JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. A12, PAGES 21,231-21,243, DECEMBER 1, 1993

Modeling the Europa Plasma Torus

RON SCHREIER AND AHARON EVIATAR 1

Department of Geophysics and Planetary Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

VYTENIS M. VASYLIONAS

Max-Planck-Institut fgr Aeronomie, Katlenburg-Lindau, Germany

JOHN D. RICHARDSON

Center for Space Research, Massachusetts Institute of Technology, Cambridge

The existenceof a torus of plasma generated by sputtering from Jupiter's satellite Europa has long been suspectedbut never yet convincingly demonstrated. Temperature profiles from Voyager plasma observations indicate the presence of hot, possibly freshly picked-up ions in the general vicinity of the orbit of Europa, which may be interpreted as evidence for a local plasma torus. Studies of ion partitioning in the outer regions of the Io torus reveal that the oxygen to sulfur mixing ratio varies with radial distance; this may indicate that oxygen-rich matter is injected from a non-Io source, most probably Europa. We have constructed a quantitative model of a plasma torus near the orbit of Europa which takes into account plasma input from the Io torus, sputtering from the surfaceof Europa, a great number of ionization and charge exchangeprocesses, and plasma loss by diffusive transport. When the transport time is chosen so that the model's total number density in consistent with the observed total plasma density, the contribution from Europa is found to be significant although not dominant. The model predicts in detail the ion composition,charge states, and the relative fractionsof hot Europa-generatedand (presumed) cold Io-generated ions. The results are generally consistentwith observationsfrom Voyager and can in principle (subjectto [imitationsof data coverage)be confirmedin more detail by Ulysses.

INTRODUCTION incorporated.Bagenal et. al. [1992],in an investigationof It has long been accepted that Io is the dominant source the paucityof O++ in the Io torusreported by Brownet al. of plasma in the magnetosphereof Jupiter and that con- [1983],found that O++ pervadesthe entiremagnetosphere tributions from the icy satellites are insignificant. A re- and that while the sulfur density drops off with increas- ported detection of Europa-associated plasma in the Pio- ing radial distance, as expected, the oxygen does not. This neer 10 data set [Intriligator and Miller, 1982]did not win again led to the suggestionthat Europa may be playing a broad acceptance. Early evaluationsof the sourcestrength role as a magnetosphericplasma source. Renewed interest of Europaranged from 8 x 1026s -• fromsputtering by ra- in the possibility of a Europa torus was stimulated by the diation belt particles[Johnson et al., 1981]down to as low Ulyssesencounter with Jupiter. Observationsmade during as 3 x 1024s -• from sputteringby corotatingiogenic ions the Ulyssesflyby of Jupiter confirmedthe existenceof signif- [Eviatar et al., 1981]. The latter estimatewas made be- icantamounts of O++ in regionsof the magnetospherewell fore the results of the low-energysputtering experimentsof off the zenomagneticequatorial plane [Geisset al., 1992]. Bar-Nun et al. [1985] becameavailable and significantly The Ulyssesinstruments were turned off, however, during undervaluesthe source rate. Later analysesby Sieveka and the close approach of the spacecraft to the planet, and no Johnson[1982] and Squyreset al. [1983]led to a deeperun- data were acquired in the equatorial plane. Our results com- derstandingof the interaction of the surfaceof Europa with plement the Ulysses ion mass spectrometer results as we the magnetosphereplasma [Eviatar et al., 1985]. strive to create a continuous latitudinal profile of plasma Baganal[1989] reported a significantenhancement of a density and composition. This, of course, implies basic time hot heavy-ion component outside the hot torus, as shown independence, which is indeed a limitation of the vMidity in Figure l a, and suggestedthat this oxygen component of the conclusions. Confirmation of the Europa source hy- might be associatedwith Europa. pothesisawaits more detailed analysisof the Ulyssesplasma These are preliminary results as the correctionsfor elec- data set. tron and ion feedthrough to the measured currents in the We present the results from a numerical model of the Eu- PlasmaScience (PLS) instrumenthave not yet been fully ropa torus. Sputtering from Europa's icy surface by mag- netospheric particles is a source of molecular and atomic water fragments, and ionization and other atomic processes • Also at Departmentof AtmosphericSciences, University of California, Los Angeles. produce plasma in the vicinity of the satellite's orbit. We first summarize what is known today about the plas- Copyright 1993 by the American Geophysical Union ma conditionsnear Europa. We then present the model and Paper number 93JA02585. examine the effect of various parameters on the results, and 0148-0227/93/93JA-02585505.00 compare the calculated density and composition with the

21,231 21,232 SCHREIERET AL.: MODELING THE EUROPAPLASMA TORUS

I0000

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_

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I0 - ,, -:

ß T•(average) :

_ _ I --- / • T•(cold) _ • T•(hot)

0,1 ,,,,I,,,,1•,1,,,,I,•1,,,,I,,,,I,,,,I .... 4 5 6 7 8 9 10 II 12 13 4 L-shell (offset) Fig, ! a, Flacl.ia].profiles of the temperatures of various components of the ion p]a.smaa.s observed by the P I.,S instrumenton Voyager.1, The plot is taken from Bage•l ['1989],

