JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 86, NO. All, PAGES 8906-8918, OCTOBER 1, 1981
EnergeticOxygenand Sulfur in the Jovian Magnetosphere
N.
GEHRELS
AND
E. C. STONE
CaliforniaInstituteof Technology,Pasadena,California91125
J. H.
TRAINOR
GoddardSpaceFlight Center,Greenbelt,Maryland 20771
This paper reportsmeasurements
made by the cosmicray subsystemonboardVoyager I and 2 in the
Jovianmagnetosphere.
Energyspectraof oxygenionsin the energyrange 1-20 MeV/nuc between5 and
20 Rj are presentedand usedto calculatephasespacedensities.There is a steeppositiveradial gradient
in the phasespacedensityof the energeticoxygenionsin thisregion,indicatingan inwarddiffusiveflow.
Solutionsof the diffusionequationassuminga diffusioncoefficientD and losslifetime T of the formsD -DoLn and T -- ToLm, where Do, To,n, and rn are constants,and L is the McIlwain parameter,are fit to the
radial phasespacedensityprofile of oxygenions with magneticmomentsof 680 MeV/nuc-G. The best
fits are found to have n + rn = 6 and 3 < n < 6. On the basisof the diffusioncoefficientupper limit obtained from thesefits, the upper limit on the rate at which oxygenions with >400 MeV/nuc-G diffuse
inwardacross10Rj is 5 x 102•ñ•ionss-•. The observations
suggest
thatoxygenandsulfurionsin the Io
plasmatorusdiffuseradiallyoutward,are nonadiabatically
accelerated
in someregionoutside17 Rj and
then diffuseinward and outward from the accelerationregion.
PARTICLE
INTRODUCTION
Observationsmade in the Jovian magnetosphereof nuclei
with charge greater than 2 and energiesbetween 7 and 14
MeV per nudeon (MeV/nuc) [l/ogt et al., 1979a, b] have
shownthat, beyond •25 Jovianradii (R•), the elementalcompositionis similarto that of the solarenergeticparticles.In the
inner magnetosphere(•<12 R•), however,the compositionis
drasticallydifferent,dominatedby oxygenand suffurwith sodium alsopresent.Observationsbetween0.60 and 1.15 MeV/
nuc [Hamiltonet al., 1981]showa similarsharpincreasein the
oxygenand suffur abundancesrelative to helium and carbon
inside •20 R•.
The likely sourceof the oxygen, sodium, and suffur is the
Jovian satelliteIo. GaseousSO2 is a major constituentof Io's
atmosphere[Pearl et al., 1979;Kumar, 1979] and is probably
the volatile that drivesIo's volcanism[Smithet al., 1979;Johnsonet al., 1979].Oxygen and sulfur are alsothe dominant speciesat plasmaenergiesin the Io torus [Broadfootet al., 1979;
Sandelet al., 1979;Bagenaland Sullivan, 1981].The evidence
that sodium is associated with Io comes from earth-based
ob-
servationsof neutral sodium optical emission[Brown, 1974;
Brown and Yung, 1976].
Since the ions in the plasma near Io typically have eV/nuc
energies[Bagenaland Sullivan, 1981],an accelerationprocess
is requiredto producethe MeV/nuc ions observed.Measurements of the gradient in the ion densitycan be usedto calculate diffusive flow directionsand can thereby indicate the location of the acceleration site. A preliminary analysisusing
Voyager 2 data between 10 and 13 R• [l/ogt et al., 1979b]determined that there is a positive radial gradient in the phase
spacedensity of the high-energyoxygenions, indicating an
inward diffusiveflow. This observationsuggests
that the accelerationregionis outside13 R•. Only oxygenwas analyzeddue
to statistical considerations.
In the present analysisthis earlier work is extendedto include both Voyager 1 and 2 data between5 and 17 R•. The
observationsare comparedwith variousradial diffusionmodels and are usedto derive limits on the accelerationefficiency.
Copyright¸ 1981 by the American GeophysicalUnion.
