Electrostatic waves due to fieldaligned electron

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Mar 1, 1992 - V. PEROOMIAN, l M. ASHOUR-ABDALLA, 1,2 S. A. FUSELIER, 3 D. SCHRIVER, 2 ... AMPTE CCE (Active Magnetosphere Particle Tracer Ex- ..... Figure 5 shows a velocity-angle distribution contour plot as .... Velocity Ckm/sec]. (,) ... T. 2.8 • o u_O. Fig. 7. Electric field spectral density versus time on a 30-min ...

JOURNAL OF GEOPHYSICAL

RESEARCH,

VOL. 97, NO. A3, PAGES 3169-3183, MARCH

1, 1992

Electrostatic Waves Due to Field-Aligned Electron Beams in the Low-Latitude Boundary Layer V. PEROOMIAN,l M. ASHOUR-ABDALLA,1,2S. A. FUSELIER,3 D. SCHRIVER,2 W. K. P.ETERSON,3 AND R. J. STRANGEWAY2 We have analyzed mass-resolvedion, electron, and plasma wave data obtained from several

low-latitude boundary layer(LLBL) crossings bytheAMPTECCEsatellite. Thedataclearlyseparate the LLBL from the adjacentmagnetosheathand magnetosphere.The availableplasmawave data were limitedto highfrequencies;thereforewe focusedour attentionon wave-particleinteractionsinvolving electrons.We found that electronbeamsare presentin the LLBL during southwardinterplanetary magneticfield, along with a simultaneousenhancementof electrostaticwaves with parallel polarization. Linear theory analysis shows that for plasma conditions in the LLBL, electron beams are

unstable to electrostatic waves' thatpropagate parallelto thelocalmagnetic field,in agreement with observations.A numericalsimulationstudyof the beam-plasmainteractionin the LLBL hasalsobeen

undertaken to examinethe saturationmechanism. The simulations showthat the beaminstability saturatesby thermalizationof the beam but that a beamlike structurecan still remain in the electron distributionfor certain initial parameters.The results suggestthat peaks in the electron velocity

distribution functionmaybefoundin theLLBL awayfromthebeamsource region. 1.

1989a,b]. For example,thec61dO + ionbeamsobservedin

INTRODUCTION

the LLBL reported by Fuselier et al. [1989b] augment the

of counterstreaming electrons in the The low-latitude boundary layer(LLBL) is a regionlying earlier6bservations earthward of the dayside magnetopausecurrent layer. It

LLBL [Ogilvie et al., 1984].Because mostofthesurface of

separatesthe shockedsolar wind plasmaof the magneto- thedayside boundary layeris onfieldlinesthatmaptOthe sheathfrom the Earth' s magnetosphere.The LLBL wasfirst auroralregion(see, for example,Eastmanet al. [1976]), identifiedalong the flanks of the magnetosphereusingrela- electron beamsoriginating in theauroralzoneat altitudes of tivelyløwtimeresolution particlemeasurements [Honeset a fewthousand kilometers maybethesource of theLLBL al., 1972;Easttnanet al., 1976]and is composedof particles electronbeams[Ogilvieet al., 1984;Sharpet •l., !980;

et al., fromthemagnetosheath andmagnetosphere. It isthroug h Coilinet al., 1982;KlumparandHeikkila,1982;'Burch

the LLBL that solarwindPlasma,momentum, andenergy are transferredinto the Earth's magnetosphere. It was not until the launch of the ISEE 1 and 2 satellites in 1977 that

1983].

..•

The observation of magnetosheath ions jn the LLBL

confirms thattransport and/ordiffusion of magnetosheat h

for its entryintothe boundary layer. plasma •m•asurement sweremade withadequate timereso- plasmais responsible

lution$oidefitifystructure in the LLBL nearthe subsolar Wave-particl e interactionsprobablyplay a role in these point.ThetSEE particlemeasurements established thatthe processessince turbulence can affect energy dissipationin thicknessof the boundarylayer is highly variable but in

the magnetopause [Axford, 1964; Bernsteinet al-, 1964;

gen6r•fis"•Uch thicker thanthemagnetopause current layer Eviatarand Wolf, 1968;Hasegawaand Mima, 1978;Haerendel, [H•&en'd;•.e•'.al., 1978; P•schmann etal.,1978i Eastman

1978]. Wave turbulence is a common feature of the

and:Honed•.-•9; Eastman,1979].; However,the ionmass magnetopause, with the bulkof the emissions attributedto spect•omete • i:hdnot havesufficient timeresolution to re- low-frequency broadbatid electricandmagnetic fieldturbuSOlxie•the LLB•Lionmassspectra (see,forexample, Peter- lence[Gurnetteta!., 1979].High-frequency narrow-•band

sonet'al. [i982]).A majoremphasis of currentmagneto-emissions nearthelocalelectron plasma frequencY, which spheric research is an investigation of thenatureof the might •be eitherplasmaoscillations or upperhybridreso.

microscaleand macroscaleprocessesoccurringin the nance waves, have also been observed in the LLBL [Gurnett LLBL. The Hot PlasmaCompositionExperiment (HPCE) on the AMPTE CCE (Active MagnetosphereParticle Tracer Explorers Charge CompositionExplorer) spacecraftprovided

eta!.,

1979].

In this paper we examine high time resolutionparticle and available plasma wave observationsmade in the LLBL by the AMPTE CCE spacecraft.we use the high time resolu-

the first energeticion composition measurements with suffi- tion particlemeasurements and associatedquasi-dcmagnecient temporalresolutionto resolvethe LLBL. The HPCE ion observationshave resolved someambiguitiesabout the

tometer measurementsto identify the exact times when the spacecraftis in the LLBL and to characterizethe densities

structure and dynamics of the LLBL [e.g., Fuselier et al.,

and temperatures of the various LLBL constituents. We

then examinethe limited resolutionplasmawave data availIDepartment ofPhysics, University ofCalifornia atLosAngeles. able on the same spacecraftin order to investigatethe types

2Institute of Geophysics andPlanetary physics,University of 3Lockheed SpaceScience Laboratory, PaloAlto,California.

of wave-particleinteractionsoccurringin and near the LLBL. The limitations (both in frequency and in time

Copyright 1992by the American GeophysicalUnion.

higher-frequency plasma wavemodes which arepresumabl•y

Californiaat Los Angeles.

coverage) of the plasma wave data require us to focus on

Paper number 91JA02703.

driven by the electron beams observed in the LLBL. We

0148-0227/92/91J A-02703$05.00

haveusedthedatapresented belowto explorefor thefirst 3169

3170

PEROOMIAN ET AL ' ELECTROSTATIC WAVESDUE TO FIELD-ALIGNEDELECTRON BEAMS

time a possiblelink between high-frequencyelectrostatic almostevenly distributedbetween occurrencesof northward emissions and field-aligned, counterstreaming electron and southwardinterplanetarymagneticfield (IMF). beamsobservedsimultaneouslyin the LLBL. On the basis To characterizethe propertiesof the LLBL, in particular of these observations, electron beam-driven instabilities are the total density, and to assist in the identification of this examined both analytically and numerically. For plasma region,we examinedeachmagnetopause crossingusingboth parameters observed in the LLBL, the observed electron the HPCE and magnetometerdata. To identify the LLBL, it beamscan be unstable.Analytic expressionsare derivedfor mustbedistinguished fromtheadjafentmagnetosheath and the growthrate of a beam-plasmatype instabilitywith a cold magnetosphere.For southwardIMF intervalsin this study, electron beamin a background of warmionsandelectrons. the magnetopausewas readily identifiablein the magnetic

Also, the generalelectrostatic dispersion relationis solved fielddataas the rotationfrommagnetosheath to magnetonumerically to obtain exact solutionsfor observed LLBL parameters. Finally, numerical simulationsare carried out to

spheric orientation. UsingtheHe++ He+ O+ andelec• tronmeasurements, the extentof the LLBL (thatregionof

establishthe lifetime of the beamsin the plasmaconfigura- magnetosheathlike plasmaearthwardof the magnetopause) tionof theLLBL. Conditions forthepersistence ofbeams in was identified. Magnetic field data are not sufficient to this regionare establishedvia a parametersearchinvolving determine the magnetopause locationfor manynot'thward changes in beamvelocity,temperature, andrelativedensity. IMF intervals.However, we have found that by usingthe

TheWave •modes involved intheinstability ofthebeams and magneticfieldandthe energeticelectron(>3 keV) flux the their saturation mechanisms are also examined and dis-

magnetopausecan be identified for northward IMF [see

cussed.