O.SO The main cluster consistsof the A, B, and C cups, which are mounted about a cone whosecentral axis points toward Earth. The D cup points perpendicularto the spacecraft- Sun direction. When the spacecraft was inbound toward Jupiter, the D cup pointed approximatelyinto the corota- tion direction during both the Voyager 1 and Voyager2 en- counters. A detailed description of the instrument and its modesof operationis givenby Bridg• •t al. [1977].This is an electrostaticinstrument which has the capability to pro- 0.01 .... ' .... ' .... ' .... ' .... ,, ,A,, vide well-resolvedparticle spectra wheneverthe flow is cold 5.5 6.0 6.5 7.0 7.5 8.0 8.5 and directed into the detectors. Such conditions held in the ;j mid-magnetosphereplasma sheet [McArutt •t aL, 1981]. Fig. 1b. Ion partitioningfrom fits to UVS spectra(except O ++ opencircles which are frommodel calculations), taken from Figure 2 showsspectra from the Voyager2 P LS instru- •l et •l. [1992]. ment obtainednear closest approach; the correspondingbest fits (giventhe input assumptions)to thesespectra are shown observations.We alsoinvestigate the relative importanceof in the panelsof Figure 3. The spectrumin Figure 2a is ob- iogenicand eurogenicsources in order to determinewhether tained 1.5 Rj south of the magnetic equator at a radial Europa providesa significantcontribution to its plasma en- distance of 10.16 /{j. Well-defined peaks appear in the A, vironment, that is, whether it is meaningful to discussa B, and C cups. Figure 3a showsa fit to this spectrumusing Europa plasma torus. a MaxwellJanplasma comprised of O+,S+, O++,SS+,Na +, andK ++ [McArutt,this issue]. Another example of a spec- EUROPA'S PLASMA ENVIRONMENT trum in which well-definedpeaks appear is shownin Figure The plasma conditionsin the vicinity of Europa can be 25 and its associatedfit is shown by Figure 3b. Figure 2c summarized as follows: The ion number density lies in the presentsa spectrum obtained at closestapproach, outside range30 to 50 cm-s [Belcher,1983]. The temperatureof the orbit of Europa at a similar distance(1.5 Rj) off the the thermal or cold component rises from 50-60 eV at L magnetic equator. Since the plasma is warm, the currents ~ 6 to 200-400 eV atL ~ 9-11, and there is an additional from individual speciesoverlap. Nevertheless,this spectrum (30%) hot componentat ~ 2 keV [Bagenal,1989]. The hot showsthe presenceof a hot locally picked-up background componentcan be attributed to pickup ions created outside plasmaas found by Bagenal[1989]. The crowdingof six of Europa's orbit and heated adiabatically. The electron ion componentsinto 50 energychannels (Figures 3a and distribution function is also describedby two components: prevents a unique determination of plasma parameters. a coldcomponent (26 eV) witha numberdensity of 36 cm -3 An agreementbetween a numerical model and the results anda hot (1.2 keV) andtenuous component (3.1 cm-3) of obtained from the analysis of the PLS spectra is an im- suprathermal electrons. Any successfulmodel of a steady portant test for the model. Though the processof fitting state torus must reproduce these observationsof Europa's ion distribution functions to the PLS spectra is not unique environment. (i.e., the A/Z-•16 componentmight be attributedeither to O+ andS++.), general characteristics of the model param- PLS OBSERVATIONS eters (e.g., the total numberdensity and the partitioning The Voyager PLS instrument consistsof four modulated- between(cold)iogenic and (hot) eurogenicplasma) should grid Faradaycups (A, B, C andD) whichmeasure ions and match those of the fits. The poor quality of the fits to the D electronsin the energy-per-chargerange 10 to 5950 eV/q. cup currentsmay imply that significantelectron feedthrough SCHRI•II•RI•T AL.: MODI•LINGTHI• EUROPAPLASMA TORUS 21,233

VOYRGER SPECTRRL DRTR 10• R CUP 106 B CUP Illl II III III III!

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JUPITER MRCNETOSPNERE B - (-36.388 , qq.816 , -71.952 ) CANNA VOYAGER 2 CHARGE DENSITY ESTIMFITE = (11.9367 ) 1979 190 2000:10.0q5 VCUP - (96.509 , 102.57q , 103.225 , 16.127 ) KM/S R = 10.290 RHO(HAG) = 10.180 Z(MRG) = -1.506 RIGID COROTATION SPEED = 127.763

VOYAGER SPECTRAL DRTR R CUP 108 lO6 B cup

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JUPITER MRCNETOSPHERE B = (-30.69q , q8.933 , -71.915 ) OIlHI'JR VOYAGER 2 CHRRGE DENSITY ESTIMRTE = (q1.8109 ) !979 !90 21!3:q6.0q2 VCUP = (100.068 , 99. 506 , 98. 880 , 1. 803 ) KH/S R = 10.157 RHO(HRG) = 10.039 Z(HRG) = -1.5q9 RICED COROTRT[ONSPEED = 125.995

Fig. 2. Plasmaion spectraobtained by Voyager2 nearclosest approach of the spacecraftto the planet: (a) 1979 190 2013:46.042UT, at radial distanceof 10.157 Rs, at centrifugalequator crossing; (b) 1979 190 2057:46.042 UT, at radial distanceof 10.179tqj, at centrifugalequator crossing; (c) 1979 190 2000:10.045UT; radial distance: 10.290 ft j, 1.5 ft j below the equator. 21,234 SCHREIER ET AL.: MODELING THE EUROPA PLASMA TORUS

VOYRCER SPECTRAL DATA B CUP 106 ACUP 106 •1 I I I I I I ILI I I I I I• --I I I I I I' I I I I I I I I I ; C

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_ _ 109 I I I I I I I I I I I I I I I 1o3 I,I I I I I I I I I I I I I I 0 32 6q 96 128 o 32 6q 96 128 CFIRNN•LcNu•MBER lo 6 lO6 --I I I '1 I'l"l"l' I I I I I I I:- _

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_ 103 I I I I I I I I I I I I I I I lO• I I I I I I I I I I I I I I I 0 32 6q 96 128 o 32 64 96 128 CHANNEL NUMBER CHANNEL NUMBER

JUPITER MAGNETOSPHERE B = (-31.981 . q7.959 . -72.010 ) GAMMA VOYAGER 2 CHARGE DENSITY ESTIMATE = (67.20qq) 1979 190 2057:q6.0q2 VCUR = (99.319 , 100.281 , 99.837 , q.9q9 ) KM/S R = 10.179 RHO(MRG) = 10.062 Z(MRG) = -1.5qO RIGID COROTRTION SPEED = 126.286

Fig. 2 (continued). contaminationoccurs (Ralph L. McNutt, Jr., private com- munication,1993). It is obviousthat any material of Eu- ropan origin cannot be describedsimply by cold corotating Maxwellian distribution functions. - + +4" + 4"' We shall discussbelow the various possibleinterpretations of these findings, while bearing in mind that the hot tem- perature profile shown in Figure la is the signature expect- ed from pickup of water group matter from Europa whereas the low temperature plasma observednear magnetic equator dN•rn,i) crossingsis consistentwith the idea of adiabatically cooled dt Io material.

MODELING THE TORUS A planetary plasma torus is created by the effectsof sun- light, cotoratingplasma and energeticparticle fluxes[Evi- afar et al., 1978;Huang and Siscoe,1987]. Its density,com- position, and energy budget depend on the nature, composi- tion, and strength of the source,radiative processes,atomic and molecular reactions, and the radial diffusioncoefficient. If the sourcestrength, transport rates, and reaction rates are given, we can determinethe relative importanceof iogenic and eurogenicmatter. In our modelwe include: (1) Sputteringof neutralsoff the surfaceof Europa by sunlight,corotating ions, and energet- ic particles;(2) electronimpact ionization and photoioniza- tion; (3) dissociativeionization of neutralsby photonsand by electronimpact; (4) chargeexchange; (5) inflowby diffu- (1) sionof iogenicplasma; and (6) lossof ionsby diffusiveflow and by collisionwith Europa. We use a zero-dimensional model similar to that which Richardsonet al. [1986]used where the following notation has been used: The sub- to describe the Kronian tori: iftwocol scripts j and k denote individual species,the superscripts SCHREIERET AL.: MODELING THE EUROPA PLASMA TORUS 21,235