Paper number 1A0944.
0148-0227/81/001A-0944501.00
FLUXES
AND
ENERGY
SPECTRA
Data from the cosmicray subsystem(CRS) low-energytelescopes(LETs) [Stone et al., 1977; Stilwell et al., 1979] were
used in this analysis.A schematicdiagram of a LET is shown
in Figure 1. The LET systemconsistsof four suchtelescopes,
LET A, B, C, and D, oriented to allow anisotropymeasurements. LET A and C were turned off inside •20 R• on both
Voyagers to reduce the noise level at the input of the pulseheight analyzerssharedwith LET B and D, respectively.Also,
the LET B and D L4 detectors,normally used in active anticoincidenceagainstpenetratingparticles,were turned off inside •-20 Rj to minimize accidental event rejection in the
high-radiationenvironmentof the inner magnetosphere.The
orientation of the instrumentin this region on both Voyagers
was suchthat LET B pointed approximatelyperpendicularto
the local magnetic field direction when the spacecraftwas
near the magnetic equatorial plane, while LET D was more
nearly field aligned.To simplifythe analysisthat follows,considerationwill be restrictedto particleswith pitch angles of
•90 ø to the field, and thus only LET B will be used. A summary of the proton measurementsmade by the LET systemin
the Jovian magnetosphereis given by Schardtet al. [1981].
The most important feature of the LET for the present
studyisthatit'provides
multiparameter
analysis
of individual
nuclei with MeV/nuc energiesand nuclear charge Z, greater
than 2, with an rmschargeresolutionof 0.1 < Oz< 0.5 charge
units, where the larger values occur during high flux periods.
Since incoming fast ions are strippedof their electronsin the
3-panA1 window of the telescope,no informationis available
about the chargestateof the ions prior to entry. The LET system alsoprovidesmeasurementsof the countingrate of particleswith energylossesEl, E2, and E3 in detectorsL 1, L2, and
L3 suchthat E1 + 0.4E2 + 0.2E3 > 9.6 MeV. Becausethe geometryfactordefinedby the collimatorand L 1 (4.6 cm2 sr) is
muchlargerthanthat definedby L 1 and L2 (0.44cm2 sr),this
rate is primarily that of particleslosingmore than 9.6 MeV in
L 1. It is called the Z > 2 rate sinceneither protonsnor alpha
particleswithin the acceptancecone of the telescopecan lose
as much as 9.6 MeV in a 35-/an silicondetector.Table 1 lists
8906
GEHRELS ET AL.' JOVIAN ENERGETIC
/--AL. FOIL
8907
in the Voyager 2 plot is due to varying distanceof the spacecraft from the magnetic equatorial plane. The peaks at day
190, 1400 UT, 2200-2400 UT, and day 191, 0900 UT are at
times when the spacecraftcrossedthis plane. The fine scale
structurein this flux is not yet understood.The inbound Z • 2
3/zm
THK.
LIGHT
O AND S
BAFFLE
flux is comparedfor the two spacecraftas a functionof radial
•.',•o,x•/•-•
LI,
2.8
cm
zx35•m
distancefrom Jupiter in Figure 3. Inside 18 R•, the Voyager 1
and 2 fluxes were the same to within a factor of ~2. There is
therefore no evidence for major temporal variations in the
heavy ion fluxes in this region between the two encounters,
and in the analysisthat follows, we will considerboth setsof
measurementsto be of the same stablepopulation.
Oxygenenergyspectrahave been calculatedfor the six periods indicatedin Figure 2 and listed in Table 2. Periods2 and
3 for Voyager 1 are each the combinationof inbound and outbound time intervals(a and b) symmetricallyspacedwith re-
/
L2, 2.8 crn•'x
35•rn
L3 4.5 crn
zx 450,u.
rn
,
"L4, 4.5 cmZx
450p.m
LOW
Fig. I.
