Evidence for Alfvén waves powering auroral arc via a static electric potential drop

Domain: earth_science
Published: 2026-01-13
Editorial outcome: accept

Abstract
Naturallightdisplaysknownastheauroraprovideacaptivatingglimpseintotheelectromagneticdynamicsinspaceplasmas.AuroraearenotexclusivetoEarthbutalsoobservedoncelestialbodiesincludingplanetsandevencomets.

Previousstudieshaveunveiledtwofundamentalauroralaccelerationmechanisms:electricpotentialandAlfvénicacceleration.However,therelationoftheenergyprocessesassociatedwiththeauroralaccelerationregionhasremainedunclearmainlyduetothelackofquantitativeanalysis.

Employingquantitativeassessmentofenergybudgetusingmulti-platformsfromthemagnetospheretoauroralionosphere,ourfindingsunderscoretheinterplaybetweenthesetwomechanisms.HereweshowthatenergycarriedbyAlfvénwavestravelsfromthemagnetospheretotheauroralaccelerationregion,forminganelectricpotentialdropthatacceleratesparticlestoproduceaurorae.SimilaritiesinauroralparticlebehaviorsbetweenEarthandJupitersuggesttheapplicabilityoftheterrestrialscenariotoJupiterandpotentiallyothercelestialbodiesintheUniverse.

Introduction
Particleenergizationintheauroralaccelerationregion(AAR)isoneofthemajormysteriesinplanetaryspaceenvironments1–4.Althoughthecharacteristicsofacceleratedparticleswerereportedfordecades5–7,keyaspectsoftheenergizationmechanismremainpoorlyunderstood.

Based on the particlefeatures,two acceleration pictures have been observed:monoenergeticacceleration(orinverted-Vstructure)produced by a quasi-static electric potential drop along magnetic field lines5,8andbroadbandaccelerationproducedbyAlfvénwaves9–11.Theenergybudgetin themagnetosphere-ionosphere couplingand thus thepartitiontoauroralparticlesisstillunclear.Themajorchallengesinunderstandingtheparticleaccelerationmysteryaretheenergysourceandtheenergyconversionforthesetwomechanisms.

Itiswidelyacceptedthatanupward-pointingelectricfieldgivestheintensedownwardmonoenergeticacceleratedelectronsthatarethemainenergycarriersthatdirectlypowerbrightauroralemissions.However,theformationofthiselectricpotentialdropisakeymystery.Moreover,thispotentialdropaccelerationwasalsoidentifiedatJupiterbytheJunospacecraft,whicharrivedatJupiterin2016toexploreits auroralacceleration region insitu12,13.Figure1 shows two typical examplesofthepotentialdropaccelerationofelectronsattheEarth(left)andJupiter(right).Theinverted-Vstructuresmarkedbytheredarrowsaretypicalfeaturesofpotentialdropacceleration13.Althoughthestructures,showingtheinverted-Vshape,aresimilaratbothplanets, their energies are significantly different. Typical energies for potentialdropaccelerationareaboutseveralkeVatEarth5,6andabout100keVorhigheratJupiter14.Theelectricpotentialdropabovetheseplanetarypolarauroralregionsisanalogoustoaspacecapacitor,butthekeyquestionis:whatcontrolstheoperationofthecapacitor?

A key insight to solve the auroral acceleration problem is to understandtheenergybudgetfromthesourceregiontotheauroralaccelerationregionandtotheauroralemissionaltitudes.Sofar,suchcomprehensiveobservationsmayonlybeachievableintheterrestrialsystem.OneEarthauroraleventonApril16,2015showninFig.1wascapturedbygroundopticalobservations,low-altitudespacecraftformeasuringelectronprecipitationabovetheauroraandtheVanAllenProbes (also known as the Radiation Belt Storm Probes, RBSP) for tracking the magnetospheric energy source. This event occurred duringanextendedmoderategeomagneticstorm.DetailsofthedataandinstrumentsarepresentedinMethods,subsectionSatellitesandinstrumentation.

