GEOPHYSICALRESEARCH LETTERS, VOL. 14, NO. 10, PAGES1007-1010, OCTOBER1987 MHD WAVE BREAKING IN THE OUTER PLASMASPHERE T. E. Moore, D. L. Gallagher • SpaceScience Laboratory, NASA Marshall Space Flight Center, Huntsville, Alabama 35812. J. L. Horwitz, and R. H. Comfort Departmentof Physics,The Universityof Alabama in Huntsville,Huntsville, Alabama 35899. Abstract.Empirical models of the average magnetospheric Plasma Parameters magneticfield, plasmadensity, and temperaturedistributions are used to construct a model of the distribution of MHD wave mode Obtaininga crediblemodel of the plasmamass density and effec- speedswithin the magnetosphere.Although the MHD wavespeeds tive temperature(required for the ion acousticspeed) is a more in generalhave a smallerdynamic range than the magneticfield difficult matter. The plasmaelectron density can be measuredfairly intensityor the plasmaproperties, considerable structure and vari- reliably by noting the frequencyof the upper hybrid resonancein abilityis foundwhich will leadto interesting"optical" effects on the passivelysensed plasma waves (Persoonet al., 1983), or by an propagationof low frequencywaves. A persistentfeature of the active plasma wave soundingtechnique (Higel and Wu, 1984). derivedoptical structure, which is qualitativelyinsensitive to known However, measurementof the ion masscomposition and tempera- variabilityof the field or plasma,is a pronouncedminimum of the ture, andelectron temperature, is dependentat presentupon accurate wave speedsin the outer plasmasphere,i.e., a magnetospheric measurementsof the low-energy"core" plasmaions and electrons. "shoal."This featuredoes not mapalong magnetic field lines,but is These measurementsare very difficult to make at the low densities confinedto theequatorial region, leading to a positiveradial gradient typicalat high altitudesdue to photoelectronemission by spacecraft of wave speedsnear synchronous orbit. The breakingof earthward surfacesand the consequentpositive floating potential relative to the propagatingdisturbances in this region may play an essential role in plasma. At present,good informationon theseparameters exists the formationof the substorminjection boundary and in the creation onlyat densitiesgreater than approximately 100 cm -3, i.e., in the of equatoriallytrapped warm ion distributions. plasmasphereand plasmapauseregions. Even with this restriction, statistical information on electron temperature is not routinely Introduction available. In orderto proceed,a plasmadistribution model was constructed The propagationof magnetohydrodynamic(MHD) waveswithin usingas muchempirical information as possible,with extrapolation spaceplasmas has long been recognized as the meansby whichthe or guessworkheld to a minimum, as describedbelow. The resulting energy and momentumassociated with transientphenomena are densityand temperaturemodels for quiet conditionsare shownin transported(Southwood and Hughes, 1983, and references therein). Figure 1 as equatorialplane and midnightmeridian cross sections. Within a systemlike the terrestrialmagnetosphere, the plasmaand The plasmaelectron density is tiedto the observationsfrom GEOS magneticfield are highlynonuniform, and this leadsin generalto a 2 at geosynchronousorbit reportedby Higel and Wu (1984). These veryinhomogeneous medium for propagationof suchwaves. Burton observations have been reduced to mean states for three levels of et al. (1970) reportedobservations of magneticfield and plasma activity: quiet, average, and disturbed. Results shown here densitiesfor four passesof OGO 5 throughthe plasmapause region, correspondto the averageconditions. The radial distributionof calculatingAlfv•n speedprofiles. We report here an attemptto equatorialnumber density uses the observationsof Berchemand constructa three-dimensionalmodel of the typical magnetospheric Etcheto(1981) from ISEE, indicatinga power law dependenceon distributionof Alfven and fast mode wave speeds,based on the radius close to Earth. We have taken the power law in the form extensivestatistical data bases now available.Our goal is to identify R-[3.5+ 0.5sin(2'n'MLT/24)] soas to reflectthe closer approach to persistentor characteristicfeatures of thesedistributions which have diffusiveequilibrium which prevails in the duskbulge region. This potentiallyimportant effects on the dissipation of suchwaves or their R dependenceis modified by an exponentialdropoff beyond a accessto various regionsof space.This approachimplies an variableR value. The scalelength of the exponentialincreases with emphasison propagationat wavelengthswhich are smaller than the the R at which the exponentialdrop begins.The exponentialdrop magnetosphericsystem, in contrastto the emphasison long continuesuntil an asymptoticnumber density is reachedwhich is wavelengthsand standing modes found in muchof the literatureon representativeof near-Earthplasma sheet values at midnight,i.e., magneticpulsations. 