Fuseliefet al., 1989a]. The He++ observationswere also This paper is organizedas follows: In section2 we discuss particularlyusefulin definingthe magnetospheric boundary, the nature of the AMPTE CCE crossingsof the LLBL and sincethereis little He ++ in the magnetosphere below17 the methodsusedto distinguishmagnetosheath, LLBL, and keV/e. magnetospheric plasmapopulations;next, in section3, we present examples of the particle data and summarizethe 3. OBSERVATIONS observations.As noted above, the limited frequencyand temporalresolutionof the availableplasmawave data neA compilation of electron and ion densitiesfor the seven cessitatethe focusingof our attentionon the relativelyhigh magnetopause crossings ispresented in Figure1. Densities frequency electron beam-driven instabilities.These instabil- for the LLBL and adjacent magnetosheathand magnetoities are discussedin section4. In section5 we present sphereare shown.The shadedregionsin this figurecorrenumerical simulationsof the plasma configurationin the spond to therangeof observed densities. ThisfigureShows LLBL.

These results are then summarized and our conclu-

sionspresentedin section 6.

thatthedensities of magnetospheric particles (suchasO+ andHe+), whilefinitein theLLBL, fall offto verysmall

valuesin the magnetosheath. Also, enhancement of.the O + density in the LLBL is seen. Notable in this figure is the fact 2. AMPTE CCE LoW-LATITUDE thatthereare discrepancies betweenthe electronandproton BOUNDARY INTERVALS densitiesin all three regions,with electrondensitiesbeing The AMPTE CCE orbit hasan apogeeof 8.8 Re. There- smallerthan ion densitiesby a factor of approximately4. fore becauseof increasedsolarwind pressurethe magneto- This is becausea significantfraction of the electrondistrispheremust be compressedfor the spacecraftto encounter bution is below the 50-eV low-energycutoff of the lowestthe LLBL and the adjacentmagnetosheath. While not rep- energy electron spectrometer. Since the AMPTE CCE does resentativeof typical conditions,compressionsof the mag- notinclude activeexperiments to measure O)pe directly,an netopauseto inside 8 Re occur frequently. These occur- estimateof the electrondensityis bestachievedby comparrencescorrespondto fast, high-density,and highly variable isonwith the local ion population.Utilizing this method,we solar wind conditions.Seven such crossings,each several arriveat an estimated rangeof 10--50 cm-3 for theelectron minutes in extent, near the subsolarpoint of the dayside densityin thisregion.Previousstudieshaveput thisrangeat magnetopausehave been examined using ion and electron 1-10cm-3, a factorof 5 lowerthanthe present results particle data from the Hot PlasmaCompositionExperiment [Eastman and Hones, 1979; Paschmann, 1979]. This factor (HPCE) and wave data from the PlasmaWave Experiment of 5 is attributed to the fact that the CCE spacecraftonly (PWE). The HPCE consists of a set of eight magnetic crossesthe magnetopause when the magnetosphere is comelectron spectrometersmeasuringflux of electrons in the pressed.This compressionis usuallythe resultof higherthan 50-eV to 25-keV range as well as a separateenergeticion average solar wind densities which result in higher than mass spectrometerwith an energy per charge rangingfrom average LLBL densities. The densities estimated here corthe spacecraftpotential to 17 keV/e [Shelley et al., 1985]. respondto an electron plasmafrequencyrange of 28-63 The HPCE is capableof resolvingthe majormagnetospheric kHz. massconstituents, namelyH +, He +, He ++, and O +. The The compilationof temperaturesis presentedin Figure 2. PWE has four channelswith center frequenciesof 0.1, 0.73, Once again, the shadedareas represent the range of ob5.4, and 30 kHz, each with a 30% fractional bandwidth. The served data. In general, the electron population in the PWE also has an extra channel centered at 178 kHz, with a magnetosphereis hotter than that in the magnetosheath, 15% fractional bandwidth [Scarf, 1985]. Data from the with the LLBL populationtemperaturefallingbetweenthese magnetometeron AMPTE CCE were also availableand used two extremes.Thisis alsothecasefor theH + ions.We note, in this study [Potemra et al., 1985]. The seven extended however,thatthe He+ population is hottestin the LLBL, intervals examined include over 70 minutes (more than 700 suggesting thatthisspecies is heateduponentryintothe spacecraftspins)in the LLBL. The crossingintervals were region,a resultin agreementwith previousstudies[Fuselief

PEROOMIAN ET AL ' ELECTROSTATIC WAVES DUE TO FIELD-ALIGNED

ELECTRON BEAMS

3171

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FiS. 1. Summary of densityranSos (in crn-3) for electrons, H + ions,He+ ions,He++ ions,and0 + ionsin the LLBL and adjacent rnasnetosphcrcand rnasnctosheath, averased over seven boundary layer crossinss with measurableheavy ion concentrations.ShadedreSionsin this fiSurecorrespondto the ranScof observeddensities.

et al., 1989a]. No temperatures are listedfor He ++ in the This is followed by a study of wave data for that specific magnetosphere andfor Hc+ in themagnetosheath owingto crossing.For each case we discussthe implications of the an insu•cicnt number of particlesfor a valid analysis.

observations as well as the correlation between observations

The O + ionshavea muchbroadertemperature rangein

of electron beams and high-frequency waves in the LLBL. the LLBL than in the magnetosphere.Since the bulk of this The casespresentedbelow were selectedfor the following ion species enters the boundary layer from the magneto- reasons.The first case presented,while representativeOf

IMF crossings, isuniquein thatit corresponds to sphereandsincewe observedan enhancement of O + in the southward LLBL (shownin Figure1), wc conclude thatthisadditional a caseof highsubstormactivity.The secondcaserepresents component of O + corresponds to the cold O + beamsof a boundarylayer crossingduring northward IMF. high-latitudepolar ionosphericorigin previouslydetected [Fuselier et al., 1989b]. With the general plasma properties of the LLBL delin-

Case 1' Southward IMF,

November 16, 1984

Particle data. This event correspondsto a boundary eated,we next examinetwo specificboundarylayer crossings. In each casewe examinethe pitch angledistributions layercrossing duringa verydisturbed timewhenKp = 8 and the phase spacedensitiesof the electronsin an attempt

and AE --• 1000, and it occursjust after a substormduring

tofindevidence offield-aligned electron beams intheLLBL.