RBSOM: MRXNELLIRN SIMULRTION , V2 RT JUPITER ON !979 !90 2000:10.0q5

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V:(-19. ]07,127.883,-12.016) KM/S BCYL:(-36.368,qq.816,-71.952) CRMMR•, BESTFIT R,Z : I6,1 I6,2 N(CM-3) = 5.88 8.70 1.50 NPER = 111,55 !11,55 111.55 NPRR : 111,55 111,55 111.55

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V:( 1.3,-17,105.397, .365) KM/S BCYL:(-30. B9q, q8.933,-71.915) CRMMR R,Z = 16, I 16,2 32,3 39,2 23, ! 32, 1 N(CM-3) : lq.12 2.65 2.q2 1.Tq q.51 2.70 NPER : 7. O0 7. O0 q. 95 q. q8 5.8q q. 95 FIPRR = 7. O0 7. O0 q. 95 q. q8 5.8q q. 95

Fi•;. 3. Best fit compositionanalysis for the spectrum shownin Figures 2• and 21,236 SCHREIERET AL.: MODELINGTHE EUROPA PLASMA TORUS

TABLE 1. Rates of Photoprocesses Reaction Rate, s-• Reaction Rate, s-• H -• H + + e- 2.7E-9 H20 -• H + + OH + e- 4.8E-10 H2 -• H + H 1.26E-9 H20 -• O+ -•-H2 -•-e- 2.16E-10 H2 -• H+ + H + e- 3.5E-10 H20 -• H20 + -•-e- 1.24E-8 H2-• H2+ -{-e- 2.0E-9 02 -• O-{-O 2.2E-9 O -• O'• -{-e- 7.84E-9 02 '• O+ -{-O -{-e- 1.87E-9 OH-• O + H 1.85E-7 O2-• O•+ + e- 1.9E-8 OH -• OH+ -{- e- ß 1.2E-8 S-• S+ -{- e- 4.07E-8 H20 -• H + OH 3.8E-7 SO -• SO+ + e- 3.2E-8 H20 -• H2 + O 5.0E-8 SO2 -• SO2 + e- 4.07E-8 H20 -• H + H + O 2.2E-8 SO2 -• S + 02 2.15E-6 H20 -• OH+ + H + e- 2.0E-9 SO2 -• SO + O 7.0E-6

Dataare from Schmidt et al. [1988].Read 2.7E-9 as 2.7x10 -9. Photoprocesses include ionization, dissociationand dissociativeionization of the nine neutral speciesincluded in the model. ß Ionization rate of OH was set equal to that of H20.

(m,n),(m,i),(a,n), and (a,i) denotemolecules, neutral and TABLE 2. Sputtering Yields Per Corotating Ion ionized and atoms, neutral and ionized, respectively.The Species Heavy Ions H + superscripts(a -]-re,i) and (a -]-re,n) imply that k is to be H20 9.5 0.6 summedover both atomic and molecular species F! O2 5.5 1.2 H2 6 0 and.FJa,n) denote thetotal output ofneutral molecules and H 11 0 atomsfrom the satellite, I•a,i) is the input ofions ofiogenic Data are from Bar-Nun et al. [1985]. origin,t•j is the electron•mpact ionization rate coefficient, (i) /3j theelectron impact dissociation rate coefficient, •) the Matter sputtered off the surfaceof Europa will differ in (d) compositionand energyspectrum from Io torusmatter. The photoionizationrate,•) thephotodissociation rate,7© heavy componentwill consistof water vapor and molecular and 7(a) the dissociativeand dielectronic•ecombination oxygen. The escapefraction of the sputteredneutrals pro- rates, respectively,trpq the chargeexchange cross section duced by cascadesputtering was estimatedby Sievekaand between neutral p and ion q, v the relative velocity between Johnson[1982] as 0.83, and we multipliedthe yield values thereactants, Nj(P ' q) thetotal population of constitue nt j by this factor. From the assumedenergy partition of the es- which is of structure s - m or a and charge state c - n or capingneutrals, one may estimatethe half thicknessof the i, nj(s,c) -- Nj(s, c)/V the densityof constituentj, V the neutral particle torus of Europa as approximatelyAr = 1 volume of the Europa torus, ne is the electron density, r is Rs; thevolume V of thetorus is thenV = 2•rrr x •r(Ar)2, the transport losstime, and c is the collisionfrequency of where rr is the orbital radius of Europa. ions with the satellite. For each constituent, F is given by Molecularions of iogenic origin (e.g., SO• + orS• +) foundby Bagenal[1985]are unlikely to be foundbeyond the hot torus F - •rar[J,2 q-4 Z YrkJrk q- vcs E Ykn• j (2) because dissociative recombination times for these ions are k k small comparedto the transport time, and thus theseions are not included in our model. Iogenic alkali ions such as where ar- 1560 km is the radius of Europa, vcn - 105km s -• the relativecorotation speed at Europaorbit, J, Na+ andK ++ [seeMcNutt, this issue] were included as sput- therate of photosputtering bysunlight (1.6 x 107cm -2 s-•) terers but not in the atomic processesunder consideration in the model, since as their abundanceis low. for H and OH [Harrisonand Schoen,1967], Jz the flux den- The various rate coefficients used in the model are listed sity of energeticparticles which sputter matter from the sur- in Tables 1 to 6. faceof Europa,taken as 6 x 10s cm-2 s-• with 20% heavy The rate coefficients for the atomic and molecular pro- ions [Sievekaand Johnson,1982]. The summationrepre- cessescan be calculatedfrom Arrhenius'equation [Bond et sentsthe flux density of corotatingions and the Y valuesare al., 1966]: the sputtering yields. Sputtering by energeticparticles oc- curs over the entire surface of Europa becauseof their large gyroradii(hence the factorof 4), whilethe other factorsaf- k=ax (05)exp(-7/T) cm s , (3) fect only one side. In order to include transport from Io in the zero-dimensionalequations (1), we parametrizethe Io where T is the electron temperature at Europa's orbit in input rate and the diffusiontransport by meansof Ij and r. kelvin. Since the bi-Maxwellian electron distribution has a The basis of this parametrizationis given in the appendix. corecomponent at 26 eV and a suprathermalhalo at 1200 eV We usethe Io torusion partitioning at 8.25 Rs shownin Fig- [Sittlerand Strobel,1987], Tables 3 and 4 list the a,/3, and ure lb (takenfrom Bagenal et al. [1992])and a valueof 5/3 7 coefficientsand the rate coefficientat both temperatures. for the ion averagecharge state (see results and discussion). For chargeexchange (Table 5), a temperatureof 1 keV was FollowingBagenal et al. [1992],the Io sourceis assumedto used in Arrhenius' equation for the ions. be composedof the ionsO+,O ++, S+,S++,SS+,Na+ and In casesof an inconsistencyamong the publishedreaction H+, in relativenumber percentage of 32.7,41, 1.7, 13, 5, 3.3 values of the same process, we chose our value according and 3.3, respectively. to the followingcriteria: first priority was given to a graph SCHREIER ET AL.: MODELING THE EUROPA PLASMA TORUS 21,237

