront current. Because dx ~ –Vxdt, Jy ~ (∂Bz/∂t)/Vxm0provides a reasonable first-order estimate of the dom-inant current. In MHD, Ey ~ VxBz and J⋅EMHD =(∂Bz/∂t)Bz/m0. This approximation holds evenwhen the Hall term is substantial, as we see by re-placing Vx withVxe in Jy and in Ey.When electronterms in Ohm’s law dominate, the Hall electric fieldin the X direction no longer equals the measuredelectric field in the plasma frame: JyBz/Ne ≠ Ex +(V×B)x, and power conversion JyEy ~ (∂Bz/∂t)Ey/Vxm0
disagrees with its MHD approximation. Such sit-uations are interesting and important because theycan lead to energy conversion in the electron restframe at the fronts.
During the tailward reconnection front’s pas-sage past P1, the electromagnetic power conver-sion density JyEy ~ (∂Bz/∂t)Ey/Vxm0 agrees wellwith its MHD equivalent (∂Bz/∂t)Bz/m0, as expectedwhen electrons are frozen into the field (fig. S14H).This agreement is also consistent with the expec-tation of a Hall current at dipolarization fronts ofan ion inertial length scale gradient (17). Theseobservations support the notions that physical pro-cesses at reconnection fronts on both sides of areconnection site are identical and that on the tail-ward side, such fronts participate in early plasmoidformation. As we shall see below, these reconnec-tion front similarities on both sides of the recon-nection site extend to processes at electron scales.
Energy Conversion at ElectronInertial Length ScalesDensity and field gradients of scale size shorterthan an ion inertial length can develop at dipolar-ization fronts; electron pressure gradients andelectron inertia are then needed to support thesecurrents (22). Tailward reconnection fronts areapparently no exception: Despite gross similar-ities in particle spectra and magnetic field at P1and P2, tailward reconnection front behavior atP2 (Fig. 3, F and G, and fig. S15) differs mark-edly from that at P1. At P2, the spin-fitEy differsfrom (V×B)y by ~30% (fig. S15F). The high-resolution Ey (8 samples/s) peaks at >30 mV/mover 250-msec (~150 km, or 4 electron inertiallengths given the density of 0.02 cm−3) when thedensity and magnetic field gradients within thefront are steepest (Fig. 3F and fig. S15, C and F).At that time, theHall electric field JyBz/Ne differsdramatically from the measured Ex in the plasmaframe (fig. S15G), implying that electron terms inOhm’s law are important. At the same time, thepower conversion density JyEy ~ (∂Bz/∂t)Ey/Vxm0(Fig. 3G and fig. S15H) is a factor of 2 larger(>250 pW/m3) than if electrons were frozen intothe plasma (Fig. 3G and fig. S15H) and twice themaximum value reported previously (15, 16).
At P3, several reconnection fronts (Fig. 2Eand figs. S6E and S16C) that exhibit classicaldipolarization front signatures are embedded with-in the BBF counterpart to the second plasmoid(Fig. 2F). Yet the spin-fit Ey can deviate by a fac-tor of 2 from (V×B)y (fig. S16E), and at high-time resolution (128 samples/s) it exhibits peaks>50 mV/m (Fig. 3H and fig. S16F) at the sharpestgradients. During those times, Ex + (V×B)x ≠JyBz/Ne (fig. S16H), implying that electron terms inOhm’s law are important. The earthward-movingpower conversion density JyEy ~ (∂Bz/∂t)Ey/Vxm0is an order of magnitude larger than its MHD ap-proximation for about 250-msec. It exhibits peaks>6000 pW/m2 over time scales of 50-msec (20 kmgiven the ~400 km/s speed of these structures,or ~1 to 2 electron inertial lengths given the den-sity of 0.2cm−3). The observed power conversion
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density is two orders of magnitude larger thanpreviously reported (15, 16).
The power conversion density at the frontsdrives sizeable cumulative increases in powerconversion past the satellites (Fig. 3E). Becausethe difference between the integral of JyEy and itsMHD approximation (the difference between thered and blue curves) is large, the cumulative powerconversion is, in great part, due to the nonidealterms in Ohm’s law. Thus, electron inertial lengthscale–size substructures at reconnection fronts areefficient power conversion regions. Contrary to ourexpectation from past simulations (19, 20), suchregions are not limited to the vicinity of theX point.Could such small-scale, locally transient, powerconversion ratesmatch the expected global energyconversion during this typical substorm?
Global ConsequencesIntegrating the electromagnetic energy conserva-tion equation (9) over a cylindrical magnetotailvolume capped at X = 0 and –60 RE, and as-suming negligible tangential magnetic flux trans-port into the volume at the magnetopauseboundary (slow solar wind flux loading) and outof the volume at the two caps of the cylinder (atthe high-beta plasma sheet), we expect the mag-netic energy reduction in that volume to equal thetime and space integral of the magnetic powerconversion within it. Because of the spatiallycoherent propagation of reconnection fronts acrosslarge distances, known on the earthward side (17)and observed here on the tailward side (Fig. 2Kand fig. S6K), we expect power conversion at thefronts to continue over substorm time scales, notjust for the short times observed in situ. The re-connection fronts that followed the second in-tensification converted 5 to 50 GW/RE
2 of powerpast P2 and P3 (Fig. 3E and figs. S15K and S16K).This occurred during the major local flux trans-port (3 to 4 MWb/RE) (Fig. 3D and figs. S15, Jand L, and S16, J and L).