whichAE peaksat 2000.Previousstudieshavealsoshown ,

3172

PEROOMIAN ET AL.' ELECTROSTATIC WAVESDUE TO FIELD-ALIGNED ELECTRON BEAMS

105 MAGNETOSPHERE

BOUNDARY

MAGNETOSHEATH

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Fig.2. Summary oftemperature ranges (inelectron volt. s)forelectrons, H+ ions,He+ ions,He++ ions,andO+

ionsin theLLBL andadjacent magnetosphere andmagnetOsheath, averaged overseven boundary layercrossings with

measurable heavyion concentrations. Shaded regions 'J'nthisfigurecorrespond to the rangeof observed data. Temperatures for-He++ in themagnetosphere andO+ in'themagnetosheath couldnotbeobtained. ,

that reconnectionoccursat the daysidemagnetopausedur-

in the magneticfielddata.The total magneticfieldis dipole-

ingthisc,r. ossing.Figure3 showsthe numberdensities of like at 0300 UT and slowly decreasesacrossthe boundary electronsand H + He ++ and O + ions as well as the total magneticfield,•on 'a 2-hour time scale. At 0300 UT the

spacecraftis in the magnetosphere and is outbound.The

layerto the levelof the magnetosheath, encountered briefly at 0421 UT. While the entire region traversed during the interval 0405-0421 UT is identified as the boundary layer,

hasnumerous encounters withboundarylayer densities ofboth•lLI + andHe++,however, arefiniteinthis thespacecraft plasmawhichcloselyresembles that of the magnetosphere. region butwell beiow themagnetosheath values. IncomparTheseencounters are especially frequentduringthe period

ison, thede•sitie• 'ofH+ andHe++inthemagnetosphere

are much lai'gerin this case than on any other crossing 0413-0421 UT. Figure 4 showsplots of the electron number density, examined,suggesting the possibilityof leakagebecauseof a and pitchangleon a 2-mintime scale.Figure reconnected and open magnetopause.The spacecraft temperature, the timeintervalduringwhichthe crossing crø•sesinto the boundarylayerat 0405UT. We notethe 4a represents increasein H + and He ++ densitiesto valuesbetweenthose into the boundarylayer occurs.To the left in this figure,at ofthemagnetosphere andmagnetosheath, accompanied bya 0404 UT, the spacecraftis in the magnetosphere.The largepopulation OfO+ ions.Thistransition canalsobeseen boundarylayer crossingis evidentat 0405:05UT, as indi-

PEROOMIAN ET AL ' ELECTROSTATICWAVES DUE TO FIELD-ALIGNED ELECTRON BEAMS Electron

cated by the increase in electron number density and the associateddrop in electron temperature. Both before and after the crossing,the electrondensitypeaksat 0øand 180øof pitch angle. At times before the boundary layer crossing, however, the peaksin the electronnumberdensityare due to

3173

Flux

16 November

1984

102' ' {I''' ''' ;clm•;•l'' I ' 'l[ { ' ' ' i Number density •

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temperatureanisotropiesand do not constitutefield-aligned beams. We will, however, show that the peaks in the electron number density during the boundary layer crossing correspondto the observedfield-aligned,counterstreaming electron beams in this region. Figure 4b showsa 2-min time interval startingat 0412 UT, when the spacecraftis in the boundary layer. The electron number density is now very sharply peaked at the above mentioned pitch angles (dashed lines). This feature, unique to this crossing,results from the presenceof an additional set of beams in the LLBL. This additional set of beams, while small in magnitudeduring the entire boundary layer crossing,is 5 times strongerat 0412:50and retainsthis level

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Evidence of the presenceof thesebeamscan be examined with the aid of electron velocity-angle distribution plots. Figure 5 showsa velocity-angledistributioncontourplot as well as cuts of the velocity distributionparallel and perpendicular to the magneticfield for a 20-s time interval immediately after the boundary layer crossing.While Figure 5a, the

(b)

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Particle and Magnetic Field Data 16 November

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0413:40 8.033 0901:26 -10.493

Fig. 4. Electron number densities and temperatures for two 2-min intervals: (a) the interval centered on the boundary layer crossingand (b) the interval with an additional set of beams. Dashed lines correspondto 0ø and 180ø of pitch angle. The boundarylayer crossingis denoted by a dotted-dashedline.

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pitch angledistributionof electrons,does not show evidence of beams because of relatively small contours and low resolution, two setsof beamscan be resolved in Figure 5b as peaks in the parallel cut of the electron velocity distribution (shown with arrows). The absence of these peaks in the perpendicularcut (Figure 5c) clearly shows that these are

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Fig. 3. CCE observationsfor a 2-hour time interval on November 16, 1984. The panels correspondfrom top to bottom to the

electrondensity, H + ion density, He ++ ion density,O + ion density, and total instantaneousmagneticfield. The boundarylayer crossing(040'•.-0421UT) is marked by dashedlines.

valley-to-peak difference of approximately half an order of magnitude. Figure 6 representsanother 20-s interval in the boundary layer, this time commencingat 0412:50, at the onset of the high spikesin the electron number density versuspitch angle plots (Figure 4b). The plots again show evidenceof two sets of field-aligned, counterstreaming electron beams in this region. However, we now see that the faster set of beams has grown stronger, with an order of magnitude increase in the valley-to-peak velocity distribution. What distinguishesthis crossingfrom all others examined is that it coincides with the occurrence of a very strong substorm (Kp = 8 and AE --- 1000). The additional set of field-alignedelectron beams observed may therefore be a result of particles being dumped into the LLBL during this substorm or of dayside reconnection associated with this event. We will next examine wave data for this day and focus specificallyon the intervals discussedabove. Wave data. The wave data for this day from the PWE instrument on AMPTE CCE are shown in Figure 7. This

3174

PEROOMIAN ET AL ' ELECTROSTATIC WAVES DUE TO FIELD-ALIGNED

ELECTRON BEAMS

Electron Velocity Space Distributions 16 Noven't•

1984

0405:20-0405:40

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Fig. 5. Velocity spacedistributionand cuts of the distributionparallel and perpendicularto the ambient magnetic field averagedover 20 s immediatelyafter the boundarylayer crossingshownin Figure4. Two setsof counterstreaming beamsare apparent in the parallel cut.

figureis a 30-min plot of the electric field spectraldensityfor the five channelsof the wave instrument, covering the time interval 0400-0430 UT. The boundary layer interval of 0405-0421 UT is shown by dashed lines. As discussed above, the electron plasma frequency has a range of 28-63 kHz; therefore waves causedby instabilitiesassociatedwith an electron beam in a background electron plasma with

and Meyer-Vernet, 1989; Strangeway et al., 1990]. The enhancedregion therefore merely representsthe new backgroundlevel of the electric field in the magnetosheath,which is denserthan the LLBL. Spikesup to 2 ordersof magnitude higher than the backgroundelectric field are presentin this plot. These spikesoccur intermittently duringthis boundary layer crossingbut are most intenseduring the time interval 0412:50-0413:10 UT, when the second set of beams is at its maximumgrowthnearfee are expectedto manifestthemselves in the 30-kHz channel of the PWE. Our discussion of strongest.The electric field for a typical spikeis 0.19 mV/m, wave data will therefore be limited to the characteristics of comparedto a backgroundelectric field of 0.01 mV/m. The this channel. highestspikes, correspondingto periods of strongelectron In examining Figure 7, we note that the electric field beamactivity, have electricfieldsof the order of 1 mV/m. As envelope or backgroundlevel is often amplified, most nota- noted above, there are intervals during which the plasma in bly from 0421 to 0429 UT. This is becauseof the sensitivity the boundary layer is magnetospheretike(i.e., 0417:30of the wave instrument to changesin density and electron 0418:00 UT). During these intervals there is very little impact on the antenna [Strangeway et al., 1988; Chateau spiking, and the electric field decreasesto the background

Electron Velocity Space Distributions 16 November

1984

0412:50-0413:11

UT

Parallel

Perpendicular

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Fig. 6. Velocity spacedistributionand cutsof the distributionparalleland perpendicularto the ambientmagneticfield averagedover 20 s during the enhancedbeam activity. The second(faster) set of beamsis now larger in magnitude.