Inthispaper,thecoordinatedmeasurementsprovideafortuitousopportunity to quantitatively evaluate the key energy conversion processesthatleadtotheformationofelectricpotentialdropintheauroral acceleration region. We quantitatively evaluate the energy budgetaboveandbelowtheAARandsuggestthatAlfvénwavespumpelectromagnetic energy to sustain the electric potential drop of theAAR.

Results
TheenergyflowaboveAAR
Figure 2a and b present coincident auroral images from the two hemispheres.TheRBSP-Aand-Bsatellites,locatedat[-4.0,4.1,-0.7]R E (Earth Radii) and [-3.2, 4.6, −1.0] R in Solar Magnetospheric (SM) coordinates(Fig.2c),crossedthemagneticfluxtubesconnectingtheauroralarcasillustratedbythefootprintsshowninFigs.2a,b,andthemeridionalviewofthemagneticfieldinFig.2c.ThelocalmagneticfieldmeasuredatRBSP-Aand-BinFig.2dshowsasignificantincreaseoftheelevationangle(around08:07:50and08:10UTrespectively),indicatingthereleaseofmagneticenergy.Tofurtherinvestigatetheenergyroute,weanalyzetheelectricandmagneticfieldsindetail.

During the auroral arc crossing, strong electric and magnetic wavesweresimultaneouslydetectedinthemagnetospherealongthesame magnetic field line, allowing us to quantitatively assess the electromagnetic energy flow above the auroral acceleration region. The observed waves are identified as Alfvén waves (Methods, subsectionIdentificationofkineticAlfvénwaves),whichplayakeyroleinacceleratingelectronsalongthemagneticfield10,15.Figure3ashows thatRBSP-Aand-Bencounteredthearcaround08:07:50UTand08:10UT(verticaldashedlines),andthattheAlfvénwavehasalargecomponentofthePoyntingfluxdirectedmainlyEarthward(i.e.,S jj).Theestimatedenergyinthewaveswasfoundtobesufficientforproducingtheobservedauroralemissions(seeFig.6).DetailedanalysisofenergybudgetisprovidedinMethods,subsectionsCalculationofPoyntingflux, calculation of electron energy flux by potential drop, and estimationoftheO+energyflux.

TheenergyconversionbelowtheAAR
TheprecipitatingelectronsshowninFig.1aarequantitivelyanalyzedinFig.6.Theintegratedelectronenergyflux(i.e.,havingapeakenergyflux about 162mW/m2) is generally consistent with the result derivedfromtheauroralemissionitself(i.e.,apeakenergyfluxabout87mW/m2), indicating that the auroral particle acceleration region abovetheDMSPsatellitewassufficienttoprovideallpowerfortheaurora.Moreover,themajorityofelectronenergyfluxwascontributed by the inverted-V structure, providing further evidence that the potentialdropisthemainprocessinconvertingtheelectromagneticenergy of the Alfvén wave to the auroral precipitating particles.To efficiently accelerate electrons towards the Earth, the electric field associatedwiththepotentialdropshouldbedirectedupward,whichwouldthusaccelerateionosphericoxygenions(O+)toescapefromtheEarth.TheionosphericO+ionswouldexperiencedifferentfractionsofthepotentialdrop,thusexhibitinganenergydispersionwhenremotelyobserved16–18.BasedontheO+dispersionfeature,weestimatethatthepotentialdropaccelerationoperatedaround1.5R altitude(Methods,subsectionEstimationoftheAARaltitude).

Thestrongcorrelationamongtheaurora,precipitatingelectrons,andescapingO+revealsthattheauroralaccelerationregionshouldbelocatedaround1.5R abovetheionosphere,andthepotentialdropisthefinalstepneededtoaccelerateelectronsforproducingtheauroralarc. To further assess the role of Alfvén waves in producing the potentialdrop,weinvestigatetheelectromagneticenergyflow,i.e.,thePoyntingflux,measuredbythetwoRBSPsatellitesduringthetraversal ofthearc.TheEarthwardPoyntingfluxisabout60mW/m2ascalculated from the spin fit electricfield(up to about100mHz) at both satellites(redlinesinFigs.3c,e).However,comparingthefrequencyspectrogramofthemagneticfieldatRBSP-A(Fig.3b)tothatatRBSP-B(Fig.3d),wenotethatthewavepoweratthesmallerkineticscalesdoes exist atboth RBSP-A and -B (>100 mHz). The availability of highercadence electric fields at RBSP-B allows us to include this power,resulting in a better estimate of the actual Earthward Poynting flux(Fig.3eorangeline).TheestimatedPoyntingfluxof350mW/m2(seealso Fig. 5c) is enough to account for the estimated kinetic energyfluxes of the inverted-V electron (162mW/m2) and the escaping O+(44mW/m2).TheestimatedenergyefficiencyfromthewavetoaccelerateelectronsandO+isthus59%,suggestingthattheenergyconversionwithinthepotentialdropislikelytobehigh.

