Calvert, B.W. Reinisch, D. Gallagher, and P.H. Reiff, Radio remote sensing of ... Waves in Communication Electronics, John Wiley, New. York, 1984. Reiff. P. H. ...
Radio Science,Volume 34, Number 5, Pages1299-1320, September-October1999
The feasibility of studying the solar wind magnetosphere interaction by active electromagneticsounding from outside the magnetosphere F. L. Doudkin Lvov Center, Instituteof SpaceResearch,NationalAcademyof Sciences,Lvov• Ukraine NationalSpaceAgencyof Ukraine,Lvov. Ukraine
M.P. Gough Space Science Centre• University of Sussex. Falmer• Brightore EastSussex• England
Abstract.A space experiment isproposed to makecontinuous remote electromagnetic soundings of thesolarwindbow shockinteraction withthemagnetosphere of theEarth.We discuss the
feasibility ofconstruction of a system thatwillallowusto carl3. • outthebowshock sounding and study solar windlocalobstacles tensofminutes before theirinteraction withthebowshock. The sounding system, placed ata distance about26Refromthebowshock, withaverage transmitter active powerof20W ata maximum antelma length of 3 kmandantelma weight ofabout100kg, wouldprovide bowshock-solar windmonitoring withspatial resolution of0.25-1Reinthe frequency range 9-225kHzanda 10%electron density. resolution. Such a system, located atthe Lagrange pointL•, could provide continuous monitoring ofthesolarwindinteraction withthe Earth'smagnetosphere.
1. Introduction
Information about the global evolution of the
magnetosphere is an important aspectof the studyof solar-magnetospheric interactions.Remote active electromagnetic(EM) soundingcan provide an important servicebecause it allowsus to studylargescale structure and dynamics of bow shock,
magnetopause, plasmasphere, plasma areas of ionospheric originthat surround the Eartk and cases
correlationsbetween key regions of magnetospheric plasma: (2) magnetosphere global evolution (the dynanfics of outer and inner magnetosphere boundaries/layers); and (3) the global estimationof solar activi.ty(for example,estimationof solar wind dynamics, estimation of thefollowingsolarwindlargescale inhomogeneities: dimensions,density, velocity, and trajectol3. •, includingestimationsof energy and pressure, andestimation of outerboundaries andinner layerinteractions in themagnetosphere).
wherethereare sharp,magneticfield-alignedexternal The main scientificobjectivesof EM soundingin boundariesof the plasmapause [Reiff et al., 1994; this case are (1) the implementationof large-scale Calvertet al., 1995].Measurements of reflectedsignal sounding (almost simultaneous reception of parameters are usedin thesemethods for obtaining information,providingspace-timecoordinates of largeinformationaboutplasmalayers[Knechtet al., 1961; scale processes in the Earth's magnetosphere); (2) the Schmerling and Langille,1969;dacron et al., 1980; Green et al., 1998].
definition of soundedzone parameters(for example,
the distances to the sounding system The main fundamental problems of these electrondensities; or to the Earth; angular coordinates (direction of interactionswhich EM soundingmay addressare (1) reflected signal arrival); and velocity. of boundary morphology(structure)of the magnetosphere and movement):(3) the soundingof large-scalesolarwind inhomogeneitiesand their interactions with the Copyright1999by theAmericanGeophysical Union. magnetosphere; and (4) the studyof the dynamicsof magnetosphere boundaries and layers(the changingof Papernumber1999RS900032. 0048-6604/99/1999RS900032511.00
their locationmid electrondensity). 1299
1300
DOUDK1N
AND GOUGH:
EM SOUNDING
FROM OUTSIDE
At present,active EM soundingof the Earth's magnetosphere has been carded out by means of satellitetopsideionosphericand in situ local plasma relaxation sounders[Jacksonet al., 1980; Oya et al., 1990; Etcheto and Bloch, 1978; James, 1991]. However, these measurements do not provide informationabout the global conditionsof the outer magnetosphere layers. Amongthe projectsthatweredevelopedfor solving this problem,that of the Inner Magnetosphere Imager mission[Reiff et al., 1994; Bensonet al., 1998] is of
particularinterest,especiallythe RadioPlasmaImager (RPI) experiment.Usingtwo orthogonalwire antennas with length about 500 m, located in the plane of rotationof the satellite,and onerigid axial antennawith lengthnear 10 m, the systemmeasures simultaneously receivedsignalsreflectedfrom a variety of areasof magnetosphere plasma.The soundingsignalis radiated by oneof the 500 m antennas fromthe satellitelocated in a circularorbit in the innerpart of the magnetosphere at a distanceabout 6-8 Re from the Earth (Re = 6371