Because most tail flux reduction during thesubstorm took place over the ensuing 30-min pe-riod, we examined whether power conversion atthese fronts is consistent with the magnetic ener-gy reduction in the aforementioned integrationvolume associated with local flux transport andglobal flux reduction over the same time period.
Themagnetic energyWLwithin a portion of thenear-Earth tail lengthL~60-RE isWL=L*F
2/2m0A;it varies during a substorm because both area (A)and flux (F) vary: dWL/WL = 2dF/F – dA/A. Inour case, the tail radius was reduced from 38 RE
to 35 RE (fig. S8C), and F from 1.2 to 0.7 GWb(Fig. 3A and fig. S8C); thus,WL decreased from4.8×1015 to1.9×1015 J, releasingDWL~2.9×10
15 Jof magnetic energy. This global energy conversionneeds to be compared with the integrated powerconversion from plasma sheet measurements. Be-causeDA/Awas smaller by a factor of 2.7 thanDF/F,we can approximate DWL/WL ~ 1.64(DF/F).
First, we consider energy conversion relatedto local flux transport. The measured flux trans-port per unit of Y distance past P3 (XP3 = –11 RE)
was DF/DY= SEydt ~ 4MWb/RE (Fig. 3D). Thisflux arrived from the X5 reconnection site at X5 =–23 RE, as a DX = XP3 – X5 = 12 RE-long lobeflux bundle reconnected and contracted. The ex-pected energy conversion per unit of Y distanceintegrated earthward of X5 is (DWDX/DY)/WDX =(DWL/WL)/DY=1.64(DF/F)/DY~1.64(4MWb/RE)/(1.2GWb) ~ 5.5 × 10−3/RE,whereWDX= (DX/L)WL
is the magnetic energy estimate of the lobe volumeearthward of X5. Thus, the anticipated energy con-version per unit of Y distance based on local fluxmeasurements is DWDX/DY ~ 5.5 × 10−3WDX/RE ~5.5 × 10−3 (DX/L)WL/RE ~ 5.5 × 10−3(12/60) 4.8 ×1015 J/RE or DWDX/DY ~ 5.3 × 1012 J/RE. Thishas a T10% uncertainty due to the location of theX5 site (8) (fig. S13) but considerably larger un-certainty due to the simplicity of the cylindricaltail model used.
The observed cumulative spatial (along X) in-tegral of the power conversion density accomplishedby the reconnection front flux bundles transportedpast P3 was 50 GW/RE
2 (Fig. 3E). Assuming thatthe reconnected flux bundles started to shrink earth-ward at 10:41:35 UT (exact timing from fig. S13)and continued for 145 s until the flows ceased lo-cally at 10:44:00 UT (Figs. 3D and 2F and fig.S6F), and that the curved flux bundle is DZ ~ 3 RE
tall in the Z direction, this shrinkage resulted in50 GW/RE
2 × 3 RE × 145-s ~ 22 × 1012 J/RE
energy release per unit of Y distance. This is sev-eral times larger than expected from DWDX/DYabove. Thus, even if reconnection fronts convertedenergy at the measured rate for a fraction of theirlifetime, they could still account for the entire en-ergy conversion associatedwith the locally observedflux transport in the reconnection outflow region.
Second, we consider energy conversion re-lated to global flux transport. Although flowbursts are localized in Y (1 to 3 RE) (12), theireffective interaction width DYeff can be largerdue to a multiplicity of bursts along X or Y, multi-ple fronts within each flow burst, or aliasing fromflow burst stoppage or rebound at the space-craft location. This effective interaction widthcan be determined from flux conservation. Theaverage flux transport per unit time we observedis (4 MWb/RE/145-s), and the total transportmust be 0.5 GWb/1800-s. Assuming that trans-port proceeds continuously during that time, DYeff ~(0.5 GWb/1800-s)/(4 MWb/RE/145-s) ~ 10 RE.The energy conversion in the same region is there-fore 50 GW/RE
2 × DYeff × DZ × 1800-s ~ 2.7 ×1015 J. On the tailward side, at P2, the observedpower conversion is smaller by a factor of 10(5 GW/RE
2); all else being roughly equal, thisadds ~0.3 × 1015 J to the total energy conversion,resulting in a total of 3 × 1015 J, close to the afore-mentioned expected energy conversion from lobeflux reduction, DWL ~ 2.9 × 1015 J, during thistypical substorm. Thus, the integrated power con-version at the fronts is also consistent with globalmagnetic energy conversion during this event.
From both in situ measured magnetic fluxtransport in the outflow region and global mag-netic flux reduction, we conclude that electron
inertial length scale processes at reconnectionfronts play a key role in magnetic energy con-version during magnetic reconnection.
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Acknowledgments: Funded by NASA NAS5-02099 andAustrian Science Fund (FWF) J3041-N16. Data obtainedfrom: http://themis.ssl.berkeley.edu. We thank J. Hohl andE. Masongsong for editorial help, the THEMIS and ancillarydata providers (http://themis.igpp.ucla.edu/roadrules.shtml),National Oceanic and Atmospheric Administration for theGOES data, NASA/SPDF for the solar wind data (http://omniweb.gsfc.nasa.gov/ow_min.html), and WDD-C2 for the AL index.
Supplementary Materialswww.sciencemag.org/content/341/6153/1478/suppl/DC1Materials and MethodsSupplementary TextFigs. S1 to S16Table S1References (33–39)
25 February 2013; accepted 22 August 201310.1126/science.1236992
27 SEPTEMBER 2013 VOL 341 SCIENCE www.sciencemag.org1482
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