ENERGY
TELESCOPE
(LET)
Cross-section
of a low-energytelescope(LET). All detectors
are silicon surfaCe-barrier detectors.
spect
to thefluxm'mima
nearIo. These
sixperiod
s arethe
onlyonesin thedatasetinside18R• forwhichtherearea sta-
tistically significantnumber of pulse-heightanalyzed events,
within20ø of Cr•e
plane
the geometryfactorsand the oxygenand sulfur energyranges andfor whichLET B waspointing
for the Z > 2 rate and for event analysis.
perpendicular
tothelocalBfielddirection.
Thislastcriterion
Plots of the livetime-corrected
Z > 2 flux as a function
of
ttrnefor the Voyager1 and 2 encounters
are shownin Figures
2a and 2b, respectively.The livetime correctionsare basedon
the calibrationof a spareCRS instrument(seethe appendix).
Inside 6.5 R•, the Z > 2 flux exhibits minima at L -- 5.6 inbound(day 64, 0934:24:t: 0001:36UT) and 5.4 outbound(day
64, 1406:24+_0001:36UT), wherethe McIlwain parameterL
is taken to be the zenocentricdistanceof the spacecraftin
units of R• at these minima. The difference between these L
values and the actual L values at the minima, owing to the
spacecraftdipole latitude (~5 ø) and the dipole offset,is less
than ~0.1. The locations of the observed minima indicate that
the particle lossesfrom the observedenergyrange are caused
by the Io plasma torus rather than Io itself since measurements of the plasma in the torus showedsharp decreasesin
plasma densityjust inside the peak densitiesat L -- 5.7 inbound (peak #2 at day 64, 0924 UT) and 5.6 outbound(day
64, 1420UT) [Bagenaland Sullivan,1981],whereasIo is never
inside L -- 5.8. Also, it was observedon the Voyager 1 inbound passthat the electromagneticwave activity associated
with the torusstoppedabruptly at ~5.6 R• [Scarf et al., 1979].
This abrupt decreaseof the wave activity inside ~5.6 R• may
be the direct cause of the inbound particle flux minimum
sincethe particle lossesare likely due to wave-particle interactions. Note that minirna in flux measurements
above a fixed
energythresholddo not necessarilycorrespondto m'mimain
the phase spacedensitiesof the particles.As will be shown,
the flux minima near Io correspondto a changein the radial
gradient rather than a minimum in the phase spacedensity
profile. The two decreases
at ~9.4 R• inboundand outbound
were causedby Europa. In contrast,the large scale structure
TABLE
1.
simplifies
the phasespacedensityanalysisthat follows.
A plot of all three-detectorevents(L 1 ßL2' L3) which were
pulse-heightanalyzed by LET B in regions 1, 2, and 3 is
shownin Figure4. The two trackson the plot are dueto oxygen and suffureventsthat penetratedL 1 and L2 and Stopped
in L3. The eventsalong the left edge of the plot are predominantly oxygen and suffur eventsthat penetrated L 1 and
stoppedin L2 and, in addition, had a small pulse in L3, most
likely due to an accidentally coincident proton (or several
electrons).Theseeventsare identifiedby the tracksthey produced on an E1 versusE2 plot. In general,different livetime
correctionswere required for the different types of events,as
discussedin the appendix.
The differential energy spectraof the oxygen events in regions2 and 4 are shownin Figure 5. A striking feature in the
region 2 spectrumis the peak at ~5.5 MeV/nuc. In order to
extend thesespectrato lower energies,we convert to integral
spectraand add a point at ~ 1.2 MeV/nuc (energy of particle
incident on the telescopewindow) calculated from the Z • 2
rate. Since the Z • 2 rate is made up of both oxygen and sulfur (and tracesof other elements)in the inner magnetosphere,
one must measureor estimatethe suffur to oxygenratio in order to obtain an integral flux of either speciesalone. In regions 1, 2, and 3, a pulse-heighthistogramfrom the L1 detector reveals two distinct maxima as shown in Figure 6. The
maximum at ~30 MeV can be understoodas the energy loss
of 5-6 MeV/nuc oxygen ions penetrating the detector. This
identificationis reasonablesincethe differentialoxygenspectrum is peakedat ~6 MeV/nuc. Similarly, a differential suffur
spectrumpeakedat ~5 MeV/nuc would producethe feature
at~ 110MeV.Therefore,
inthese
regions,
thesulfurtooxygen
Nominal
GeometryFactor,*cm2sr
Z > 2 rate
4.6
LET
Parameters
Element
Oxygen
Sulfur
Event analysis
(L 1 ßL2)
0.44
Oxygen
Sulfur
EnergyRange,•'Mev/nuc
1.1--•25.