TABLE 3. Rates of Electron Impact Dissociation, Ionization, and Dissociative Ionization Reaction a /• -• k(26 eV) k(1.2keV) Ref. H + e- -• H + + 2e- 1.8E-8 2.8E-8 1 H2 +e--•H+H+ e- 3.22E-9 0.35 102000 2.58E-8 1.4E-7 2 H2 + e- --• H+ 2E-8 4E-8 3 H2+ e - --•H % +H+2e-+ 2e- 1.1E-7 6E-8 3 O+e--•O + +2e- 3.9E-8 8E-8 1 O + +e--•O ++ +2e- 5E-9 3E-8 1 OH+ e--•O+H+ e- 1E-8 2.02E-7 ß OH+e--•OH + +2e- 2F,-8 7.2E-8 ß H2Oq- e- --• H2 q-O+ e- 9.43F•10 0.5 81234 2.28F•8 2.02F•7 4 H20+ e- -• OH+H+ e- 9.43F•10 0.5 59301 2.45F_•8 2.02F•7 4 H20 q- e- --• H20 + q- 2e- 2E-8 7.2E-8 3 H20 + e- -• H + +O+2e- 6E-11 1.2E-9 3 H20+e--•O%+H2+2e- 6E-11 1.8E-9 3 H20+e--•OH + +H+2e- 3E-9 1.8E-8 3 H2Oq- e- --• H + +OH + 2e- 1.2E-9 2E-8 3 02 + e- -+ O+ O+ e- 9.43E-10 0.5 59417 2.45E-8 2.02E-7 4 02 + e---• O+ +2e- 2E-8 1.6E-7 5 02+ e- -•-0 • +O+ 2e- 2.4E-9 6E-8 5 S+ e- .-• S+ +2e - 1.6E-7 1E-7 6 S+ +e---•S ++ +2e- 2E-8 2E-8 6 S++ + e- --• S3+ + 2e- 7E-9 1E-8 6

Read3.22E-9 as 3.22x10-9. 1, Lotz [1967];2, Millar et •I. [1990];3, Kieffer [1969];4, Schmidt et al. [1988];5, Banksand Kocharts [1973]; 6, Brownet al. [1982].The a, /3,and ff are coefficientsof Arrhenius' equation. The calculated rates are given for both thermal and suprathermalelectrons. Rates are in cm3 s-1 . ß Ionization rate of OH was set equal to that of H20.

TABLE 4. Rates of Recombination Reaction c• /• -• k(•6.eV) k(1.2keV) H + q- e- --• H 3.5E-12 -0.75 0 1.96F•14 1.1E-15 H+ + e- --• H + H 9.8E-9 -0.5 0 3.1E-10 4.55E-11

g•q-e-+ e- --• H2O ß 2.25E-7-0.4 0 1.4E-84E-12 3.06E-95E-14 O ++ + e- --• O + ß 1.5E-11 1F,-13 OH + + e- • O + H 7.5F_,-8 -0.5 0 2.37F,-9 3.48F,-10 H20 + + e- --• OH + H 2E-7 -0.5 0 6.31F,-9 9.29F,-10 H20 + + e- --• O + H2 2F,-7 -0.5 0 6.31E-9 9.29E-10 O+ + e- --• O + O 1.95F,-7 -0.7 0 1.54F,-9 1.06F,-10 O•+ e---+ 02 t 4E-12 -0.7 0 3.17E-14 H30 + + e- --• H20 +. H 3.5E-7 -0.5 0 1.1E-8 1.63E-9 H30 + + e- --• OH + H2 $ 2.34E-7 -0.5 0 7.4E-9 1.0E-9 H30 + + e- --• OH + H + H 6.5E-7 -0.5 0 2.05E-8 3.02E-9 H• + e- --•H2 q- H 1.1E-11-0.5 0 3.47E-135.11E-14 H•' q- e- --• H q- H q-H 1.1E-11 -0.5 0 3.47E-13 5.11E-14 02H + q- e- --+ 02 q- H 3E-7 -0.5 0 9.47E-9 1.39E-9 S+ q- e- -• S ß 7E-12 5E-14 S++ q- e- -• S+ ß 3E-11 1E-13 S3+ + e- --+ S++ ß 1E-10 2E-i3 SO+ q- e- -• S + 0 2E-7 -0.5 0 6.31E-9 9.29E-10 S2+ q-e- --• Sq- S 2E-7 -0.5 0 6.31E-9 9.29E-10