Figure4summarizestheenergyprocessesmeasuredinthemagnetosphere,auroralaccelerationregion,andprecipitation.OurobservationssuggestthatthesourceregionthatultimatelypowerstheAARlocates in near-Earth magnetotail, converting free energy to Alfvénwaves (i.e., shear mode waves), which efficiently transmit electromagneticenergyalongthemagneticfieldstowardthepolarregions.A significantportionoftheenergywouldbeconvertedwithinthepotentialdropthatcanaccelerateelectronstoformtheoften-observedinverted-Vstructure.Inthisstudy,theauroralelectronsaremainlyenergizedbythepotential drop, rather than directly from the parallel electric field ofAlfvénwaves(eitherthekineticorinertialAlfvénwaves19).

ThepotentialdropabovetheEarthisquasi-staticonthetimescaleoftheelectrons’transittime,whichisontheorderofseconds.Thisquasi-static nature invoked many theories based on electrostatic solutionstotheVlasov-Poissonequationsincludingdoublelayerandelectrostaticshocks20,21.Althoughsuchelectrostaticstructurescouldexplainmanyfeaturesofthepotentialdrop,howthesteadystateisreached requires electromagnetic treatments. For example, AlfvénwavescoulddevelopparallelpotentialdropofseveralkVduringthewavepropagationtowardtheionosphere22–24.Alfvénwavescouldalsocouple to the ionosphere and thus develop potential drops due to turbulence25, anomalous resistance26, and wave-wave modeconversion27.OurobservationsfavoranelectromagnetictheoryastheAlfvénwavesarecloselyrelatedtotheelectronandionaccelerationthroughthepotentialdrop.Accordingtoourobservation,themainwave energy, carried by the “regular” Alfvén waves at magnetohydrodynamic(MHD)scales,istransportedalongthefieldlinestowardstheionosphere.TheexactmechanismonhowAlfvénwavesaredissipatedthroughthepotentialdropistheremainingquestionforfutureinvestigations.

The Alfvén waves thatweobserved were wellwithin the inner-magnetosphere, where the Earth’s dipole field dominates. Downstreamofthesolarwind,theEarth’sfieldlinesarestretchedintoatail-configuration, within which localized dynamical processes such asburstybulkflows(BBFs)transportfreeenergytowardtheEarth28–31.A BBFcontainslocalizedfastflowsthatexciteshear-modewavesaroundthe sides due to flow shears and compressional waves around theEarthward head. We propose thatthe observed Alfvén waves couldarise from either the shear mode waves of BBFs or the mode-conversionfromthecompressionalmodewaves32,33ofBBFs.AstheseAlfvénwavestendtobemoreintensearounddensitygradients34,itseemstofavorthegenerationthroughmode-conversion22.

Potential drops were found to exist at both Earth and Jupiter,suggesting a common energy process across planets with globalmagnetic fields. Itisnatural to expectthat similar processes wouldexistatothermagnetizedplanetssuchasSaturn,consideringmanysimilarauroraldynamicsamongsttheseplanets35–41.Nevertheless,thepotentialdropmagnitudeatJupitertypicallyexceedsthatofEarthbyoneorderofmagnitude.Althoughitisstillamysteryonthecontrollerof the magnitude, we can reasonably speculate that the planetarymagneticfieldstrengthplaysakeyrole.Themagneticfieldatauroralsource region is 7-8 Gauss at Jupiter42,43, which is about 20 timesgreaterthantheoneatEarth.Thevalueisquiteconsistentwiththeenergydifference,providingahintonthepossiblecontroller,whichisyettobeunderstood.Althoughelectricpotentialdropisanimportantstep formagnetospheric energy conversion to auroralparticles, we shallalsopointoutthatauroralelectronsmayalsobedirectlyacceleratedbyAlfvénwaves44,45,andauroralemissionsarefoundinvariedtypesofcelestialobjects,suchascometwithnomagneticfield46,Marswithcrustalfield47,48andJupiter’smoons49.