PEROOMIAN ET AL.' ELECTROSTATIC WAVES DUE TO FIELD-ALIGNED

Wave

1984

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16 November

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Fig. 7. Electricfieldspectraldensityversustimeona 30-mintimescaleencompassing theboundarylayercrossing in case I (dashedlines). Shownare the five channelsof the PWE instrumentplus the magneticfield magnitude.The interval of enhancedbeamactivity is also shown(dottedlines).The 30-kHz channelshowsenhancementin the form of spikesduringtheboundarylayercrossing.The waveactivityin thischannelis especiallystrongduringthe enhanced beam interval.

level. Also, these intervals correspond to periods during which field-aligned electron beams are not seen. This is further evidencethat the spikingseenhere is associatedwith the presence of field-aligned electron beams in the lowlatitude boundary layer.

Figure 10 shows the average velocity space distribution and the correspondingcuts in the distribution for a 97-s interval commencingat 2307 UT. No beamsare seenin the parallelcut to the distribution,suggesting that the peaksseen in Figure 9 are a result of a temperatureanisotropy.We will

Case 2: Northward IMF,

establish the connection

now examine wave data for this day in an attempt to October 6, 1984

between

beam distributions

ob-

servedin the previous case and the wave growth observed Particle data. The observations for this day are repreduring those crossings. sentative of three crossingsexamined during which the IMF Wave data. The wave data for the crossingbeing examwasnorthward.Plottedin Figure8 arethe densities of H +, ined are presentedin Figure 11. The electric field spectral He++, and O + ionsand the ZGSEcomponent of the magdensityplottedfor the five channelsof the wave instrument netic field for 1 hour starting at 2230 UT. During this period on a 30-min time scale beginningat 2300 UT. The boundary the spacecraftis in the magnetosheath and is inbound,as can layer crossingpinpointedabove and occurringduring the be seenfrom the abundance of H + ionswith magnetosheath energies combinedwith an absence of magnetospheric O + period 2304-2313 UT is shown by dashedlines. For this ions. The boundarylayer crossingoccursat 2304UT and has crossing,however, the 30-kHz frequency channelhas relaa 9-minduration,asindicatedby theenhancement of O + ion tively little wave activity. The envelopeof the electric field densitytogetherwith the decrease in the H + ion density. has factor of 2 changes,but these correspondto changesin For further discussionof this crossing, see Fuselier et al. the local electrondensityas the spacecraftentersthe boundary layer from the denser magnetosheath. [1989b]. We now examineplotsof the electricfield polarizationfor We now examine the electron data for this day. Presented the boundary layer crossingsdiscussedabove. Figure 12 in Figure 9 is a 2-min plot of the electronnumberdensityand temperaturecommencingat 2306UT, whenthe spacecraftis showsplots of the electricfield amplitudeversusthe angle in the boundary layer. The electron number densitiescorre- between the antenna orientation and the instantaneous magspondingto pitch angles of 0ø and 180ø, respectively, are netic field direction for the 30-kHz channel of the PWE shown with the dashedlines. These pitch anglesonce again instrument for selected times during the boundary layer correspond to maxima in the electron number density. crossings. The panels are arranged such that the instantaneous Clarification of the nature of this distribution is achieved by examiningthe velocity spacedistributionof the electronsfor magneticfield is alongthe y axis. The wave data are plotted this time. as a log of the wave amplitude,with the center of the circle

3176

PEROOMIAN ET AL.' ELECTROSTATIC WAVES DUE TO FIELD-ALIGNED

Particle and Magnetic Field Data 6 October

x --='1011

,

•E •• Z

1984

'- "• - •v•'l, ,•i• '•

O

c • 05 •



••

•l•'/•

'••

•.,

ELECTRON BEAMS

isotropic and shows no preferred direction for the wave electric field. We recall that counterstreaming electron beamswere presentin only the case representedby Figure 12a. The results shown here will be compared to linear 0,151 o.o• theory in the next section. • 1.748 In all, we have examined seven LLBL crossingsfor this . + 8.927study, all of which closely followed the above mentioned • 20.18

0.342

cases. The four cases with



100

.

',

0 -100

150 ..........

,,,,•

......

•,,

'• 100 •

II

+

I

z

0

....

•'E 0.8

' ....

• ....

I,,

,

z



'•

o

0.2

'• ....

I



. -17keV/e O+

ß z 0 ..... •'•'::••

'1'

, , ,

I

I T'

'F1

•Jl•

I

all showed

the LLBL. During the three events in this study that correspondedto northward IMF boundary layer crossings, no evidence for increased wave activity was found in the

0-17keV/eHe+

.......

IMF

correlation between the observation of beams and waves in

.

+ 0.4 0

southward

evidence of field-aligned,counterstreamingelectron beams and a correspondingincreasein wave activity uponentering the low-latitude boundary layer. The one southward IMF crossingduringa strongmagneticsubstorm(shownabove as case 1) had two sets of counterstreaming, field-aligned electron beams with higher streamingvelocities than those found in other southwardIMF crossings.For this crossing, there is stronger wave activity in the LLBL than on other southwardIMF crossings(see Figure 7), again suggestinga

'

LLBL. For these cases, no electron beams were observed in the energy channels above the instrument cutoff. Since

Ogilvie et al. [1984] reported observationsof peaks in the electron distribution as low as 20 eV and below the cutoff of

the HPCE instrument, it is conceivable that the electron beams in these cases were too slow to be observed and too

i,

weak to give rise to instabilities.The particle and wave data presentedabove therefore suggesta strong correlation be2230 2300 2330 tween the observation of field-aligned, counterstreaming Universal Time electron beams and enhancedwave activity in the LLBL. Our goal is to understandthe microprocessesand macroFig. 8. CCE observations for a l-hour interval on October 6, 1984(taken from F•elier e• al. [1989b]). The panelscorrespond processesoccurringin the LLBL and in particular to examfrom top to bottomto the electrondensity,ZGSE componentof the ine the possibility of using the data presented above to magnetic field, H + ion density,He++ ion density,and O+ ion extend our understandingof wave-particle interactionsocdensity.The boundarylayer crossing(23•2313 UT) is markedby curring in the LLBL. As noted in section 2, the simultadashed lines. neouslyobtainedplasma wave data are restrictedto higher frequencies characteristic of electron-plasmainteractions. correspondingto the minimumvalue in the interval sampled We have therefore focused our attention on the electron (min) and the unit circle correspondingto the maximum beams identified above. In the next section we undertake a value (max). The anisotropyfactor shownin the figuregives linear theory analysis of electron beams in a warm electron the ratio of maximum to minimum variance of the points plotted. The variance is defined with respect to the maximum variance line, which is labeled by the angle it makes with respectto the vertical. The maximum varianceline is a Electron Flux 6 October 1984 good indication of the direction of the electric field with lO2 respectto the ambientmagneticfield. When plottingthe data we have offsetthe data by an angleof 11ø. This corresponds to a rotation in the clockwise sense of 11ø when looking down on the figure. This offsetwas determinedfrom polar100 _ ization studiesof plasmaoscillationsin the solar wind, and whistler mode and upper hybrid resonance(UHR) waves in II ß I the magnetosphere.These data showeda consistentrotation of the order of 11ø on the average. The causeof this offset i has not yet been determinedbut may be due to geometryor possibletiming errors. o IVL•/,V. •! V Y ,VIV. v, V -1 Figure 12a is a l-min averagecorrespondingto the polar- •-< UT 2306:20 2306:40 2307:00 2307:20 2307:40 ization data for the boundarylayer crossingon November L 8.327 8.325 8.322 8.320 8.317 LT 1254:36 1254:43 1254:50 1254:56 1255:03 16, 1984(case 1). The wave electric field duringthis crossing MEat -1.219 -1.231 -1.244 -1.256 -1.268 is peakedstronglyalongthe ambientmagneticfield direction Fig. 9. Electron numberdensitiesand temperatureson a 2-rain and has nulls perpendicularto the field, suggestingfield- time scalecorrespondingto an interval during the boundarylayer aligned propagation of the observed waves. Figure 12b, crossingin case2. Dashedlines correspondto 0øand 180ø of pitch representativeof the crossingon October 6, 1984(case 2), is angle.

