DUSTY

PLASMAS

IN THE SOLAR

SYSTEM

C. K. Goertz

Departmentof Physics andAstronomy Universityof iowa, iowa City

Abstract. The processes that lead to chargingof dust groin charge and a systematicvariation due to motion grains in a plasma are briefly reviewed. Whereas for single grains the results have been long known, the reductionof the averagecharge on a grain by "Debye screening" has only recently been discovered. This reductioncan be importantin the Jovianring and in the rings of Uranus. The emerging field of gravitoelectrodynamics which deals with the motion of charged grains in a planetary magnetosphereis then reviewed. Importantmechanisms for distributinggrainsin radial distance are due to stochastic fluctuations

1.

through plasma gradients. The electrostaticlevitation model for the formationof spokesis discussed,and it is shownthat the radial transportof dust containedin the spokesmay be responsiblefor the rich radial structurein Saturn'srings. Finally,collectiveeffectsin dustyplasmas are discussed whichaffectvariouswaves,suchas density wavesin planetaryringsandlow-frequencyplasmawaves. The possibilityof chargedgrains forming a Coulomb latticeis briefly described.

of the

INTRODUCTION

Dust is quite commonthroughoutthe universeand representsmuchof the solid matterin it. On the other hand,thegaseous component of matteris oftenionized(at leastpartially),and thusthe dustcoexistswith plasmaand forms a "dusty plasma." The evolutionof the solar systemfrom its solarnebulastageto its presentform has passedthrougha stageduringwhichalmostall solidmatter was in the form of dust which we will define here as solid

objects smaller than 1 cm. Larger objects such as meteorites,planetesimals, andplanetspresumablyevolved throughcoagulationof dust. Althoughthe propertiesof theearly solarnebulaare not well known,it is very likely that the gaseouscomponentwas also partially ionized. Thusthe early solarnebulamustbe thoughtof as a dusty plasma. In many cases one observesthat the dust is not uniformly distributedin space. For example, comets possesslong dust tails and trails. Dust in planetary magnetospheres is concentratedin rings whose radial width is often quite small. Some rings showradial and azimuthal(longitudinal)opticaldepthmodulations.Much of this paper will deal with explanationsfor thesestructureswhichrely on electricand magneticforcesactingon dust particles. This is not to say that all structuresare electromagneticallyinduced, but we now have good reasonsto believethat theseforcesare importantand need to be consideredif one wants to understandthe spatial distribution of dust.

For thepurposesof thispaperwe definea dustyplasma as an ensembleof dustparticlesimmersedin a (perhaps partiallyionized)plasmaconsistingof electrons,ions,and neutrals. Dusty plasmas occur in many astrophysical contexts,but this paperwill only deal with dusty plasmas in the solarsystem.Usually,the strongestforceactingon dustparticlesin the vicinityof starsor planetsis gravityor radiationpressure. However, in a dustyplasmathe dust particlesare, in general,chargedandwill thereforealsobe affectedby electricand magneticfields often in subtleand surprising ways. In addition,thedustparticlesmaychange the propertiesof the plasmaitself and changethe dispersion relation of various,usually low frequency,plasma waves.

Dust particlescan be chargedby various means,for example, by photoionizationor absorptionof charged particles. If suchchargeddustparticlesexist in a plasma, i.e., in a conductingfluid, the interactionbetween the particlesandexternallyappliedelectricandmagneticfields (e.g., a planetary magnetic field) is modified by the presence of theplasma.For example,a negativelycharged dust,or for thatmatterany negativelychargedparticle,will be surroundedby a plasma which is not charge neutral everywhere buthasa positivechargedensitynearthegrain becauseit tendsto attractthe positiveions and repel the negativeelectrons.This positivechargedensitypartially screensout the negative dust charge and reducesthe strengthof the interaction.This "debyescreening"effect is a unique consequenceof the fact that the dust is immersedin a plasma.