0.9-~
120.
3.6-~23.
4.5-~50.
* Each of four telescopes.
'• Energy lossin the 3-•m Al window (seeFigure 1) has been added to the detectorthresholdto give
the incident energyof the particle.
8908
GEHRELS ET AL.: JOVIAN ENERGETIC
dOVIAN
16
i
_
i
14
i
12
i
i
i
I0
i
!
6
8
RADII
6
4.89
i
i
O AND S
i
I
8
i
i
i
i
I0
i
i
12
i
i
14
i
i
16
I
i
18
i
(o)
VOYAGER
1
8
i
i
:3a
i
i
2a
I
i
2b
!
3b
DAY 64
JOVIAN
16
18
i
i
14
,
i
12
i
!
65
RADII
II
10.5
I0.11
i
,
i
10.5
,
_ (b)
II
12
i
14
,
VOYAGER
i
2
.--8
6
5
4
I
i
0
6
12
DAY 190
18
0
6
12_
DAY 191
Fig. 2. Livetime-corrected
Z > 2 flux (seeTable l) for (a) Voyager1 and (b) Voyager2 closestapproach.The day
number meansday of year 1979.The numberedtime intervalsrefer to regionsin which oxygenspectrahave been calculated (Table 2). Note that the vertical scaleis linear.
ratio in the Z > 2 rate can be directlydetermined.In regions
4, 5, and 6, the L1 pulseheighthistograms
do not have separate oxygenand sulfurmaxima,so the ratio cannotbe measureddirectly.In theseregionsthe ratio wasestimatedusing
L1 ßL2 data.Table 3 liststhe valuesof the oxygenfractionof
The oxygenintegralenergyspectrain regions2 and 4, ineludingthe Z > 2 points,are shownin Figure 7. The fiatteningof the spectrumin region2 below •5.5 MeV/nuc correspondsto the decreasein differentialintensityseen in
Figure 5. The spectrumremainsfiat between3.5 and 1.4
the Z > 2 rate usedfor the different regions.Note that, since MeV/nuc, which implies that in this interval the differential
the oxygenand sulfur energythresholdsfor this rate are dif- intensity remains below the peak value of ~300 (cm2 sr s
ferent, the numbersare not equal energy-per-nucleonabun- MeV/nuc)-'. A likely causeof this flatteningin the integral
dance
fractions.
Theexact
oxygen
threshold
energy
fortheZ spectrumis that particle lossmechanismsnear Io are more ef> 2 rate must also be determined in order to use the Z > 2 ficient for lower energy particles. Pioneer 10 observations
flux as a point in the integral spectrum.The threshold level showedsuch a preferential lossof lower energyprotonsnear
varies between 1.1 and 1.4 MeV/nuc due to discriminator
Io between1 and 20 MeV [Trainor et al., 1974].To usethe two
thresholdshiftscausedby high flux levels,and was measured spectrapresentedin this section,as well as spectrafrom other
during the calibrationof the spareCRS instrument(seethe regions,for gradient and flow direction determinations,and
appendix).The resultsare listed for each region in Table 3.
thus restrictthe region where the energeticions are acceler-
GEHRELSET AL.: JOVIANENERGETICO AND $
I
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8909
Sinceparticleenergies
changein the diffusion
process,
the
radialdiffusion
theorydealswith particlephasespaceden-
1
INBOUND
sitiesat constantfirst adiabaticinvariant rather than three-diVoyager I
mensional
spacedensities
at constant
energy.The radialdiffusion equation is
Voyager:> -
Ot=L2
•0(D
•-••Of)
+ •C•'(L)
- •'(L)
Of
(1)
where f is the phasespacedensityat a particular M, D is the
diffusioncoefficient,L is the Mcllwain parameter,and •C•(L)
and •(L) representlocal sourcesand s•ks, respectively.