km and is the averageradiusof the Earth). However, RPI is not designedto studythe solarwind-bowshock interaction. Some ideas were proposedfor a global radio soundingof the magnetosphere [Wilhamset al., 1992; Green and Fung, 1994; Klimov et al., 1995], but they are not practicalat presentbecauseof significant technicalandfinancialproblems. The majortechnicaldiffictflfiesfor realizationof the scientificobjectivesof EM sounding arethefollowing: 1. In order to obtaina global picture,the distance betweenthe soundingsystemand the soundedobject must be not less than the magnetosphere'saverage diameter (about 30 Re). This means that to radiate sufficientsignalpower, the transmittingantennamust havea highvalueof currentmomentM = I x/• (where I is the antenna current and It is the effective antenna
THE MAGNETOSPHERE
must work in the frequencyband 9-200 kHz, i.e., practicallyin the VLF range.Working in this frequency range raises the following technical problems: (1) Antenna-radiated power decreases inversely proportionalto the square of frequency (at constant value of current momenttun); (2) antenna reactance increases approximately inversely proportional to frequency and antenna length. Therefore for transmittingat constantoutputtransmittervoltage the radiated power will decreaseproportionally to the fourthpower of antennalengthand the fotmh power of frequency;(3) the antenna-receiverpower matching coefficient is proportional to the fouah power of frequencyand the fourthpowerof antennalength.This meansthat receivedsignalpowerwill severelydecrease with decreasingfrequency and antenna length (for antennaswith low criticalfrequency,seesection3); (4) the antenna length is limited by half radiated wavelength, because by further increasing antenna length the number of diagram pattern lobes in the antennaalso increasesand there are abruptchangesof antennaimpedanceat its resonancefrequencies.The directionandnumberof lobesdependon radiatedsignal frequency,and many lobes make the determinationof reflectedsignaldirectionimpossible. 3. It is clear that the main requirementsof a soundingsystemconfigurationand its positionrelative to the bow shockare (1) convenience of deploymentin space;(2) minimal dimensionsand mass;(3) maximal
simplicit3•; (4) maximal stabilityof soundingsystem configuration;(5) minimal power consumption; (6) directionaldetemfinationof reflectedsignal;(7) EM som•dingof bow shock separateareas; (8) constant conditionsfor EM sounding;and (9) long system lifetime.Condition4 for large-sizeantennasrequires rotatingspacecraft. Condition5 requiresgoodmatching antennas with input (output) electronic circuits.
length).In this casethe powerof the radiatedsignalis
Condition 2 is connected with condition 5, and
proportional to ( I x It )•. Thecurrent in theantenna is
condition 1 is connected with condition 3. Condition 7
limitedby thermallossesthatincreaseproportionally to the squareof the current.So the transmittingantenna must be long enough since thermal (ohmic) losses increasemore slowly with increasingantennalength (proportional to its length).Also,the antennawill have large massbecausedecreasing antennadian•eterleads to increasingthermal lossesthat increase inversely proportional to the squareof the antennadiameter.
is connected with condition 6 and,in themain,depends on signal-to-noiseratio in receiver input circuits. Condition 6 requires, in the general case, three orthogonalsynchronously operatingreceivingantennas to determinethe signalanSvaldirection[Calvertet al., 1995]. This leadsto the followingproblems:(1) an increasing of antenna mass; (2) complicated deployment of antennas in orbit;and(3) problemswith 2. The densities of solar wind and bow shock axial antenna implementation (this antenna is plasmas arelow,approximately from1 to 500cm-3, perpendicularto spacecraftrotationplane). In orderto with very.low electronplasmaresonancefrequencies providethe rigidity the antennamust be very.short (aborn 10 m length) but this is ineffective at low (from about 9 to 200 kHz). As a result, for evenwhencomplicated measures are taken reconstructionof electrondensityprofiles the system frequencies
DOUDKIN AND GOUGH: EM SOUNDING FROM OUTSIDE •
MAGNETOSPHE•
1301 1
to match the antenna with the receiver (because
sensitivity thresholdsof signal power for antennas differ by 4-5 ordersof magnitudebetweenan antenna lengthof a few hundredmetersanda 10 m antenna).To providetensionfor a long axial antenna,a subsatellite with a periodically operatingcorrectingthruster is
2 Y•
required. Thisstrongly limitsthesystem life by thefuel resources.