HSSO• q- e- -•--• SSO q-q- H S 1E-72E-7 -0.5 0 6.31E-93.1F•9 4.64E-109.29E-10 H2S+ + e- --• S + H + H 1.5E-7 -0.5 0 4.37E-9 6.97E-10 H2S+ + e- --• HSq- H 1.5E-7 -0'.5 0 4.37E-9 6.97E-10 HSO + + e- --• SO + H 2E-7 -0.5 0 6.31F_.9 9.29E-10 S2H+ q- e- --+S2 q- H 1.5E-7 -0.5 0 4.37E-9 6.97E-10 S2H+ q- e- -• HS q- S 1.5E-7 -0.5 0 4.37E-9 6.97E-10 HSO•+ q- e- -• S02 q-H 2E-7 -0.5 0 6.31E-9 9.29E-10 HSO•q- e- -• SOq- H q-0 1E-7 -0.5 0 3.1E-9 4.64E-10 HS02•+ e- -• SO+ OH 1E-7 -0.5 0 3.1E-9 4.64E-10 Data are from Millar et al. [1991].Read 3.5E-12 as 3.5x10-12. Ratesare in cm 3 s-1 ' ß Brown et al. [1982]. t Schmidtet al. [1988]. TABLE 5. Rates of Charge Exchange Reaction o• • '7 k(1 keY) H+ + H.-• H2+ 2E-20 1 0 7.7E-16 H+ + H.-• H+H + , 3.5F_,-8 H + +O--• H+O + 7F_,-10 0 232 7E-10 H++OH._•OH + +H 2.1E-9 0 0 2.1E-9 H++H2--•H+H2 + 1E-10 0 21200 1E-10 H + +H20--•H+H20 + 8.2E-9 0 0 8.2E-9 H+ +02 --•H +02+ 1.1 7E-9 0 0 1.17E-9 H+ +S•S+ +H 1.3E-9 0 0 1.3E-9 H+ + SO • SO+ + H 3.2E-9 0 0 3.2E-9 H+ + S2--• S2++ H 3E-9 0 0 3E-9 H +H--• H2 +H+ 6.4E-10 0 0 6.4E-10 H + H2--• H• + + H 2.08E-9 0 0 2.08E-9 H! + H2--)- H• + H•+ 3.6E-9 0 0 3.6E-9 H• +O-•OH + +H 1F_,-9 0 0 1E-9 H! +OH-•OH + +H• 7.6E-10 0 0 7.6E-10 H +OH-•H•O+ +H 7.6E-10 0 0 7.6E-10 H +H•O-•Ha O++H 3.4E-9 0 0 3.4E-9 H! + H•O-• H•O+ + H• 3.9E-9 0 0 3.9E-9 H! +O•-•H+O•H + 1.9E-9 0 0 1.9E-9 H +O2--•H2+O2+ 8E-10 0 0 8E-10 H + H20 --• H30 + + H2 5.9E-9 o o 5.9E-9 H! +O--•OH+ +H2 8E-10 0 0 8E-10 H! + OH--• H20 + + H2 1.3E-9 0 0 1.3E-9 H! +O2-•O2H+ +H2 5E-9 o 150 5E-9 H! +S-• HS+ + H2 2.6E-9 0 0 2.6E-9 H! +SO-•HSO+ +H2 1.9E-9 0 0 1.9E-9 H,• + S2--• S2H+ + H2 2.0E-9 0 0 2.0E-9 H• + SO2-• HSO2+H2 1.3E-9 0 0 1.3E-9 O: +H--•H+ +O 6.8E-10 0 0 6.8E-10 O+ +H2-• OH + +H 1.7E-9 0 0 1.7E-9 O+ +O•O+O + • 1.8F,-8 0 ++OH-•OH + +O 3.6E-10 0 0 3.6F,-10 O+ + OH -• H + + 02 3.6F_,-10 0 0 3.6F,-10 O + +H20-• H20 + +O 3.2F_,-10 0 0 3.2F,-10 O+ +02--•O2+ +O 1.9F_,-11 0 0 1.9F,- 11 O+ +SO2--•O2++SO 8E-10 0 0 8E-10 OH+ + H2 --• H20 + + H 1.olE-9 0 0 1.01 E-9 OH+ d- OH --• H20 + + O 7E-10 0 0 7E-10 OH++O-•O• + +H 7.1E-10 0 0 7.1E-10 OH+ + H20 --• H30+ + O 1.3E-9 0 0 1.3E-9 OH+ + H20 --• H20 + + OH 1.59E-9 0 0 1.59E-9 0 0 5.9E-10 OHON + d-+O2-•2• S --• S +OHON 4.3E-105.9E,-10 0 0 4.3E-10 OH + + S -• SO+ + H 4.3E-10 0 0 4.3E-10 OH + + S -• HS+ + O 4.3E-10 0 0 4.3E-10 H20 + + H2 -• H30 + + H 8.3E-10 0 0 8.3E-10 H20+ d-O -• O•+ d-H2 4E-11 0 0 4E-11 H20 + + OH -• H30+ + O 6.9E-10 0 0 6.9E-10 H20 + d- H20 -• H3 O+ d- OH 2.1E-9 0 0 2.1E-9 H20+ d-02 -• 02+d- H20 4.3E-10 0 0 4.3E-10 H20 + d- S -• S+ d- H20 4.3E-10 0 0 4.3E-10 H20 + + S -• HSO+ + H 4.3E-10 0 0 4.3E-10 H20 + d- S -• HS+ d- OH 4.3E-10 0 0 4.3E-10 H3O+ d- S2 -• S2H+ d- H20 2.0E-9 0 0 2.0E-9 O++O2--•02+O• õ 1.3E-8 2.5E-9 OO• +d- SH2 -, -•S+ O2H + 02+ d- H II 5.4F,-10 0 0 5.4E-10 O•+ S -, SO++ O 5.4F,-100 0 5.4E-10 O2H + + O -, OH + 02 6.2E-10 0 0 6.2E-10 O2H+ + S --• HS+ + 02 1.1E-9 0 0 1.1E-9 O2H+ + H2 -• H3+ + 02 6.4E.-10 0 0 6.4E-10 O2H+ + OH -, H20 + + 02 6.1E-10 0 0 6.1E-10 O2H+ + H20 -• H30 + + 02 8.2E.-10 0 0 8.2E-10 S+ +O2--•O + +SO ô 2E-11 0 0 2E-11 S+ d- 02 --• SO+ d- O 1.5E-11 0 0 1.5E-11 S+ d- H2 -* HS+ d- H 1.1E-10 0 9860 1.1E-10 S+ + H2 -* H2S+ 1E-17 0 0 1E-17 S+ + OH --• SO+ + H 6.1E-10 0 0 6.1E-10 SO•+ d-H2 -• HSO2+ d- H 1.7E-11 0 0 1.7E-11 SO•+ 02--• 02 + + SO2 2.5E-10 0 0 2.5E-10 HS$ + H -• S+ + H2 1.1E-10 0 0 1.1E-10 SCHREIERST AL.: MODELINGTHE EUROPAPLASMA TORUS 21,239

TABLE 5. (continued) Reaction c, /• -• k{1keV) HS+ + H2 -+ H2S+ + H 2 E- 10 0 6380 2 E- 10 HS+ + H2 -+ H3S+ 2.4E-16 -0.8 0 3.2E-19 HS+ + O -+ SO+ + H 2.9E-10 0 0 2.9E-10 HS+ + O -• S+ + OH 2.9E-10 0 0 2.9E-10 HS+ + H20 -• H30 + + S 7.8E-10 0 0 7.8E-10 HS+ + S -• S+ + HS 9.7E-10 0 0 9.7E-10 H2S+ + H -• HS+ + H2 2E-10 0 0 2E-10 H2S+ + H2 -+ H3S+ + H 6E-10 0 2900 6E-10 H2S+ + O -• HS+ + OH 3.1E-10 0 0 3.1E-10 H2S+ + O -• SO+ + H2 3.1E-10 0 0 3.1E-10 H2S + + H20 -• tt30 + + HS 8.1E-10 0 0 8.1E-10 H3S+ + H -+ H2S+ + H2 6E-11 0 0 6E-11 S2H+ + H2S -+ H3S+ + S2 2.9E-10 0 0 2.9E-10 HSO•+ + H20-• H30+ + SO2 2.13E-9 0 0 2.13E-9 Data are from Millar et al. [1991].Read 2E-20 as 2x10-2ø. Ratesare in cm 3 s-1 . * Newman et al. [1982]. • Massey and Gilbody[1974]. $ Stebbingset al. [1964]. õ Banks and Kockarts[1973]. ô Fehsen]eldet al. [1967]. II Schmidtet al. [1988].