7. . ,

(cm)'3II

10-2 ,,,,

I

/•Temp. (keV)

,[li,, I .......

PEROOMIANET AL' ELECTROSTATICWAVES DUE TO FIELD-ALIGNED ELECTRON BEAMS

3177

Electron Velocity Space Distributions 6 October 1984

2307:00-2308:37

UT

Perpendicular

Parallel

asc

ld 24

80,000

0-25

...

-

/

o•'"ld2e• •

1•32_



-80,000 -80,000

0

(•2e

-34-•

10

80,000

...............

(•34

•, ,,

-80 •0

0

80,•0

llll'11111111111llllllllll[llll

-80,000

I

0

80,000

Velocity [km/sec) (,)

(b)

(c)

Fig. 10. Velocityspacedistribution andcutsof thedistribution parallelandperpendicular to theambientmagnetic fieldaveraged over97sduringtheboundary layercrossing shownin Figure8. Neithertheparallelnortheperpendicular cuts of the distribution show evidence of an electron beam.

background, corresponding to conditions found in the

have shown that waves near the plasmafrequencygrow becauseof electronbeam-driveninstabilities.The plasma

LLBL. 4.

configuration found in thelow-latitUde boundary layerin-

LINEAR THEORY

cludesmanyplasmaspeciesbut can be generalizedby cold, The interactionof electronbeamswith stationaryplasma symmetric, coUnterstreamingelectron beams and a back-

is welldocumented. Theoretical analysis [Bunernan, 1958; ground9f warmplasmathatincludeselectrons,protons,and HasegaWa, •1975;Melrose,1986]and experimental work heavyions.



Wave Data 6 October 1984

-51 I I

I

I

I

I

I

178kHz I

-8

/ i 30 kHz "I .......... ß

-'t -7

5.4 kHz

• ....

111 tI1111111111 IllLi

I

I

....

....1.hL•.•: u •..• tJ.LJ,,

'•,11

' _



II .

I• ' ' I

I

1'i

'

I ' '

_

•.-

._

,......

-- _,u_.•

..---

I ' ' '1 ' I

I ....

I

'

-5t ....... . :,............ '-'200 • i• ""

_

I

'

i

ii

._

i

•- I

730 Hz

I

I

!

I

100

I

I

,

I

ß

I

....I I

I

2300

2305

I

2310

'

I

....

2315

Universal

I

2320

....

t

2325

....

I

5.6

'-'N

2.8



o

u_ø

2330

Time

Fig. 11. Electricfieldspectraldensityversustimeona 30-mintimescaleencompassing theboundary layercrossing in case2 (dashedlines).Shownare the five channelsof the PWE instrument plusthe magneticfieldmagnitude. The

30-kHzchannel duringthiscrossing isrelatively quiet,andlittledifference canbeseenbetween thetraversed regions.

PEROOMiANET AL.' ELECTROSTATIC WAVES DUE TO FIELD-ALIGNED ELECTRONBEAMS

3178

This is a fourth-orderequationin towith two solutionsnear to • +-k ß %. To find the positivebranch solutio n, we

El,ectricField Polarization Data Ordered by B Field. Offset = 11.00 o

substitut e to• k. v0 into the thirdtermof equation(3),

Logscale

2

2

topb

topb

1

0=1-(to k v0)24(k'v0)2 +k2Ae 2(-0.1 +i) (4)

-11.90

Solvingfor to, we obtain

topb -0.1+ i -1/2

ß 2 to=k'Vb + topb 1- 4(k.Vb)2 + k2)t e

For very hot ba,ckground electronsthe l.a. st term in the

-40.57

16 Nov 1984 ,

squarerootgoesto zero,andaninstability resultsif topb> 2kvb. Thisis theclassictwo-fluidstreaminstability. How-

6 Oct 1984

0412:20-04 !3:20 UT Anisotropy = 2,650 ,

ever,keeping thethermal electron termandTaylor exPand -

2307:00-2307:30 UT Anisotropy = 1,114

min=6.46xl0'8

min= 8.95x10'8

max= 8.0,9x 10'6

max= 3.16x! 0'6

(-)

(5)

ingt•e brackets gives

• topb

1

i

, =k'vb-+Wp•b 2 2k•2A to 1+8(k' Vb) 2+20k2Ae ,• , (6)

(b)

Fig. 12. Electricfieldamplitudeversusanglewithmagneticfield for the boundarylayer intervals examinedin the above cases.(a)

The boundarylayer crossingexaminedin case1, duringa time of enhanced beamactivity,showingstrongparallelpolarization of the

Thislast.expression showsthata differentinstability is possible owingto a LangmuirmodeD0pplcrshiftedby the electronbeam. For the negativesolutionthe last term in

brackets coniributes positive wave growth as'aresult ofhot

inverse La,n. daudamping. Thisisin contrast tothe electric field.(b) Thecrossing in case2, duringwhichnoevidence electron situationwith a background of onlycoldelectrons,wherea purelyfluidlikestreaminginteractioncauseswave growth.

of electronbeamswasfound;thereis no apparentpolarization.

In the low-latitude boundary layer, however, the back-

groundelectrons are warm,andwe therefore expectthe growthof wavesin thisregionto resul t froma mixtureof a In this sectionwe first analyticallysolve the dispersion two-stream fluidtypeinstabi{ity anda kineticinstability relation for the interaction ,of the beams with the warm whichitselfoccurs because of inverse Landau damping of

electron background, andwethenutilizea numerica! root theho(electrons. ThevalueofSe inequation (1)determine• finderto solvethe generalwarm plasmadispersionrelation which type of instabilityis dominant.The analyticderivation exactly. The ion contribution can be neglectedsince We aboveassumed se < 1 for thebackground electronsandthus

considerhere only high-frequencyphenomena.The dispersion relation for symmetric, counterstreamingcold electron beamsin a backgroundof warm electronsis givenby

isprimarilymadeupof thekineticinstability. Fromequation (6) the growth rate is given by

y • topb/2k2A 2 0=1

--

(7)

Substituting thetypicalboundary layervalues forAeandtop0

(to--k'Vb)2 (to+k'Vb)2

andusing k' v0'• tope in theinteraction region, weobtain values for Y/tope ranging from0.06to 0.19forno/no= 0.0!

1

+ A2A 2I1+ s,Z(s,)] (l!

to 0.10.