Using a fortuitous set of coincident observing platforms measuringdifferentfacetsoftheEarthauroraleventonApril16,2015,we providestrongevidencethattheelectromagneticenergyoftheAlfvénwavespowerstheEarth’sauroralarcthroughastaticpotentialdropthatconvertsthisenergytokineticenergyofinverted-VelectronsandO+ionoutflows.OurfindingsunderscoretheinterplaybetweentheAlfvén waves and the potential drop and provide a comprehensiveviewofhowauroralarcsformonEarthandpotentiallyotherplanetsandastrophysicalobjects.

Methods
Satellitesandinstrumentation
TheVanAllenProbes,alsoknownastheRadiationBeltStormProbes(RBSP-A and -B), containtwo identicalsatellites in equatorialorbitsaroundtheEarth.Theorbitalapogeeis5.8R (EarthRadii)andthusiswellabovetheauroralaccelerationregion(AAR),whichistypically1-3R abovetheionosphere50.Datausedincludetheelectricfield,magneticfield,thermalplasmameasurementsfromtheElecticFieldandWaves instrument (EFW)51,52, the Electric and Magnetic Field InstrumentSuiteandIntegratedScience(EMFISIS)53,54,andHeliumOxygenProtonElectroninstrument(HOPE)55.Routinely,EMFISISprovides3Dmagneticfield ~Bat64samples/secandEFWprovides2Delectricfieldat32samples/secwithintheplanethatisperpendiculartothespin-axisofthesatellites.Thespin-axiselectricfieldiscalculatedbasedonthe ~E(cid:4)~B=0 assumption from the ideal magnetohydrodynamic (MHD) condition.Here ~Eisthe3Delectricfieldintherestframeoftheplasmacorotating with the Earth and ~B is the background magnetic fieldobtained by low-pass filtering ~B 0 over a 20min window (0.83 mHz).

HOPE measures the thermal plasma from several eV to 50keV per chargeforelectron,H+,O+,andHe+,withacadenceof22secandapitchangleresolutionof18deg.

EFWprovides,inadditiontothesurveyresolution(32samples/sec)electricfield,aspinfitelectricfieldatthecadenceofonesampleperspin period of the spacecraft (about 11sec)52. The survey resolutionelectric field is available when all four EFW spin plane probes areworkingproperly,whereasthespinfitelectricfieldisavailablewhenatleast two of them work. In this event, only RBSP-B had the survey electric field, yet both RBSP-A and -B have the spin fit electric field.

Coordinate
TheSolarMagnetospheric(SM)systemiscommonlyusedwithintheportion of the geospace dominated by the Earth’s dipole field. Thez-axisisexactlyalignedwiththeEarth’sdipoleaxis.They-axisisperpendiculartotheSun-Earthlineandz-axis.Thex-axiscompletesthetriadsystem.Inaddition,thefield-alignedcoordinate(FAC)isusedtopresent the electric and magnetic fields and Poynting flux. In thiscoordinatesystem,theb-axisisalongthebackgroundmagneticfield ~B 0;thew-axispointsazimuthallywestward;theo-axispointspoloidaloutward.

