Time Dependent Convection Electric Fields and Plasma Injection
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VOL. 84, NO. A8 JOURNAL OF GEOPHYSICAL RESEARCH AUGUST 1, 1979 Time DependentConvection Electric Fields and PlasmaInjection STANLEY M. KAYE AND MARGARET G. KIVELSON Instituteof Geophysicsand PlanetaryPhysics and Departmentof Earth and SpaceSciences Universityof California, Los Angeles,California 90024 Large-scaleelectric fields associated with stormsor substormsare responsiblefor inward convection and energizationof plasmasheet plasma. Calculations based on steadystate convection theory show that the responseto such electricfields qualitativelyaccounts for many featuresof the injectedparticle distribution,but quantitativeagreement with the theoryhas not yet beenobtained. It is knownthat the predictionscan be improvedby introducingthe conceptof convectionin responseto a time dependent electricfield. On the other hand, time dependentcalculations are sensitiveto the choiceof initial conditions,and mostmodels have failed to incorporatethese conditions in a realisticand self-consistent manner.In thispaper we presenta morecomplete model consisting of realisticinitial conditionsand time dependentconvection to explaina typicalsubstorm-associated electron injection event. We findvery good agreementbetween the observedelectron flux changesand thosepredicted by our model. INTRODUCTION ciatedparticle phenomena. One data setwhich has been ana- Transport of collisionlessplasma sheetplasma to the inner lyzedby severalauthors is that of Williamset al. [1974],who observed electron flux enhancements near L = 5 in the dusk to magnetosphereresults from large-scaleelectric fields associ- ated with storms or substorms.As was shown by previous midnightsector on Explorer45 shortlyafter substormonset. workers [Chen, 1970; Kivelson and Southwood,1975; Stern, They tried to explaintheir observationsby invokingplasma convectionin the electricand magneticfield model developed 1975; Cowley and Ashour-Abdalla,1976a, b], the maximum earthward penetration of the adiabatically conv½ctingtail by Mcllwain [1972] to describeparticle injection at geosta- plasmais delimitedin the steadystate by spatialboundaries tionary orbit. Williams et al. found that the magnitudeof determinedby the magnitudeof the convectionelectric field M cllwain'ssteady state electric field wasinsufficient to inject electronsto the low L valuestraversed by Explorer 45. The and the constantsof the particle motion. For magnetospheric Williams et al. paper stressedthat the dispersionof arrival plasmasthe relevantconstants are the two adiabaticinvariants times differedfor high- and low-energyelectrons. Following # and J, where # is the magneticmoment and J the bounce substormonset the delay of the initial flux increaseat the integral.The convectionboundaries, often called'Alfv6n lay- satellite increasedwith energyfor low-energyelectrons (<8 ers' [Wolf 1970], separatespatial regionsin which qualita- tivelydifferent particle drift orbitsare present.For electronsof keV) anddecreased with energyfor high-energyelectrons. To account for this behavior, the authors postulatedan ad hoc prescribed# and J, an Alfv6n layer separatesdrift orbitswhich radial electric field in addition to the Mcllwain field in the are closed about the earth from those which are open to the magnetopauseand tail and thusseparates regions of enhanced evening sector. plasma sheet electron fluxes (antiearthwardof the Alfv6n Subsequently,Kivelson and Southwood[1975] assumeda layer) from regionsof reducedplasma sheet electron fluxes dipolemagnetic field, corotationelectric field, and uniform (earthwardof the Alfv6n layer). For protonsthe natureof drift cross-magnetosphericelectric field and invokedsteady state adiabaticconvection theory to explain the energyand time paths in differentspatial regionsseparated by Alfv6n layers can be more complex [Chen, 1970]. dependentelectron flux increasesin the samedata. Assuming Becausesatellite particle detectorsmeasure particle energy that the flux increasein a givenlow-energy channel occurred when the outbound satellite passedthrough the SSDB and and pitch angle,not # and J, it is convenientto identifya type of boundarysimilar to an Alfv6n layer but definedin termsof entereda regionaccessible to plasmasheet electrons of that energy,they calculated the points of intersectionof thesatellite energyand pitch angleinstead of # and J [Kivelsonand South- wood, 1975]. We introduce the nomenclature'steady state trajectorywith the SSDBsfor a uniformconvection electric field. Althoughthey were successfulin explainingthe energy demarcation boundary' (SSDB) for this related boundary which is determinedby the convectionelectric field magnitude dependenceof arrival times,they obtainedonly qualitative and specifiedfor a particleenergy W and