1.0 cm'3 (Strangewayand Kaye, 1986),and is somewhathigher at noon with a smooth variation over intervening local times. This MHD Wave Opticsof the Magnetosphere asymptoticplasma sheet density falls slowly with radius (as R-•). The positionat which the exponentialdrop beginsis locatedfor a particularlocal time so as to producethe correctnumber density at Magnetic Field geosynchronousorbit as specifiedby the GEOS 2 dataset. A crude indicationof the magnetopauseposition was introduced by invoking We have usedthe Mead and Fairfield (1975) empiricalmagnetic a typical magnetosheathdensity outside the boundaryindicated in field model, which providesfour differentstates of magnetotail Figure 1, panelsA and C. stretching: superquiet, quiet, disturbed, and superdisturbed. The plasmacomposition is takenfrom Horwitz et al. (1986), i.e., Referenceis madeto the originalpublication for field line maps, approximately75% H +, 20%He +, and5% O +. In thepresent model, intensitydistributions, and other documentationconcerning this evidencefor heavyion enhancements relative to thesenumbers in the model.Though we haveused all fouractivity levels, here we only plasmapauseregion (Roberts et al., unpublishedmanuscript) and in showresults for the quietmodel. Other magnetic field modelscan the near-Earthplasma sheet (Strangeway and Kaye, 1986)has not easilybe substituted,but this model was considered to be adequate been factored in. The net result is a mean ionic mass of 2 amu. It is withinthe region of interest,taken to be thatregion within a radial anticipatedthat more sophistication in this parameter will be incor- distanceof 12 Re geocentric. poratedin futureversions of thismodel, when statistical data bases canprovide the properjustification. Such adjustments will tendto reducethe wave speedsderived for theseregions. Copyright1987 by the AmericanGeophysical Union. The "effectivetemperature" plays two roles in thisstudy. It is used to definethe soundspeed contribution to theMHD fastmode speed. Papernumber 7L6609. As well, it could be usedto controlthe plasmascale height along 0094-8276/87/007L-6609503.00 magneticfield lines, along which good thermalconduction is 1007 1008 Mooreet al ßMHD Wave Breaking A PLASMA DENSITY 12 B PLASMADENSITY . MODELN3 ' ,, • • 3 MODELN3 CM-3 "'".••.,,, • .,••'• • ..2 LT=00CM-3 30000.0 30O00.0 18 lO 12 RE 3000.0 - 3000.0 1000.0 0 •-' 1000.0 300.0 300.0 100.0 •-• I 100.0 10000.030.0 I I I 10000.0 3O.O 10.0 10.0 3.0 ' 2 3.0 1.0 • 1.0 0.3 ' -- 3 0.3 0.1 • '• :•:'•-- 0.1 0.0 4 0.0 0LT .. 0 I 2 3 4 5 6 7 8 g 10 11 125 RE PLASMA TEMPERATURE c D PLASMA TEMPERATURE 12 .. ß -.-' -- MODEL N3 3 MODEL N3 LT = 00 ELECTRON ,. 2: ELECTRON VOLTS VOLTS 30000.0 1OOO0.0 1 30O00.0 '2 4 6: 8 1000.0 0 3000.01000.0 1012RE 3000.0300.0 ) t 10000.0300.0 ! 00.0 -• 1 100.0 30.0 30.0 10.0 3.0 •' 2 10.03.0 1.0 1.0 0.3 3 0.3 0.1 0.1 0.0 4 0.0 0LT 5 0 1 2 3 4 5 6 7 8 9 10 11 12 RE Fig. !. Contourplots of theequatorial and midnight meridian distributions of plasmaelectron density and effective temperature accordingtothe model used in this work. assumedto maintain isothermalconditions. In practice, the com- boundaryof the plasmasheet, including the entireplasmasphere, the binationof low meanionic massand centrifugal reduction of gravity equatoria!!yassigned temperature and density values are simply in the nearly corotating frame of the low-energy plasma in the mappedalong magneticfield lines to low altitudewhere the topside plasmasphereleads to very small gradientsof plasmadensity along ionosphereis not modeled.This procedureleads to very low densi- magneticfield lines (Gallagher eta!., 1987). This assertionis of ties at low altitudes in the region conjugateto the plasma sheet, coursesuspect in the topsideionosphere at the feet of the field lines, producingan "auroral plasmacavity" consistentwith the observa- wherea largedensity gradient exists. However, this regionis outside tionsof Persoonet al. (! 987). In the polar regionoutside the plasma the regionof presentinterest (above 0.5 R•. altitude) and will not be sheetboundary field line, the resultsof Persoonet al. (1983) are used dealt with here. to provide densitiesaccording to a simple expressionwith a power Sinceelectron temperatures representing the full energydensity of law in radius.Clearly the detailedstructure of the F layer ionosphere the plasmaare not readily availablethroughout the magnetosphere, is not addressedby thesetechniques. However, the agreementwith we assign"effective" temperatureequal to the ion temperaturewith auroral plasma cavity values observedby Persoonet al. (1987) guidancefrom the work of Comfort