TheidentificationofkineticAlfvénwaves(KAWs)
Intensive low-frequency electromagnetic waves like those shown inFig.3havebeenroutinelyobservedintheEarth’splasmasheetanditsboundary layer during geomagnetic active times11,34,59. Such wavesoften have a broadband frequency spectrogram over ion gyrofrequencies,suggestingthattheyarenotcyclotronwaves,andthatthebroadbandnatureisaresultofDopplershift60.ConsideringtheDopplershiftduetotherelativevelocity~v f betweenthespacecraftandlocalplasma,thedispersionrelationforAlfvénwavesinkinetictheoryisω=k k=v A 1+k2 ? ρ2 i .Hereωistheangularfrequency,k kandk ?arethe parallel and perpendicular wave vectors, respectively, v A is theAlfvénspeed,andρ i= k B T e =m i =ω ci istheionacousticgyro-radiusrelatedtotheelectrontemperatureT e,ionmassm iandioncyclotronangularfrequencyω ci.ThisdispersionrelationdescribesthekineticAflvenwaves,forplasmabetaβ2ðm e =m i,1Þ15,61,wherem eandm iaretheelectronandionmasses,respectively.

TheparallelphasespeedofkineticAlfvénwavescanbeapproximatedintermsofthewavefrequencyinthespacecraftframef SC as
v A u u t 1+ f2 S v C 2 ρ2 i ð1Þ

Here,sincethelocalplasmacontainedbothH+andO+,weusedthe averaged ion mass m i=ðn H m H+n O m O Þ=ðn H+n O Þ and the associatedioncyclotronangularfrequencyω ci=eB=m i.E ?,out andB ?,west aretheelectricfieldalongtheo-axisandthemagneticfieldalongthew-axis, respectively. The axes are defined in Methods, subsectionCoordinate.Theflowspeedv f istakentobe42km/s,whichisscaledfromtheangularspeedoftheazimuthaldevelopmentoftheauroralarcshownin Fig.3a.GiventhearcdevelopedprimarilyazimuthallywithoutsignificantchangeinMLat,weinferthattheazimuthalflowisthedominantcomponent64,65.

Figure5showsthecomparisonbetweenthemeasuredE/Bratioand the wave dispersion relationship as a function of f SC. Thequantities are averaged over the two minutes interval marked inFig.3cande,coincidingwiththelargestPoyntingflux.ForRBSP-A,since only the spin fit electric field is available, the comparison islimitedtof SC below100mHz.Withinthisfrequencyrange,wecanseethatthemeasuredE/Bratio(black)isconsistentwiththelocalAlfvénspeed(red)derivedfromotherindependentmeasurements(Fig.5a).ThisandthesamecomparisonatRBSP-B(Fig.5c)suggestthattheselow-frequencywaves(f SC<100mHz)are“regular”Alfvénwaves(shearmodeatMHDscales).KinetictheoryshowsthatAlfvénwavesexistastheinertialAlfvénwavesforβ≪m e =m iandthekineticAlfvén waves for m e =m i ≪β≪115. The difference between the twomodesisobviousatkineticscales,whichDopplershifttohighfrequenciesinthespacecraftframe.AtRBSP-B,whichhashigherresolutionelectricfieldmeasurements,thebehavioroftheAlfvénwavesatkineticscalesisconsistentwiththedispersionrelationshipofthekineticAlfvén waveshowninEq.1(orangelinesinFig.5c),suggestingthattheAlfvénwavesobservedatRBSP-BarekineticAlfvénwaves.Giventhesimilarhigh-frequencywaves(>100mHz)asseeninthemagneticfield(Figs.3b,d),weinferthatRBSP-Aalsoobservedthe“regular” and kinetic Alfvén waves and with similar magnitude toRBSP-B.Figure.5banddshowthatthepowerofthePoyntingfluxassociated with the Alfvén waves peaks around the 10 mHz frequencyrange.

We note thatin this paper, the term Alfvén wave refers to theshear-modeAlfvénwavesincludingthewavepoweratboththeMHDandkineticscales,whichcorrespondtothe“regular”andkineticAlfvénwaves,respectively.