pitch angle a. The agreementwith the timing of theobserved flux increases. They madeno attemptto interpretthe subsequentflux decreases. SSDB is the same as the boundary called LA(qb)by Kivelson and Southwood[1975] and called the critical boundary by Using the sameconvection model as Kivelsonand South- Kivelsonet al. [1979]. Now, the SSDB is not a particle drift wood[1975], Cowley and ,4shour-,4bdalla[1976a] interpreted the Williams et al. data in a slightlydifferent way. For each orbit, sinceenergy is not a conservedquantity, but it does energychannel of thedetector they calculated the electric field delimit the spatial region inside of which an electron whose necessaryto placethe correspondingSSDB at the satellite local energyand pitch angleare the prescribedW and a is on a closed orbit. Outside the SSDB an identical electron will be on positionof the observedflux increase in thatenergy channel. an openorbit and thusmay have a sourcein the plasmasheet. They found that differentconvection electric fields were re- Later in thispaper we extendthe definitionof the demarcation quiredto accountfor increasesin differentenergy channels. boundaryto includetime dependenteffects. Theyconcluded that the convectionelectric field had eithera Steadystate convection theory has been used with differing strongspatial or a strongtime dependence. degreesof successby many authorsto explain substorm-asso- Furtherapplications of convectiontheory were presented in a companionpaper by Cowleyand ,4shour-,4bdalla[1976b], Copyright¸ 1979by the AmericanGeophysical Union. who turned their attention to the storm time proton noseevent Paper number 9A0533. 4183 0148-0227/79/009A-0533501.00 4184 KAYE AND KIVELSON: TIME DEPENDENT CONVECTION observednear duskby Smithand Hoffman [1974] on Explorer To illustratethe use' of ourmodel, we reinterpret the sub- 45. They arguedthat the observeddistribution was a natural storm electron observationsof Williams et al. [1974], the same steadystate spatial feature produced by adiabaticconvection, data set analyzed by Kit)elsonand Southwood[1975] and Cow- but their model predicteda nose penetrationmuch further ley and Ashour-Abdalla[1976a]. For reasonableinitial and earthward than was observed.Cowley [1976] later broughtthe final convectionelectric fields, whoseamplitudes are the only predictedand observednose positions into agreementby in- free parameters,we can model the times and positionsof the voking proton lossat the strongdiffusion rate over the entire plasmapauseand of flux enhancementsand decreasesin the trajectory. four different energy channelsof the Explorer 45 particle de- The above interpretationsof particleinjection all relied on tector in terms of crossingsof the TDDB. For a simple con- use of steadystate convectiontheory. Implicit in the steady vectionfield model we obtain very good agreementwith obser- state model is the assumptionthat the plasma particleswill vations. have sufficienttime to reach their steadystate configuration, We find that in our time dependentpicture of substorm- an assumptionwhich cannot be valid consideringthe time associatedconvection, the initial particle boundaries are as scaleof a substorm.At substormonset there is a major change crucial to the calculation as the incorporation of the time in the magnitudeand configurationof the earth'selectromag- dependenceitself, sincethe position of a particle within the netic fields. The tail field strengthtypically increasesby •1 first tensof minutesafter onsetdepends greatly on its location kV/RE, and the SSDB moves >•1 RE earthward [Kit)elsonet al., at onset. We suggestthat any time dependent convection 1979]. Particlesnear L = 5 (B = 150 7) need •100 min to model must incorporaterealistic initial conditionsconsistent adjustto the changedconditions. On the other hand, particle with quiet time observationsto give good quantitativeresults. phenomenasuch as those observedby Williamset al. [1974] ANALYSIS OF DATA are sometimes seen • 10 min after substorm onset, and on such a short time scale the use of steady state theory cannot be The particle observationsreexamined in this study are the justified. low-energy(0 to 7.1 keV) electronflux increasesand decreases A time dependentmodel of plasmasheet response to the seenaboard Explorer 45 shortlyfollowing a substormonset on convection electric field was presentedby M. Ejiri, R. A. December 12, 1971 [Williams et al., 1974]. As the Explorer 45 Hoffman, and P. H. Smith (unpublishedmanuscript, 1978), particledetectors measure particles with energiesdown to only who attemptedto explainthe observedposition (L • 4.5) and 1.5 keV, the presenceor absenceof the thermal (•0 keV) energy(W • 15 keV) of the protonsinjected inside the plasma- component was inferred by the measurementfrom the on- pause (proton nose event) during a magneticstorm. They board