Thesubstitution of to= -k. v0 intoequation (3)givesrise

to an instability symmetric to that discussedabove. Thus Species subscripts are b for beam electrons and e for eachbeam excitesits own instabilityby interactingwith the backgroundelectrons.Here Z(s,) is the plasmadispersion function withse = to/22/2 kve[FriedandConte,1961 ]. The backgroundand is somewhatindependentof the other beam. Having establishedthe physicalnatureof the instability,we difficulty in obtaininganalytical solutionsto this equation lies in the numericalvalue of the argumentof the Z function. nextpresentresultsobtainedby solvingthe generaldisperSubstituting valuesfromtheboundary layercrossing on sion relation numerically. The warm, magnetizedelectrostatic dispersionrelation is given by ,

October19, 1984,at 0456UT, discussed above,for example, gives a value of se = 0.84. This is 'in the nonexpandable regimeof the Z function. We will thereforesubstitutefor the

Z functionnumericalvaluesfrom tablesby Fried and Conte [1961].For s = 0.84, we write 1 + sZ(s)•

-0.1 + i

e(to, k)=1+Y• A2 ,• k2 ,• 1+ 2l/2kllv ta e-y•2

(2)

ß ,•Z' 2l/2kllvta Y})=0

Substitutioninto the dispersionrelationgives 2

topb

2

topb

1

2 (-0 ! + i) 0=1- (w- k'Vb) 2--(to+'k'Vb) 2+k2A e '

(3)

(8)

wherea is the sumoveral! species (e-, H + He++ and O+), ya = kñvta/• •, and In(y) is the modifiedBessel function.

PEROOMIAN ET AL.' ELECTROSTATIC WAVES DUE TO FIELD*ALIGNED

ELECTRON BEAMS

3179

10• ....

frequency is possible because of the presence of electron beamswith velocities near the backgroundelectron thel'mal velocity(see,for example,Fuselieret al. [1985]).Also, since

10o

growth parallel to the ambient magnetic field, the waves shouldbe polarized parallel to B. This is in agreementwith the polarization data presented in the previous section, suggestingthat the observedwaves are probably causedby

DISPERSION

RELATION

the electron beam-driveninstabilityhas maximumwave

the mechanisms discussed above.

5.

(•pe 1•1

In section

NUMERICAL

4 it was shown

SIMULATIONS

that

electron

beams

in a

backgroundof warm electrons are unstable, with a wide

rangeof unstablefrequencies centeredaroundfee' The questions we wish to answer in this section pertaia to specificnonlinearphenomenasuch as wave saturationand wave modesassociatedwith the instability.

1OF 2

Toexamine thenonlinear phenomena associated withthis instability, a l_2--dimensional electrostatic codewRhfulldy-

namics forbot•electrons andions isutilized. Since onlythe 1OF 3

- 100

electrondynamics areimportant in thisstudy,theionscan -60

-20

20

60

100

be considered as a charge-neutralizing immobile back-

ground. Thecodehasonespatialdimension (thex axis),and threevelocitydimensions (vx, vy, aod,v z) andusesperiodic Fig.13. Dispersion relation for cold,field-aligned counter-boundary conditions. The magnetic fielddi.rectioncanbe kc/COpe

streamingelectronbeamsin a background of warm electronsand ions. Shownare the real (solidline) and imaginary(dashedline)

partsof (o(normalized tOoye)versus kc/OOpe.

varied with respectto the simulationaxis, •t

Sincethe

electronbeam-driveninstabilitystudiedhere is polarizedin

thedirection parallelto theambientmagnetic field,theangle between themagnetic fieldandthesimulation axisis setto

is k = 2,n'rn/L, wherern = 0, 1, Figure 13shows thedispersion relation solved withinput zero.Thewavenumber

2, ..., andL is thesystem length,basedon theperiodic runs the system 1984.For thiscrossing, wc estimate ne -- 50.0 cm-3. boundaryconditions.In all the simulation -1

parametersfrom the boundarylayer crossingon October19,

included arctwofield-aligned counterstreaming beams, each length isL = 1024A e, and•t = 0.2%, e.

The initial conditionsof the simulationare modeledusing

with a density equal to 5% of the total electrondensity and with velocitiesof -+8000km/s. As expected,becauseof the electrostaticnature of the instability, maximumwave growth

theplasma distributions observed in theLLBL aadincMale

occurredat 0 = 0ø. The dispersionrclati0n shownin this

(2) a coldelectronbeam,and (3) a neutralizing,stationai'y

three species:(1) a warm, stationaryelectron backgrom•l,

figurewastherefore solved with0 - 0ø.Also,thedensities of ion background.Figure 14is an overlayof electronvelocity the various ion speciesarc given by nil+ -- 0.9669n0, space distributionsand shows a comparisonof the initial

usedin the simulations to modelthe LLBL tiHe+,He•+;+ "0.0305t]0,andno+-- 0.0026n0. PlottedinFigure configuration andthe actualdistribution fromobser13arctherealandimaginary parts of(o,normalized to(ope, velocitydistribution versuskc'/t. Ope.We notethat the peakof the growthrate vationsin the LLBL. The solidline representsthe LLBL shown in Figure6b, whilethedashed lineis the occursfor kc/oope - 30 and corresponds to a valueof interval ,distribution. usedinoneofthesimulations inthisSection (see 'y/O•pe = 0.06. been This result is of the same Orderof magnitudeand in the Figure 16). The -modelelectrondistributions':•bave

range predicted bythesimple analytical calculation donein •hosen tocom.pensa•e fortheunmeasured buti•erred(frOm iondensities) electron densR• range intheLLl•L. thissection.Thissuggests a closeCOrrelation between the measured actualgrowth mechanism and the simplifiedversionpre- Section 3 established ranges for electron temperatare and sented above, and it confirms that the results obtained are

densityin the LLBL. In order to compensatefor the wide

independent of theions.Also,asthe symmetry ofthe figure i'angeOf observedparameters,severalsimulationrUnswere suggests, eachbeaminteracts withthebackground indepen-performedby varyiiigthe beam-to-backgrOund densityratio dently, and the deletion of one of the beams from the (nt,/ne), beamvelocity(ut,), andbeam-to-baCkground eleC: calculations does not affect the contribution of the other

beamtø the instability.

trontemperature ratio(Tb/Te).Thisallowedusto examine thecontributions• of verylow or veryhighenergybeams.

This electron beam-drivenmode is unstablefor a large rangeof k valuesand correspondsto a frequencyrangeof

The low-energybeams, for example, are marginally stable and do not contributesignificantlyto the wave spect-rum, 5.0-76.0 kHz. This would result in the observation of wave While increasingthe beam speed eventually quenches.the enhancement in a widefrequencybandaroundthe electron instability(see previoussectionand Table 2). The tem.Pera-

plasma frequency (0.1-1.2%,• forn = 50cm-3) andthus ture ratiosusedherealsoallowfor the rangeof observed can accountfor wave activity detectedin the 30-kHz channel

temperatures in the LLBL andincludethe contribution of

of the PWE instrumentdiscussed in the previoussectiøn (see the bulk of the electronpopulationwhichgoesunmeasured In thismanner, wehavecovered a Figure 7, for example). Wave growth below the plasma by theccE spacecraft.

3180

PEROOMIAN ET AL.' ELECTROSTATIC WAVES DUE TO FIELD-ALIGNED

. Observations{ .......