Thecalculationofpoyntingflux
The“AlfvénicPoyntingflux”,whichisthePoyntingfluxassociatedwithAlfvénwaves,hasbeenextensivelystudiedinthepastseveraldecadesin the Earth’s magnetosphere in terms of observations9,34,59 andsimulations66,67andhasbeenrecentlystudiedonJupiter68.ToresolvethefrequencydependenceofthePoyntingflux,weadoptthefollowingequationtocalculatethePoyntingfluxspectrogramasafunctionoftimetandfrequencyinthespacecraftframef SC
~S f SC,t = ~E f SC,t × ~B f SC,t ,
where ~E f SC,t and ~B f SC,t aretherealpartoftheMorletwavelettransformation.ThevectorPoyntingfluxisintegratedoverthecoveredfrequency
~SðtÞ= f h df SC ~S (cid:3) f SC,t (cid:4)
ThisisthePoyntingfluxpresentedinFigs.3c,e.Theupperfrequencylimitf h isusuallylimitedbythecadenceoftheelectricandmagneticfields.Thelowerfrequencylimitf lisusuallydeterminedbythedurationofthesignificantPoyntingflux.TobestestimatethetotalPoyntingflux,thelowandhighfrequency(cid:3)limits(f landf h)arechosento enclose the main power in ~S f SC,t . This procedure has beendocumentedandusedinmanypreviouspapers34,62,69.Atypicalchoice of the low frequency limit is 5.5 mHz9,70, which captures the mainPoynting flux power ingeneral.Here, the low frequency limits f l ischosentobe0.6mHz,whichreturnsaslightlylarger(2%)maximumPoyntingflux.HereweestimatetheuncertaintyofthePoyntingflux~SðtÞisontheorderof2%,relatedtothelowerlimittobeused.

Calculationofelectronenergyfluxbypotentialdrop
DMSPelectronmeasurementsdonotcoverallsolidangles.Therefore, estimating the energy flux associated with the inverted-Velectrons depends on assumptions of the electron distribution.Typicalinverted-Velectronsareisotropicinpitchangleexceptthelosscone71.Inthisstudy,we assumesuchadistributiontoestimatethe electron energy flux. The results are shown as the blue line inFig.6b.Independently,weestimatetheauroralenergyfluxbasedontheDMSPSSUSIsnapshot.TheresultsareoverplottedasreddotsinFig.6b.Theenergy fluxofthe inverted-Velectronscorrelates wellwiththatoftheauroralarc.Thisiswellexpectedastheinverted-Velectronsarethedirectenergysourceforexcitingtheionosphericatomswhichemittheaurorallight.

DMSP F19 crossed the auroral arc of interest that is shown inFig.2b.Thearccorrespondedtothethirdinverted-Velectronstructure inFig. 6b. The peakelectron energy flux is 162mW/m2. In thispaper,tocompareenergyfluxesatdifferentaltitudes,theyarenormalized to 100km altitude according to the scaling of a constantmagneticflux.Thepeakauroralenergyfluxis87mW/m2,whichis54%oftheestimatedelectronenergyflux.ThepeakPoyntingfluxatRBSPisestimatedtobe350mW/m2(Fig.3e).InMethods,subsectionEstimationoftheO+energyflux,weestimatethekineticenergyoftheO+outflowstobe44mW/m2.Theenergyconversionrateofthepotentialdrop from the electromagnetic energy of the Alfvén waves to thekineticenergyoftheinverted-Velectronsis46%.Therateis59%ifO+outflowsarealsoincluded.Hence,theenergyconversionsfromthePoyntingfluxtotheinverted-Velectronsandthentoauroralemissionsarebothhighlyefficient.

EstimationoftheAARaltitude
O+ outflows with clear energy-time dispersions are routinelyobserved during strong auroralactivitiesonEarth18,72. Such dispersion is also observed in this event, as shown in Fig. 7d. The anglebetweentheO+velocityandthebackgroundmagneticfield,whichiscalledthepitchangle,waswithin30deg(Fig.7c).Thedispersioniscausedbyatime-of-flighteffectofO+atdifferentenergies.Hence,tracingtheseO+backwardintimeandspacealongthemagneticfieldline allows us to determine when and where they originated. ThetracingresultsareshowninFig.7.ThetestparticlesforthetracingaremarkedasorangedotsinFig.7dandareselectedasfollows:foreachtimetag,thetestparticle’senergycorrespondstothemaximumflux.Figure7eshowsthetracingresults,whereeachorangelineisthetimehistoryofthemotionofatestparticlealongthefieldline.Thecrossingregionofthehistorytracesisdeterminedtobearound2.5R geocentricdistances(1.5R altitude),correspondingtothelocation of minimum spread (standard deviation) of the tracing lines(Fig.7f).Aspreviousstatisticalstudieshaveshownthatthetypicalaltitudeofthepotentialdropis2-4R geocentricdistances(Karlssonetal.52andreferencestherein),ourtracingresultisconsistentwithtypical expectations. In addition, our tracing determines the timewhen these O+ are generated to be around 08:08:14-08:09:42 UT(markedbytheverticalredlines).Thistimeisabout30secafterthepeakoftheEarthwardPoyntingfluxoftheAlfvénwaves(Fig.7a).Thetime lag may be related to the travel time of Alfvén waves to theionosphere(typically10–15sec)andthetraveltimeofO+fromtheionospheretoandthroughthepotentialdrop.