TABLE 6. Steady State Densities of the Torus Model Case a Case b Case c Case d Case e DE, R• s-• 4 x 10-4 4 x 10-4 4 x 10-4 4 x 10-4 2 x 10-4

Io's source strength,amu/s 6 x 1029 6 x 1029 3 x 1029 1.2 x 103o 6 x 1029

Energetic particles flux, cm-2 s-1 6 x 108 1.2 X 109 6 x 108 6 x 108 6 x 108

Neutral Species H 13.6 (0) 20 (0) 20 (0) 10 (0) 9.6 (0) H2 0.4 (0) 0.6 (0) 0.5 (0) 0.3 (0) 0.3 (0) O 5 (0) 7.4 (0) 7 (0) 3.5 (0) 3.3 (0) 02 1.5 (0) 2.4 (0) 2 (0) 1 (0) 1 (0) OH 1.3 (0) 2 (0) 1.6 (0) I (0) 0.9 (0) H20 1.3 (0) 2 (0) 1.6 (0) 1 (0) I (0)

Major Ion Species H+ 3.5 (1.3) 4.7 (1.3) 2.4 (0.7) 5.8 (2.6) 9 (2.6) O+ 15 (12.6) 16 (12.6) 8.3 (6.4) 27 (24) 28 (23) 0 ++ 17.1 (16.9) 17.1 (16.9) 8.4 (8.4) 34.9 (34.7) 37.5 (36.3) O2+ 0.3(0) 0.5(0) 0.2(0) 0.4(0) 0.8(0) OH+ 0.2 (0) 0.4 (0) 0.2 (0) 0.4 (0) 0.7 (0) H20+ 0.2 (0) 0.3 (0) 0.2 (0) 0.3 (0) 0.5 (0) S+ 0.6 (0.6) 0.6 (0.6) 0.3 (0.3) 1 (1) 0.8 (0.9) S++ 5 (5) 5 (5) 2.5 (2.6) 9.7 (9.8) 9 (9) S3+ 2.3 (2.3) 2.3 (2.3) 1 (1) 5 (5) 6 (6) Na+ 1.3 (1.3) 1.3 (1.3) 0.7 (0.7) 2.6 (2.6) 2.6 (2.6)

Minor Ion Species H+ 0.06(0) 0.09(0) 0.05(0) 0.07(0) 0.13(0) H} 5.10-• (0) 1.10-s (0) 5.10-• (0) 4-10-• (0) 2.10-s (0) H30+ 1-10 -4 (0) 3-10 -4 (0) 1.10 -4 (0) 1.10 -4 (0) 3.10 -4 (0) 02H + 4.10 -5 (0) 1.10 -4 (0) 5.10 -5 (0) 4.10 -5 (0) 1.10 -4 (0) SO+ 4.10 -5 (0) 7.10 -5 (0) 3.10 -5 (0) 6.10 -5 (0) 8.10 -5 (0) HS+ 2.10 -6 (0) 3.10 -6 (0) 2.10 -6 (0) 3.10 -6 (0) 4.10 -6 (0) Ne- 75 (70) 78 (70) 40 (36) 145 (137) 156 (140) Nion 45 (40) 48 (40) 24 (20) 87 (80) 95 (80)

Europa's source strength,ions/s 2 X 1027(0) 3.4X 1027(0) 1.7X 1027(0) 3 X 1027(0) 3 X 1027(0) Densitiesare in cm-3. Case a, normal parameterscharacteristic of Europa'senvironment. Case b, enlarged energetic particle flux. Case c, reduced iogenic corotating flux. Case d, enlarged iogenic corotating flux. Case e, reduced transport rate. The number densities for the case of no Europa are given in parentheses. 21,240 SCHREIERET AL.: MODELINGTHE EUROPAPLASMA TORUS presentingthe measuredquantity versusthe incident energy of the electronsor ions, as in Kieffer [1969],and if two or Europa I 1.7% more different sets of Arrhenius' coefficientswere given, we Io oxygen 68.0% chosethe most recentof them. Miller et el. [1991]summa- rized rate coefficientsof 2880 gas-phase reactions among 313 speciesinvolving 12 elementsfor use in astrochemical models; part of this data was used in our model. Equations(1) weresolved numerically by startingwith an Io sulfur 20.3% empty magnetosphere,turning on the sourcesand sinksand and alkalis integratingthe equationsover time until (after some50-100 Fig. 4. Calculated composition distribution at Europa's orbit days) the numberdensity of all the speciesreached steady for case a. state. For comparison,we run the model with no Europa source to determine what the plasma conditions would be al ions is the same; a Europa sourcecauses the total density without Europa. to increasefrom ,,, 40 to ,,, 50 cm-3 due to the enhancement of the water group ion plasmafrom Europa. Thus the con- RESULTS AND DISCUSSION tribution of Europa, while insignificantin comparisonwith The steady state densitiescalculated for varioustransport the Io torus source,nonetheless affects the plasma composi- rates, iogeniccorotating flux and energeticparticle flux are tion locally. This is consistentwith the resultsof Be9enel et shown in Table 6. In order to study the sensitivity of the el. [1992],which show that oxygento sulfurratio increases model to the input parameters,five differentsets of input pa- outside the hot torus, consistentwith a Europa source. rameters were used. Parameters characteristic of Europa's During the parameter study the following results were environment are presentedas case e. In case b the energet- found: ic particle flux was enlargedby a factor of 2. The iogenic 1. Photo-sputtering is an insignificant process. It con- corotating flux was multiplied and divided by 2 in casesc tributes at most one half of one percent to the number den- and d, respectively. The influence of the transport rate was sityof certainspecies such as OH andOH + . examinedby reducingit by half in case e. For each set of 2. Elimination of the atomic processesoccurring in the results the number densities which result if there were no Europa torus increasesthe neutral cloud of water fragments Europa sourceare given in parentheses. by two orders of magnitude, leaving the ion densities and Pickup oxygenions at 9.4 Rs would fill a shell in phase partitioning almost unchanged. spaceat m 874 eV and would not be resolvedin the PLS 3. A changein the energeticparticle flux causesonly a spectra. Spectra not near the magnetic equator have low slight changein the water-groupneutral and ion number count rates with no distinct current peaks indicative of a densities. It does however affect Europa's source strength tenuous,hot plasma. During equator crossings,additional sincethe sputtering rate is also changed.This is due to the well resolvedMaxwellian spectra are observed,as shownin overwhelmingeffect of the transport. the spectra in Figures 2e and 2b. The common cold tem- 4. Changing the Io's sourcestrength by a factor of two perature of theseions and the presenceof high- ionization leads to almost similar changesin the number densitiesand states and alkali ions are consistentwith transport from the to a smaller effect in Europa's sourcestrength. Io's orbit over a timescalelong enoughfor thermahzationto 5. An increase(decrease) in the transport rate is al- occur.(We note that the questionof whetherplasma trans- most equivalentto a decrease(increase) in the Io's source port from Io outwardis adiabaticor whether heatingoccurs strength. remainsan outstandingissue [Abe end Nishide,1986].) The Sievekeend Johnson[1982] computed the Europasource need, dictated by the shapeof the spectrum,to place an ion rateto be 8 x 1026s -• , aswas previously estimated by John- between those of mass-to-chargeratios of 16 and 23 raises son et el. [1981]. Our model, which includessputtering thequestion whether it is a localwater group ion, H20 + or causedby both corotating iogenicthermal plasmaions and OH + or anotherion suchas doublyionized potassium. The radiation belt particles, givesa sourcestrength ,,, 2.5 times resolutionof the PLS instrument along with the possibility greater. The sputteringyields usedhere for perpendicular of nonzero spacecraftpotential, does not allow us to differ- incidenceto the surface[Johnson et el., 1989]. The yields entiate uniquely betweenadjacent values of mass-to-charge (and thusthe sourcestrength) are enhancedfor nonnormal ratiossuch as 17, 18, and 19•• whichmight be ascribedto incidence. OH+, H20+, and K++ respectively.We referthe readerto Particles originating at Europa diffuse inward as well as the companionpaper by McNutt [thisissue] for the physical outward, and it is of interest to ask if they can make a considerationsof why this peak should be associatedwith significantcontribution to the resolutionof the Io energy doubly ionized potassium. crisisdiscussed by Shemensky[1988] and by Smith et el. Our calculated values of the parameters which are char- [1988].If the pickupenergy is 1 keV andthe sourcestrength acteristic of Europa's environment are presented as case e is as given in Table 6, the power added to the Io torus, of Table 6 and as shown in Figure 4. An interesting re- includingadiabatic heating, would be ,,, 3 x 10•2Wif all suit of the model comesfrom the comparisonbetween the particlesreaches the torus. In fact, only 10% of them will number densities of the ions with and without Europa. A diffuseinward, so Europa will not greatly affect the energy neutral cloudof water fragmentswith a densitygreater than balance of the Io torus. 20 moleculesper cm3, noneof whichwould exist without the The degreeof ionization in the plasma can be obtained sputteringprocess, is immersedin the torus plasma. With or by dividingthe total ion numberdensity by the total charge without Europa source,the density of sulfur and alkali met- (electron)density. Typical valuesfor the warm and cold SCHREIERET AL.' MODELING THE EUROPA PLASMA TORUS 21,241