Simulation

Als0, in the caseillustratedin Figure14, with two setsof electronbeams,it i•, expected thatthe instability resulting

{ ;""

Model

ELECTRON BEAMS



from the strongerand faster set of beamswill overwhelmany

effectswhichmightarisefrom the slowerset of electron beams. -

Run1'nb/rte = 0.05. Thissimulation runcorresponds

1d28-:

to the interaction of a dilute cold beam with a dense warm

-

background plasma.The resultsof this run are shownin

-

.

_

Figure15.Figure 15aisa superposition oftheinitialwarm

.

ß

electronbackground distribution functionat t = 0 (dotted

-

line)andaftersaturation at t = 1000•0•e I (solid line).The

1($3o -

effecton thisdistribution canbe seenas a p!atea'Uing or flattening atv -• 1.47Vte. Figure15bshows a similar pl0tof

-

-

-

the cold electron beam distribution at the same times. The .

profile ofthebeam att = 1000o•-e I shows thatthebeam has

.

-

1l•32 -

.,'

.'

'80,000

.

0

80,000

Velocity Ckm/sec) Fig. 14. Comparisonplot of electron velocity distributionsob. served in the LLBL (solid line) and utilized in the numerical

simulationruns(dottedlines).

lost kinetics{reaming energyand is highlyth•rmaliZedfor thes_e parameters. Figure15cis a timehistoryof theelectric field energy density for this run. This figure shows a sharp

peakinwaveenergy at t • 50o•-e •, followed bya gradual decrease toalevel halfthemagnitude oftheinitial Peak.•This suggeststhat the streaminginstability affects the plasmain the initial stages of the simulation run while the kinetic

instabilitydueto inverseelectronLandaudampingoperates on a much longer time scale.

e = wide range ofpossible densities andtemperatur9s. fibtuallyRun 2: nbearn/n

0.11.

This case correspondsto a

observed in theLLBL andhavenotusedunrealistic param- denser electron beam propagatingthrough the background eters.We will firstVarynbine andshowresultsfromtwo plasma,whichresultsin a strongerinstabilitythanfor run 1. casestudiesandthenpresenta summary of othercases Figure 16 showsthe resultsof the simulationrun for this where differentparametersare varied. The initial conditions case. The three panels in this figure correspondto those in for the two case studies are that the electron beam-toFigure 15. Figure 16a, the plot of the warm electrondistribackground temperature ratio was Te/Tb = 500 and the bution, now showsmuch m6re deformationfrom the interbeam speedwas llb/Vte = 1.47. Only one electronbeamis actionwith the enhancedbeam-driveninstability.Figure Used in the simulations here, since as demonstrated in the

16b shows that the beam, although thermalized after satu-

previoussection,the counterstreaming beamsgive rise to

ration,is stillidentifiable asa beamwith a Peakat a slightly reducedstreaming speed.Figure16c, corresponding to the

instabilitiesthat are more or lessindependentof each other.

Energy Density

Velocity Distributions

= 500, nbeam/ne = 0.05 Te/Tbeam ColdEleci•'onBeam

Warm Electron Background 3600

ß ''1

......

•.....

I ....

-

t=0

,--,

1800

ElectricFiBidTimeHistory 5800

1400

3400

700

0

-5.0

.

,

-2.5

0

Vx/ Vte

lOOO

0

,

2.5

5.0

-40

-2O

0

2O

(Vx/ Vte)v'Te/Tt)

4O

0

500

COpet

(,.) (b) •, (c) Fig. 15. Simulationresultsfor an electronbeam streamingin relationto a warm ion and electronbackground(run I in section5). Here nb/ne = 0.05. (a) The warm backgroundelectronvelocitydistributionat t = 0 (dottedline) and

t = 1000O)•e • (solid line).(b)Thecoldelectron beam distribution forthesame times asinFigure 15a.(c)Theelectric

field energy density versus time.

1000

PEROOMIAN ET AL.' ELECTROSTATIC WAVES DUE TO FIELD-ALIGNED

ELECTRON BEAMS

3181

Energy Density

Velocity Distributions

Te/Tbeam - 500, nbeam/n e - 0.11 Cold

Warm Electron Background 3400

28OO

.." ':;t = 0

Electron

Beam

Electric Field Time History

' ' ' I ' ' ' I ' ' ' • ' ';..'_

14000

'i • :•pe t= '---'

1400

1600

c• 7000 OJpet =1000

-5.0

-2.5

0

2.5

5.0

Vx/Vte

0 -40

ß.I• -20

0

20

:ii i

LLI

40

1000 0

CVx/Vte) v"Te/Tb

500

1000

toper

(b)

(-)

Fig. 16. Simulationresultsfor run 2 in section5, with nb/ne = 0.11. The resultsare shownin the sameformat as Figure 15.

wave energy time history, peaks at a larger value and has a higher saturation level than the previous run. Several other simulation runs were made by varying beam-to-backgrounddensity ratios but keeping all other parameters constant. The results of this survey are shown in Table 1. The table lists the beam-to-background density ratios in the first column, the peak and saturation wave energylevels in the next two columns,and the percentageof the beam persistingafter saturation in the last column. The first two rows in this table correspond to runs 1 and 2 discussedabove. In the casewith nb/ne = 0.05, the beamis destroyedand is not expectedto propagatevery far after the instability has saturated. When the density is increased,as in

creasingspeed, as can be seen from the peak wave energy and the beam survival percentage. This is due to the availability of more free energy associatedwith larger beam speeds. However, when the relative drift between the beam and the backgroundexceedsa critical value, the plasmais no longer unstable. For the run with v b/vt,, = 20 (last row in Table 2), the instability is quenched, as is evident from the relatively low peak and saturation wave energies. Finally, several simulation runs were carried out by varying the background-to-beamtemperature ratio. Nine runs were made while varying the temperature ratio from

Te/Tb = 10 to Te/Tb = 500. The resultsfrom theserunsare

shown in Table 3. The beam survival percentage decreases the nb/ne = 0.11 case, a weak marginallystablebeamlike with increasedtemperature ratio, suggestingthat the instadistribution is present after saturation. An increasingly bility becomesmore and more fluidlike as Te/Tb is inlarger portion of the beam persists as the density ratio is creased. The peak wave energy also increases with increas-

increasedfrom the initial nb/ne = 0.05 to nb/ne = 0.43. ing T,,/Tb, further suggesting a fluid instability. However, the beam is destroyed rather quickly if this ratio In this section we have discusseda parametric search exceeds0.67. This effect is accompaniedby a large increase performedin order to determinethe range of temperatures, in the peak wave energy, suggestingthat the beam does not velocities, and densities over which an electron beam can survive the initial instability. interact with backgroundplasmacharacteristicof the LLBL Next, we varied the electron beam speed while keeping and survive the interaction. We have shown that while a nb/ne = 0.11 and Te/Tb = 500 fixed. Table 2 showsa dilute beam is destroyed in the interaction with the backsummaryof six runs during which the beam speedis varied groundplasma, a strongerbeam persistsafter saturation. We from Vb/Zlte= 1.47 to vb/Vte-" 20. The initial interactionof have also shownthat changingfactors such as beam velocity the beam with the background plasma increases with in- and beam-to-background temperature ratio also affect the

TABLE 1. Wave Energy and Beam Survival for Varying Beamto-Background Density Ratios

rtb/rt e 0.05 0.11 0.25 0.43 0.67 1.00

(E2/8•p2Ae2)peak (E2/8•p2Ae2)saturation % Beam 5,900 14,800 36,800 63,400 98,700 386,000

2,800 4,500 3,000 3,000 5,000 8,000

13 16 26 56 10 6

TABLE 2.