NotethatO+outflowscanbegeneratedbytwomechanisms.Oneisthroughparallelaccelerationofapotentialdrop(0degor180pitchangle)andtheotheristhroughperpendicularheating(90degpitchangle)ofavarietyofwaves73–75.Theperpendicularlyheatedionswillbeelevatedinaltitudebythemirrorforceduetothedipoleconfigurationandhencefoldedtoward0degpitchangle(or180deg)astheiraltitudeincreases.AtRBSP,thefoldingissosignificantthatthepitchangledistributions of parallel accelerated and perpendicularly heated O+cannotbeclearlydistinguished.However,withtheDMSPinverted-Velectronobservations,weinferthattheO+outflowsof1–10keVareduetoparallelaccelerationsbecausetworeasons:Firstly,theinverted-Velectronsare1–10keV,suggestingtheexistenceofapotentialdropof1–10kV;Secondly,thetimingoftheO+outflowsisconsistentwithaparallelacceleration,(c.f.Fig.7a,b).

EstimationoftheO+energyflux
WecalculatetheenergyfluxoftheO+outflowusingthetestparticlesdeterminedintheprevioussubsection.WeassumethatthedistributionofO+hasaspreadof3energybinsaroundtheenergyofthetestparticlesandthatthedistributionisuniformin[0,30]degpitchangle.InFig.7,theintegratedenergyfluxisnormalizedto100kmaltitude(blacklineinFig.7b).Tofurthercorrectfortheenergy-timedispersion,wetracethisenergyfluxbackwardintimeandobtainthetracedenergyflux(orangelineinFig.7b).Thepeakvalueofthetracedenergyfluxis44mW/m2.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review of “The energy source powering aurora through a static electric potential” by S. Tian and coworkers.\nThe authors present a case study based on multi-point observations made on the surface of the Earth and in surrounding space that shed light on how the magnetosphere is coupled to the ionosphere. Specifically, they show how kinetic Alfvén waves launched from the magnetotail lead to the formation of a quasi-static magnetic-field-aligned electric potential above the ionosphere that accelerates particles down into the atmosphere to produce an observed auroral arc.\nI recommend this paper be rejected, with re-submission encouraged. The manuscript needs a significant amount of work, but I think the authors should be prompted to try again if they think they can better explain the significance of the key result they present.\nMajor, overall comment: The context and importance of the results presented is not clear to me as a space physicist who is not en expert on this specific topic, and it certainly will not be clear to the reader. What exactly is mysterious about energy dynamics associated with the auroral acceleration region? What is the reason this mystery has persisted, despite many observations? Are there competing ideas to explain whatever the specific problem is? What is it about the observations presented here that allows the present authors to do better? Is it really surprising that changes in the magnetosphere are caused by Alfvén waves propagating through the system? Why does resolving the proposed mystery matter, what are the implications for this field and beyond?\nI suspect these questions may be answerable (giving the authors the benefit of the doubt). Combining this with the current absence of clear answers in the text is the basis of my recommendation to reject, encouraging re-submission.\nAbstract: There is very little content here. See above comments. Most of the questions I list should have been answered by the end of reading a revised version of the abstract.\nWhy include Jupiter at all? Seems done for the sake of it, without a clear rationale. This physics likely happens in some form at every planet, in the Solar System and beyond, so why only show some data from Juno at Jupiter? I suggest limiting the scope of the manuscript to the Earth system, highlighting implications for other systems in the discussion.\nFigure 1: Poor quality, needs work to improve clarity of axes labels, etc.", "reviewer_2": "Review of manuscript “The energy source powering aurora through a static electric potential” by S. Tian et al.