Reviewsof Geophysics, 27, 2 / May 1989

Copyright1989 by the AmericanGeophysical Union

pages271-292 8755-1209/89/89RG-00424

$5.00

Papernumber89RG00424 ø271

ø

272'Goertz:

DUSTY PLASMAS IN THE SOLAR SYSTEM

Several effects which will

be discussed below are a

27,2/REVIEWSOFGEOPHYSICS

tionalforce on a typicalring particlewith the electromagneticforce in a corotatingmagnetosphere, one finds that it is, indeed,often muchlarger and that the motion of sucha particleis to a very high degreeof accuracydescribedby the normal Kepler motion. However, subtle deviations from Keplerianorbitsare importantin rings. Electromagnetic forcesacting on chargeddust particlescan provide for thesedeviations.The studyof the motionof charged

directconsequence of the fact thatdustparticlesin a dusty plasmaare charged. For example,if two dustparticles carry the samesign of charge,they repeleachother,and the cross sectionfor collisions(e.g., stickingcollisions necessary for coagulation) is reduced.On the otherhand, it is possiblethat somedustparticlescarryoppositesigns of charge,in which casetheseparticleswill attracteach other and coagulatemuch faster than if they were un- dustparticlesin a planetarymagnetosphere is the subject charged.The distributionof dustin the vicinityof comets of "gravitoelectrodynamics."This will be discussedin or in planetarymagnetospheres where plasmasexist is section 3. Because the motion of charged dust particles in a significantlyaffectedby the electromagnetic forcesacting on the chargeddustparticleswhichmay causechangesof planetarymagnetosphereis not exactly Keplerian, radial the dust particles'angularmomentumand hencelead to transportof dustcan occur,at timesvery rapidly. Sucha orbital decay. This electromagnetically inducedradial transportcan causea redistributionof angularmomentum for transport of small dust particles is important for the in tings which has importantdynamicalconsequences maintenanceof the ephemeral(optically thin) rings of the evolutionof planetarytings. Thesewill be described Saturn and Jupiter. Finally, the electromagneticallyin section 4 as well as the electrostatic levitation model for induced angular momentumtransportcan significantly theformationof the "spokes" in Saturn'stings. It will be affect the evolutioneven of the opticallythick main rings shownthat the spokesmay be responsible for the surprisof Saturnwhosevisualappearance reflectsthe distribution inglyrich radialstructureof theopticallythickB ring. When the dustnumberdensitybecomesvery large and of big (meter size) particles which are not directly the intergraindistanceis small, the grains may interact influencedby electromagnetic forces. The fundamentalquantityoneneedsto know in orderto with each other via electrostatic Coulomb forces, and assessthe importanceof electromagnetic forceson dust collectiveeffectsmay occur. Dustparticlesmay thennot particlesis their chargeto massratio. The chargeis the move independentlyof each other but in a coherent product of the dust grain's surface potential and its fashion. The numberdensityof the dustparticlesmay be capacitance.The surfacepotentialis relativelyeasy,but modulatedcoherentlyby a wave propagatingthroughthe by no meanstrivial,to calculatefor a singlestationarydust dust medium. In addition, dust grains may changethe grainin a plasmaby balancingthe currentsdue to plasma dispersionpropertiesof low-frequencyplasmawaves. The ions,electrons,photoelectrons, andsecondaries. However, possibilityalsoexiststhatthe Coulombinteraction energy when the number of dust grains becomeslarge, the exceedsthe thermalenergy of the dust particles. In that potentialat any grain'ssurfaceincludescontributions from caseone expectsdust grains to exhibit long-rangeorder the chargeson all othergrainswithina "Debye sphere," andform liquidlikeor evenlatticestructures.This will be andthusthechargeon thegrainitselfcouldbe quitesmall. investigatedin section5. Dusty plasmashave not been studiedextensively,and The Debye spherecharacterizesthe region throughout which the electric field of a point chargeplaced in a many questionsmust remain open at this time. In below to plasmais felt in thisplasma.BeyondtheDebyespherethe particular,the relevanceof the effectsdiscussed electricfield is significantlyreducedbecauseof the fact naturalphenomenasuch as planetarytings or cometary that the plasmainsidethe Debye sphereis not neutralbut dusttailsis notclear,simplybecausetheplasmaproperties carriesa net chargeoppositein sign to that of the point and the grain characteristicsare not well known. Our charge. Thus grainswhich are separatedby more than a modelsare also rather simple,assuming,for example, Debye length do not interactelectrostatically with each sphericalgrains of radius a. Usually, all grains are other. Thesequestions will be discussed in section2. assumedto have the samesize. Some of the charging Many of our applicationswill deal with dustin plane- currentsare neglected,etc. Severaloutstandingquestions for future theoreticaland observational tary rings which all exist inside the planets' magneto- and suggestions spheresand which thusmustbe regardedas examplesof work will be discussed in the final sectionof this paper. dustyplasmas. The questionarises,of course,of whether The field of dustyplasmasis quite young,and a critical the fact that ring particlesare chargedhasany observable readermay doubtthe wisdomof writinga reviewpaperat or importantdynamicconsequences.Traditionaltheories thistime. However,thefieldis evolvingquiterapidly,and of tings (for reviews, see Greenbergand Brahic [1984]) excitingdiscoverieshave been made which even space neglectthe chargeeffectscompletely,usuallywithoutany scientistsare not aware of. This review paper cannot detailedjustification. When one comparesthe gravita- possiblycoverall aspects,but it is hopedthatreadersnot