Io tori are ,-, 4/3. The degreeof ionizationincreases to stituents. If we bear in mind that the creation of most 5/3 in the outer regionsof the warm torus, which may be O++ takesplace in the outerreaches of the Io torus,where understood in light of the local enhancementof suprather- suprathermalelectrons were observed [McNutt et al. 1990], mal electron flux in this region as reported by McNutt et al. we can explain the nonsimilarity in the sulfur and oxygen [1990]. abundancereported by Bagenalet al. [1992]. As might be expected, the results are sensitive to the If we ignore Europa's contribution to the plasma en- transport rate and plasma temperature. Early estimates vironment we are led to a picture contrary to observa- lEviafar et al., 1985]predicted that there wouldbe no Eu- tion. We must therefore conclude that Europa's surface ropa torus becausethe ions would be swept away in the rapid is sputtered by iogenic matter and is, therefore, a source outwash of the Io matter. Reducing the transport rate from of magnetosphericplasma. If there were no effective Eu- 4 x 10-4 /•j2 s-1 to 2 x 10-4 /•j2 s-1 (casee), increasesthe ropa source, no intensification would have be observed in total numberdensity to • 100cm -3, whichcontradicts ob- the abundance of oxygen ions and their profile would re- servations.A highertransport rate (8 x 10-4 /•j2 s-l) re- semble that of iogenic sulfur. The survival of eurogenic wa- ducesthe total numberdensity (which includes the iogenic ter group ions will depend on the transport rate. We have ions)to • 20 cm-3, muchless than the observedvalues. shown that the transport rate at Europa orbit must satisfy Since the source strength and diffusion rate are both obser- 5 x 10-6 < 1/r < 2 x 10-5 s-• in orderthat densitiescom- vationlyconstrained (determined by Io torus) the calculated parable to those observed be derived by the model. This densities appear quite reasonable. rate is not consistent with L 3 diffusion and the observed Onemight ask why the ratio of H30+ to H•O+ is aslow transportrate at Io. Siscoeet al. [1981]point out that the as 5 X 10-4 whereasin a cometarycoma H30 + is the most strong gradient in flux tube content on the outside ledge of abundant ion within 20,000 km of the nucleus[Balsiger, the warm torus implies the diffusionexponent is as large as 1990]. The main reactionswith whichHsO + is involved 12. Thorne[1983] shows that this valueof the exponentfits andtheir rate coefficients(in unitsof cms s -•) are the Armstronget al. [1981]observations of the intermediate H20 + + H20 -• H30 + + OH k = 2.1 x 10-9 energyparticles (magnetic moment of 70 MeV/G) very wen. Although Europa's contribution to the total plasma content H30+ + e- -• OH + H + H 7i = 2.05x 10-s is small compared to that of the Io torus, it has an effect on H30++e- -•H•O+H 72-1.1 x10 -s the local plasma composition. From the model, we estimate H30++e- -•OH+H• 73-7.4x10 -9 (4) Europa'ssource strength as 2 x 10•7 moleculesper second (casea). For a Europacollision frequency of c = 2.4 x 10-s s-• and Httangand Siscoe[1987] have classified Europa's torus as a transportrate of œ = 1 x 10-5 s-• the rate equation heterogenicand heterotropic, that is, generated by sputter- ing from an external source with a transport mechanism externally imposed. We have demonstrated that the strong dnH3ø+dt = kx nil2o x diffusion induced by the iogenic plasma inhibits the growth of the Europa torus and prevents it from reaching densi- [1T +c + + + x x ties comparable to those of the Io torus. In the absenceof a strong Io source, the transport rate would be lower, and gives for steady state the ratio: would result in a denser and larger Europa torus. Trans- •H30+ _ k X •H20 port might then become autotropic, that is, self-driven and self-limiting. - + + x + +c) 2X lø-' Had the SWICS instrumentof Ulysses[Geiss et al., 1992] where the electron and the neutral water densities are 75 been operative at the equatorial plane, it might have differ- and 1.3 cm-3, respectively,according to the resultsof case entiated iogenic potassium ions from lighter Europan water a. Despite the neglect of atomic interaction with the oth- group ions. Since the scale height of pickup water ions is er ions and neutral species, this value is close to the model much larger than that of cold iogenicpotassium (6.7 R• ratio, whichindicates that reactions(4) are the mostsignif- comparedto 0.33 R•), any intermediateA/Z ions detect- icant processesin the plasma.This insignificanceof H30+ ed by Ulysses far from the plane will be associated with (in contrastto cometarycomea) is a resultof the largedisso- the presence of the Europa plasma source. Indeed, a ten- ciative recombination rate and the low abundance of neutral tative identification of water group ions is made by Geiss water molecules. et al. [1992]on the basisof preliminaryUlysses data anal- ysis. Further analysis of data from Ulysses and from the CONCLUSIONS forthcoming Galileo encounteris expected to provide an ul- Matter sputtered off the surface of Europa differs in com- timate resolution of this question. We expect the Galileo position and energy spectrumfrom Io torus matter. If ion- spacecraft to find, either by means of observation of UV ized by electron impact ionization near Europa, molecular emission or by using a mass spectrometer, a neutral cloud ions will have very broad energy spectra and thus should be of hydrogen,oxygen, and water moleculesat the orbit of Eu- distinguishablefrom the cold matter that has diffused out ropa. The plasma instrument will measure a small increase from the Io torus. Both P LS spectra and the model results of • 10% in the local numberdensity (attributed mostly showa partitioningof ,-, 40 (cold)ions per cm 3 of Io origin to water group ions) and a small reductionin the ioniza- and5-10 (warm) ions per cm 3, presumablyof Europaorigin. tion state at that location. A residual Europa atmosphere We have shown that a Europa source results in an en- is a mostspeculative idea but certainlyworth examining(by hancement of the total abundance of oxygen-bearing con- occultationtechniques). 21,242 SCHREIER ET AL.: MODELING THE EUROPA PLASMA TORUS