\nFrom an auroral event on 16 April 2015, the authors evaluate data simultaneously obtained with four different means at three different altitudes in a unique constellation between satellites and aurora. The data covered electric and magnetic fields measured by the two radiation Belt Storm Probes, RBSPs, near 5.8 RE, electron fluxes measured by the Defence Meteorological Satellite Program, DMSP, at 840 km height, and observations of all sky cameras on the ground. The authors focus on the energy flow into the acceleration region of the auroral particles, differentiating between electrostatic and wave acceleration. The paper is composed of a Main part containing the results and a Method part meticulously describing how the data were obtained and analysed. The central quantity to be derived was the Poynting flux and its comparison with the flux of the electrons and upward accelerated O+ ions. The main conclusion was that kinetic Alfvén waves, excited in the source region encountered by the RBSP spacecraft, were carrying the energy into the acceleration region between 2 and 4 RE altitude with sufficient power to cope for the observed particle fluxes.\nThe paper is most interesting. The separation into main results and methods is very beneficial for the reader and illuminating for the expert. All parameters and the instrumentation are well described. Much emphasis is placed on the identification of the waves, their spectra, and energy fluxes. A particularly nice piece of work is the determination of the height of the acceleration region from the dispersion of O+.\nI have a few reservations about two conclusions. (1) The authors suggest that the Poynting flux carried by kinetic Alfven waves is absorbed in the auroral acceleration region (lines 117/118, 142/143, 171/172, 535/536), admitting, however, that they are unable to propose a mechanism. It is commonly thought that kinetic or inertial Alfven waves in the magnetosphere have frequencies higher than shown in Figure 3 and are absorbed at low heights generating strongly field-aligned electrons with a diffuse energy spectrum. By contrast, the Poynting flux derived from the RBSP wave data is dominated by the low frequencies. These are most likely an expression of the plasma dynamics at the source region, as indicated by the strong changes in tilt angle of the magnetic field (Figure 2d). The main effect of the agitated plasma is bending or shearing of the magnetic field, which is transported along the field lines towards the ionosphere by regular, not kinetic Alfvén waves. On the other hand, the concentration of the wave energy flow into downward and westward direction is surprising. Some comments on that may be helpful. With respect to the interaction with the AAR, I find the paragraph from lines 176 to 187 not very illuminating on this subject.\n(2) The derivation of the relative velocity of spacecraft and plasma from Figure 3a is rather questionable. The narrow, elongated shape of the arc suggests that it is generated from a boundary. The variation of the brightness along this boundary likely reflects variations of the agitation from higher altitude, as for instance by a BBF. However, I do not see how much this affects the conclusions.\nOverall, a good paper, worth to study. Can be published essentially as is, after response to my comments.\nGerhard Haerendel", "reviewer_3": "The paper \"The energy source powering aurora through a static electric potential\" addresses the energy transport / balance in the auroral magnetosphere-ionosphere (M-I) by presenting an event study based on Van Allen / RBSP, DMSP F19, and ground THEMIS optical data. While the fundamental components of the energetics involved are understood nowadays rather well, close quantitative estimates are scarce, if at all. In this respect, the manuscript fills a significant empty spot and my overall assessment is that, essentially, the paper is suitable for publication in Nature Communications. However, I think the message can be better streamlined and the contribution made by the paper better pinpointed, as detailed below.\n1. The authors emphasize the 'mystery' around auroral acceleration and particle energization, related to the relationship between quasi-static and Alfvenic acceleration (L27, 39, 45, 50, 203), as well as the 'discovery' made. I feel a bit hesitant on using those words, since the matter has been broadly addressed in the literature - as proven also by the rich selection of cited papers. The fundamental building blocks were summarized in several monographs (e.g., Auroral Plasma Physics, Springer, 2003"}, "author_response": ""}]

Decision letter