27,2/REVIEWSOFGEOPHYSICS

Goertz:

DUSTY PLASMAS IN THE SOLAR SYSTEMo273

familiar with this field may find the questionschallenging increaseswith Iwl. Thus the chargeon a movinggrain and exciting, at least, and may even be motivatedto tends to be more positive than on a grain at rest with contribute to this field in the future. respectto the plasma. However, this is not necessarily always the case,as discussedby Whipple, to whom we refer the reader for more details. 2. THE CHARGE

OF A DUST

GRAIN

IN A PLASMA

The electron current is

not affectedby the slowrelativedrift betweenthe dustand

theplasmas because w • cewhereceisthethermal speed of 2.1.

Isolated Grains

the electrons. Becasue the ions are much heavier than the

Thereare severalprocesses whichcausethe chargeon a electrons (mi •) me),theioncurrent is,for•)• = 0, much grainto be nonzero,and the calculationof the equilibrium smallerthan the electroncurrentdensity, and the grain charge on a grain can become quite complex if all becomesnegativelycharged. This reducesthe electron processes are included. For grainsin a plasmawith a current and increases the ion current. The flux of secondaries dependson the energyE of the temperature Te for electrons (massme)andT/ for ions (massmi) the fact thatthe flux of electrons havinga plasmaelectronsand the surfacepotential. If the grain is thermal velocity of ce = (kTe/me) •t2(k is theusualpositive,someof the secondaryelectronsmay be recapBoltzmannconstant)is larger than that of the heavierions turedand not contributeto the chargingof the grain. The

which have asmaller thermal velocity ci = (kTi/mi) •/2will temperature of thesecondaries, T•,is of theorderof a few makethe grain chargeQ and its surfacepotential•s

104K. The net charging current of the secondaries

negative.The densityof electronsandionsfar away from the dusty plasmawhere the plasmais chargeneutral is

dependsalso on the material propertiesof the grains characterized by the secondaryyield parameter•5and has been discussed in detail by Meyer-Vernet[1982], who has no(noe = noi).Ontheotherhand,theprimary electrons can, if they are energeticenough,releasesecondaryelectrons, derivedexpressions for the secondarycurrentusing the whichcausesthe surfacepotentialto becomepositive. The yield function absorptionof plasmaions also tendsto make the surface potentialpositive. The currentsof primary electronsand 15(E)= 7.415mE/Em exp[-2(E/E,•) •r2] ionsare, of course,affectedby the surfacepotentialof the grain(of radiusa) itselfanddependon therelativevelocity whereEa is a characteristic energyat whichtherelease of w between the plasma and the grain. If the surface a secondaryelectron peaks. Integrating this over a potentialis negative,electronsare repelled,and the current Maxwellianprimaryelectrondistributionyields to the grainscarried by them is reduced. On the other hand, ions are attracted, and their current is increased. For Jsec = 3.7•SmJe = Fs(E,•/4kTe) q)s 0

q)s>0

where

F5(x)= xa I t5exp[-(xt2 + t)] dt 0

(2)

Ji = Joi(1- zi e O)s /k Ti )

Fs• (x)- xa I t5exp[-(xt2 + t)] dt

•), Ea = 3.36x 105Ttu2 4

(lO) 2

-2

C

0

I

I

I

i

2

4

6

8

I0

TIME (MIN)

For fluffy aggregates, T, is about10 N/m andE• is 3 x 5

2 Figure3. Theevolution of thesurface potential •, of grains with 10 V/m;foriceT t is between 10 and10 N/m andEa radius 8 9 a varyingfrom 1ganto 6 I.tm. In all threepanels,initially,

varies between 10 and 10 V/m.