Wave Energy and Beam Survival for Varying Electron

Vb/Vte 1.47 2.50 3.50 5.00 10.00 20.00

Beam Velocities 2

(E:Z18w'P •Ae2)peak(E218w'P • Ae)saturation % Beam 14,800 96,500 440,000 1,030,000 10,800,000 3,580

4,500 30,000 20,000 10,000 1,300,000 1,800

16 11 9 9 5 80

3182

PEROOMIANET AL.: ELECTROSTATIC WAVES DUE TO FIELD-ALIGNED ELECTRONBEAMS

TABLE 3. Wave Energy and Beam Survival for Varying Background-to-BeamTemperature Ratios 2

understandthe mechanismsresponsiblefor the generationof high-frequency waves in the LLBL.

2

Te/Tb (E2/8•rp 2Ae)peak (E2/8•rp 2Ae)saturation %Beam 10.0 30.0 50.0 70.0 100.0 200.0 300.0 400.0 500.0

2,600 3,550 5,600 7,780 7,850 11,200 12,700 13,800 14,800

1,700 1,850 2,800 2,500 3,000 3,500 4,000 4,000 4,500

69 57 38 32 31 26 9 13 16

6.

SUMMARY

AND CONCLUSIONS

In this paper we have examined particle and wave observations made in the LLBL by the AMPTE CCE spacecraft and explored the interdependence of the high-frequency electrostatic emissions and field-aligned, counterstreaming electron beams observed simultaneouslyin this region. The sevendata intervals examined correspondto intervals during whichthe LLBL was inside8.8 Rœand thereforeto timesof relatively fast, high-density, and variable solar wind. The available

HPCE

ion and electron

data for a total of over 70

min in the LLBL have been compiled and averaged. Ions of

interaction, with the instability becomingmore fluidlike with

magnetospheric origin(O+ andHe +) comprisea significant

increasedbeamvelocityand Te/To.

fraction of LLBL

Run 2, discussed earlier in this section, most nearly resemblesthe actual configurationof the LLBL. The beam and thermal speeds used in the run are based on actual observations, and the assumed temperature ratio correspondsto a beam temperature of 3-12 eV. The beam in this simulation run effectively survives its interaction with the backgroundelectronpopulation,confirmingthe existenceof the beam in the LLBL long after saturationof the instability. Dependingon its initial velocity and temperature,therefore, an electron beam can interact with the plasma of the LLBL

detection in the adjacent magnetosheath. The limited (in frequency and temporal resolution) plasma wave data resulted in our centering the investigation of wave-particle interactions on the higher-frequencymodes driven by elec-

and

"survive"

even

after

the

saturation

of instabilities

associated with this interaction, thus sheddinglight on the simultaneous

observation

of electron

static waves in the LLBL.

beams

and electro-

We note, however, that there

remainsthe problemof determininga sourcefor the electron beams seen in the LLBL.

The numerical

simulations

in this

section have shown that the instabilities involved in generating the high-frequencyemissionsassociatedwith the electron beams act very quickly, and although a high level of saturation exists, waves are not driven unstable for a very long time. In order for the waves to be seen all the time, therefore, there would have to be either a sourceregionvery close to the LLBL or a source of continuous injection of electron beams into this region. Several studies have addressedthe possiblesourceof electron beamsin the LLBL. The high-latitudepolar ionosphereis one possiblesource.At the streamingvelocities observedin the LLBL the electron beams would have to travel of the order of 10 s in order to

tron beams. tributions

ions but are near or below the threshold

We therefore

in considerable

have examined detail.

the electron

For one interval

of

dis-

the beam

speeds, temperatures, and densities were derived from the data. Plasma wave data obtained from a high-frequency channel during this interval were examined, and a strong correlation between the presence of electron beams and wave

enhancement

was noted.

The

nature

of the beam-

plasma interaction was examined analytically and in a simulation based on plasma parameters similar to those observed. On the basis of this investigation we draw the following conclusions: 1. The complement of particle and wave instruments on the AMPTE CCE spacecraftprovide data that significantly improve our knowledge of the structure of the LLBL during intervalswhen the magnetopauseis inside 8.8 Rœ. 2. When AMPTE CCE was in the LLBL, counterstreaming electron beams were observed during the four intervals

of southward

IMF.

These

electron

beams

were

absent or below the energy or intensity threshold of the instrument during the three northward IMF LLBL crossings. 3. High-frequency, parallel-polarized electrostatic wave enhancements

and electron

beams

in the LLBL

were

de-

tected simultaneously. These wave enhancementswere abreach the LLBL. Therefore, unless the ionosphere is a sentfor the three northward IMF crossingswhen no electron continuoussourceof electron beams, this streamingprocess beams were detected. The wave intensity was most intense would be too slow to replenish the electron beams that are for the LLBL crossing with a second, faster set of counterthermalized in the LLBL. The source for the electron beams streaming beams. remains to be determined. However, a clue to the nature of 4. Linear theory has shown that the counterstreaming the faster set of beams present in case 1 can be discerned. electron beams are unstablefor the parametersobservedin Case 1, as mentioned earlier, represents a case where the LLBL and that the wave growth is due to a mixture of reconnection is taking place in the dayside magnetopause fluid and resonant instabilities. Maximum wave growth is during a period of high substormactivity. Careful examina- parallel to the ambient magnetic field in agreement with tion of Figure 7, the wave spectra for this day, shows a observations. sporadicand spiky naturefor the mostintensewaves(during 5. Numerical simulationsof the plasma conditionsin the 0412:50-0413:10 UT), hinting at a local generation of the LLBL have shown that dense beams with Ub < 2Vte are thermalized by the unstable waves but retain a beamlike extra set of beams in this example. Another problem not addressedhere is the fact that the distribution after saturation. injection of electron beams into the plasma of the LLBL In conclusion, we have found that the high-frequency represents a boundary value problem rather than the initial wave amplificationobservedin the LLBL can most likely be value problem addressedhere for simplicity. Beam injection attributed to the presenceof counterstreaming,field-aligned simulation would therefore be required in order to better electron beams during periods of southward IMF and that

PEROOMIAN ET AL.: ELECTROSTATIC WAVES DUE TO FIELD-ALIGNED

the beamsare not expected to be destroyedas a result of the instabilitiesinvolved in the physicsof beam-plasmainteractions, explainingtheir persistencein the low-latitude boundary layer. However, this study has not pinpointed a source for the electron beams, and the question of electron beam replenishment remains unresolved.

Acknowledgments. The authors would like to thank J. Berchem for his helpful commentson the magnetopausecrossings,R. Walker for his helpful suggestions duringboth the researchand writing, and M. W. Chen for her insighton numericalsimulations.Magneticfield data in this paper were provided by T. Potemra, principal investigator for the AMPTE CCE magnetic field experiment. This study has been supported at UCLA by NASA Solar Terrestrial Theory Program grant NAGW-78 and by NASA Marshall Space Flight Center contract NAG8-795 and at Lockheed by NASA contract NAS5-30565. Computing was performed on the Cray Y-MP at the San Diego SupercomputerCenter and on the Scientific Computing Systems SCS-40 at UCLA. The Editor

thanks

K. Takahashi

and another

referee

for their

assistancein evaluating this paper. REFERENCES

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V. Peroomian, Department of Physics, University of California, 405 Hilgard Avenue, Los Angeles, CA 90024. D. Schriver and R. J. Strangeway, Institute of Geophysics and Planetary Physics, University of California, 405 Hilgard Avenue, Los Angeles, CA 90024.

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3183

(Received July 19, 1990; revised October 17, 1991; accepted October 18, 1991.)

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