APPENDIX: RELATION OF TRANSPORT AND SOURCE where • is the value of n averagedover the interval --Ar < TERMS TO THE DIFFUSION COEFFICIENT x < At. The value of C2 is fixed by matching(A4) to Equations(1) in the text are formulatedin terms of the solutionsof the diffusion equation in the external region r > total content N of the various specieswithin the volume V rE + At. Since there are no sourcesin this region, $, which of the Europa torus. Plasma flow into and out of the volume is givenby (AS) is constantand mustbe equalto Sourwhich is represented by the diffusion term is givenby (A7). For D givenby (A2) the solutionfor n in the region r > rE is: )] = where D is the diffusion coefficient assumed, for simplicity, n(r) •-- 2•.DESo., h log (•) v = 3 to vary as a power law in the radial distance r, - (A9) whereR is the distanceat whichn = 0. Equatingn(r•) to where DE and rE are the values at the orbit of Europa, n • givesC2; to lowestorder in •, theresult is is the equatorialnumber density (related to N of equation 1 DE (•) •y • = t•/V), n i• • •½• •i• of • •o• •o• the magneticfield and • • r -3 is the equatorialmagnetic ; = 2rEAr•. (A10) field strength. We wish to appro•mate the term (A1) by where the simpleforms of equation(1), I for plasmainput from the Io torusand -N/• for plasmaloss.

Eoal•atio• of • and the factor • may be regarded as of order unity. The We consider first only the contribution of plasma from value of e must be assumed to be very small; the flux Sin within the volume of the Europa torus, r• -•r < r < of Europa-generated plasma is also constant for r < rE r• +•r. We define• • r- r• and write (in the steady and hence equal to its value at r = 6 R j, but for r < 6 R.• state •mit) diffusionis generally assumedto be extremely weak. Evaluation of I We now consideronly the contribution of plasmacoming from the Io torus. With all the Europa-related and non- where • represents aH the local nontransport source and transportterms neglected, equation (1) in the steadystate lossterms of equation(1) and •r << r• has been usedto limit can be reduced to: neglectaH variationof D, r, • and • in (A1). Equation (A3) has the solution I n V = --r (A12) - + ß+ where n is to be taken as the density at r = rE produced by diffusionfrom an Io sourceof strength S and r is defined by where C• and C• are integration constants.The total diffu- (AS). The valueof n is now givenby a solutionidentical to sive flux at a given distance r is given by (A9) exceptfor the replacementof Sourby S:

S = -2•rBD• n(rE)= 2•rDEhS / •r dx x •_• (A13) and the di•erence between the values of S at r = r + •r Combining(A13) with (AS) and recognizingthat the same determinesC•; from (A4) we obt•n the followingrelations: integral occurs in both, we obtain I S Sou, = 2•R•QAr - C* = V = 4•rrEhAr(1- e) (A14) where C* = 2•'rEDECi. If we define e as the ratio of inward For reasonsalready stated, e may be neglected. to total flux, -Sin Acknowledgments.The work at Tel Aviv Universitywas sup- Sour-- Sin' ported in part during the initial stages by the United States- Israel Binational Science Foundation under grant 88-00120 and in then equation(A6) becomes the latter stages by the German-Israeli Foundation for Scientific Research and Development under grant 1-0199-163.07/91. The work at the Max-Planck Institut ffir Aeronomie was supported SinSour = 2•rrEQAr(2--e2•rrEQAr e) (A7) in part by the German-Israeli Foundation for Scientific Research and Development under the same grant. The MIT portion of this The loss time r is evidently defined by work was supported by NASA under contract 959203 from the Jet Propulsion Laboratory to the MassachusettsInstitute of Technol- ogy and by NASA grant NAGW 1622. The work at UCLA was supported by the National Aeronautics and Space Administration Qr = •C2 -- •.D••-9-(Ar) 2 (A8)under grant NAGW-87. Aharon F,viatar expresseshis apprecia- SCHREIER ET AL.: MODELING THE EUROPA PLASMA TORUS 21,243 tion for the hospitality of the Department of Atmospheric Sciences L.J. Lanzerotti, and E.M. Sieveka, The neutral cloud and heavy of UCLA during the summer of 1992. Ron Schreieracknowledges ion inner torus at Saturn, Icarus, 77, 311-329, 1989. helpful discussionswith Amiel Sternberg. We are grateful to T. Kieffer, L.J., Low-energy electron-collisioncross-section data, I, J. Millar for allowing us to use the UMIST ratefile and to Ralph Ionization, dissociation, vibrational excitation, At. Data, 1, L. 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