7

For silicates the critical

fieldstrength varies between 3 x 108and3 x 109V/m.For

metals, Ea_-1.5x 10•øV/m(forreferences, see Grtin etal.

q•,= 0. The plasmatemperature is constant (kT = 1 eV) for 5 min, after which the temperatureoscillateswith a periodof 1 min. The amplitudeof thetemperature oscillation is AkTequalto

eV. [1984]). Electrostaticdisruptionfor particleswith rough (a) _+0.2eV, (b) _+0.3eV, or (c) _-+0.4

27,2/REVIEWSOFGEOPHYSICS

Goertz: DUSTY PLASMASIN THE SOLARSYSTEM*277

surfaceshasbeentreatedby Hill and Mendis [1981]. The electrostaticstresstendsto erodebumpson the surfaceand renderthe grainsmore spherical. For 1-gm grainsthese

effects limitthe surface potential to about103V (for

electron field emission) or30V if Tt_-104 N/m 2. 2.2.

Ensemble of Dust Grains

•

Thepotential inthevicinity ofasingly-charged grain is • givenby the solutionof Poisson'sequation:

A2{ = (e/to) [he({) - ni({)1

(11)

For a Boltzmanndistributionof the plasmaelectronsand singlychargedionswe have

5

I0

15

n,({) = noe+'*/kT' (12)

o

ni(0))= noe-•*/•T' Thedensityno is theelectron densityfar awayfromthe dustwherethe plasmapotentialis zero and the plasmais chargeneutral. The surfaceelectricfield is givenby

Es =Q/4neoa 2

(13)•

An analyticsolutionof (11) and (12) for eO)/kT 0). If the grain'sorbit is slightlyperturbedin the equatorial plane,its motioncanbe describedas an ellipticalgyration about the guiding center of a grain which moves on a circular orbit with frequencyfO. The frequencyof the radialoscillationis givenby

2 2 + 4fog fO r - fog fo+ fO2

(26)

a 1-gmparticle orbiting Saturn atL = 2 where W_l - - 103

m/s (Keplerian orbit), wehave R=2.5x 10'5•)s >f•a:)and thus that orbit Saturn at the local corotafion rate occurs at a

to, =--•-+f•a:1+ f•2 .]

distance of re = 1.625R e fromSaturn.Thiscorresponds (28)reasonably well to the inner edge of the B ting. If the

Thesetwo oscillation frequencies (c%,to,) are changed grainsare launchedin thering planewith the localKepler slightly when the oblatenessof the planet is taken into

velocity, the orbit will not be circular becauseof the

force. For thiscasethe stabilitylimit is account [Schaffer andBurns,1987]. Bothtotand% are electromagnetic closetof•a:(atleastforlargeparticles). foundtobeexactly at theinneredgeof theB ringatrc= Several interesting consequencesresult from these 1.5245Rs [Northrop andHill, 1983]. Forr < rc a grain considerations.The known planetarymagneticfields are not purely dipolar but containquadrupoleand ocmpole components.If the variationof the magneticfield seenby a groin moving throughthe nondipolarmagneticfield of planet matchestheseoscillationfrequenciesor harmonics thereof,the excursionof the grainsfrom circularorbitscan growexponentiallyin time. SchafferandBumsshowthat the magneticfield variation seen by the grain acts as a periodic forcing term which can producelarge resonant responsesin the grain orbits. The enhancedvertical excursionof groinsat a vertical resonancelocationmay lead to a thickeningof the ting. The resonances occurat specificradial distanceswhich may correspond to various observedfeaturesof the radialopticaldepthprofile of the Jovianring. However, the matchbetweenpredictionsand observationsis only partial, and more work needsto be doneto betterunderstand thesemagneticresonances.This should be especially interestingfor the Uranian rings whichexistin a highlynondipolarfield.

Outsideof synchronous orbit (wheref• = f•a:),negativelycharged grainsin prograde orbitshaveto> f•K and could thus be in a 1'1 resonance with a satellite interior to

the grain orbit. Positivelychargedgrains could be in resonance with a satelliteoutsidethe grainorbit. Mendis

et al. [1982]showthata grainwith a frequency torwill movein an undulating orbitwitha wavelength 3,givenby

with a velocitydirectedaway from the ring planewould notreturnto theringbut wouldbe lostintotheatmosphere

of Saturn.Beyond rethegrainis stablytrapped andcanbe reabsorbed by the ting. Thus a continuous productionof groinswould yield an erosionof the rings and hencea

decrease of opticaldepthinsider• but notoutside of it. The workof NorthropandHill, however,doesnot really

apply todustgrains, forwhich, ingeneral, tog