4. Turbulenceof plasmaboundariesleads in the
general caseto thediffusereflection of EM wavesand thereflectedsignalbeingmuchweakerthanat smooth boundaries(specularreflection). 5. Changing of the "sounding system-
magnetosphere" configuration with the rotationof the Figure1. Configuration "spacecraft-bow shock-Earth" for sounding system aroundtheEarthandwiththerotation differentformsof bow shocksurface.Numberscorrespondto the Earth aroundthe Sun leadsin partsof the orbit to
the followingforms:1, hyperboloid; 2, paraboloid; and 3,
limitedglobalmagnetosphere sounding. Also,thereare spherical headandconicaltail,withsotruder at letterA. limitedopportunities for useof solarsailsto provide tension for the axial antenna.
Thus while we can see the importanceof using
globalmagnetosphere sounding, we notethatthereare significanttechnicaldifficulties.An estimationof magnetosphere EM soundingfrom outside the magnetosphere is now considered below.Attentionis concentrated on the problemof EM soundingof the solarwind bow shockwave of the magnetosphere of the Earth and also on the feasibility of studyingthe interactionbetweenthe solarwind inhomogeneities and the bow shock.
Obviously,the soundingsignalfrequencyrage will then be limited by
1< fn -•=0 at f•> dø's.Thismeans thatEM wavesaremoreor less fully reflected from the shock in this frequency range(equation (2)). Since the solarwind has spaceinhomogeneities of density and velocit3• of its particles. then it exerts
a mirror surfaceand diffuse usesa frosted surface(such
as a mirror and an ordinarybilliard ball). The specular model gives, as a role, more optimisticestimationsof reflected signal because of the inverse square dependenceon productfocusingfactor and distanceto target [Calvert et al., 1995]. Nevertheless,we will use both modelsof scatteringfor estimationsof reflected signallimits. Completing the descriptionof our model, we consider as average value R•m=15 Re, yo=26 Re [Kallenrode, 1998, chapter 10] (see Figure 1). This gives us the equationof hyperbola(rotating of one aroundx axis cremesthe hyperboloidsurface)
•_(•2 _•,2)o.5,
(9)
wherevalueswith a tilde meanthatthey are normalized
totheradius oftheEarth:.• =y R•:• etc.In thiscase,
DOUDKIN AND GOUGH: EM SOUNDING FROM OUTSIDE THE MAGNETOSPHERE
1303
a=Rrr•.For a sphericalmodelwe assme that the tail we may considereach elementarypart of surfaceas part of the bow shock conjugateswith the head tiaO; and (2) the reflectedsignalbecomesdepolarized. Usually, pulsed operationis used for far remote spherical partof radiusa by tangent conefrompointA, wherethe soundingsystemis located(seeFigure1). In sounding(with harmonic filling of current pulses), thiscase,•o • 15.Anequation fortheparabolic model permittingus to usethe sameantennafor transmitting and receiving of EM fields. Clearly, when using a is similar to (9): soundingpulse with width At, the spatialresolutionof the sounding systemis limitedby valueAr=O.5VgAt • y = (2•(• - •))o.5, (10) 0.5cAt,where Vg is the groupvelocity.of the wave package.For diffusescattering this meansthat reflected In this caseat • = 2• = 30, we have •o -•21.2. In all signalsat the observationpoint will exist during the cases,AO=b, ro=a+b, where ro is the minimal distance
from soundingsystemto bow shock. Thus for an upper estimate of reflected signal strengthfor diffuse scatteringwe will use a model of hyperboloidbow shock, and for low estimationthe sphericalmodelof bow shockwill be used,sincein this last casethe tail part doesnot give any contributionto the reflectedsignal.
time that is equalto the time of interactionof the wave packagewith all visible parts of the target (for mirror scatteringit is duringtime At only). Sincethe EM wave of the dipole sourceis spherical for the configtmation shownin Figure 3, eachpart of the surface gi,dng a resolvable contribution to the
scattering field (duringtimeAt) is thecircularelement in the distancerange r•-r•_j= Ar, n=1;2;3;....iN. We will
consider this element as a circular pixel.
3. Estimation of Reflected Signal
Obviously, thequantity of EM fieldenergyinteracting with sucha pixelmaybe writtenin theform [Felsen
3.1. Diffuse Scattering
and •larcm, itz, 1973, chapter5]
To avoid the uncertainty of estimation of echo direction.it is necessaryto use antennaswith only one lobe pattern. From condition (2) the linear electric dipole antennais the most effective and simple [King and Smith,1981, chapter3]. The uppervalue of antenna lengthl is limitedby the condition
(13) Sn
t
where Yl = [Ex H] is Poynting'svector, S• is the
pixel area; dS• is a vectorialelementof the pixel surface,whichis equalto productelementareato outer
[k,wl