Equation (1) can be used•th measurementsof the gradient
of f to obta• quantitative •fomation about d•usive flows
and pa•icle losses.We therefore calculate the phase space
densitiesof the energeticoxygen ions from the measured •tensities.
The d•erential •tensity j and the •tegral •tensity J are
related to the phasespacedensityf by
f•,L,.):J"(•[
L)= p•1dj.(E,
dEL)
(2)
whereE is the k•etic energy.Specia•g to the a = 90ø case
andchang•g va•ablesfromE andp to M givestheequation
f(M,L,• = 90ø)= y(M,
L) Jx(M,
L)
2m•
B•(L)
I0
15
20
(3)
25
where• = -[d log(JD/d log(•]. Therefore,at a givenvalue
of M, the change• phasespacedensitybetweentwo radial
tionsof spacecraft
distance
fromJupiter,inbound.
Thetriangles
in- positionsL• and L: can be directlydetem•ed by measuredicatemagneticequatorialcrossings.
mentsof the magneticfield strength,the •tegral •tensity,
dovion [•odii
Fig. 3. Voyager I and 2 livetime correctedZ > 2 fluxesas func-
and the slopeof the •tegral •tensity at M:
ated,it is usefulto relatethe intensitymeasurements
to a dif-
f(M, L9
fusion theory.
•(M, L9 J•(M, L9/•:(L9
f(M,L••= T(M,
L•) Jx(M,
LO/B•(LO (4)
COMPARISON OF SPECTRA AND GRADIENT
If spectral•fomation is not available, it is often assumed
DETERMINATION
that•(M, L•) = •(M, L:). Asisshownbelow,thisassumption
The radial diffusiontheorythat will be adoptedfor the is not valid • the presentcase.The •'s for measurements
at
presentanalysisassumes
that particlesconservetheir firstand adjacentradialpositions
wffitypicallydifferby a factorof 2,
secondadiabatic invariants but not their third in the diffusion sothatorderof magnitude
est•ates of thephasespacedenprocess
[seee.g.,SchulzandLanzerotti,1974].Conservation
of sitygradientcanbe madeby us•g Jx/B•, whiledetailedstudthe firstinvariantor magneticmoment,M -- pff/2mB where ies requireus•g (4).
rnistheparticlemass,
B isthemagnetic
fieldstrength,
andpi
In Figure 8, Jx/B • is plottedas a functionof M at ten difis themomentum
perpendicular
to theB fielddirection,
gives ferentradial positions• the magnetosphere.
AH measurea linearscalingof energywith magnetic
fieldstrength,
E -- mentsweremadeat or nearmagnetic
equato•alcross•gsand
MB (nonrelativistic),
for thespecial
caseof mirroringparticles aH thoseexceptthe 7.6 and 20.0 Rj po•ts weremadewith
(pitchangle,a -- 90ø).For theseparticles,
p -- p• andthesec- LET B po•t•g with• 20ø of the planepe•endicularto the
ondadiabaticinvariant,whichis theintegralof theparticle's magneticfielddkection.Magneticequato•alcross•gswere
momentum
alongtheguidingfieldline,is identically
zerofor ident•edbyus•g B fieldmagnitude
anddkection
data[Ness
particles
mirroringat themagnetic
equatorial
plane.
et al., 1979a,b; N. F. Nesset al., p•vate co•unication,
TABLE2. Region
Definitions
andMagnetic
FieldValues
Usedin Spectral
Analysis
Region
Time
RadialInterval,Rj
I
2a
64/1106-64/1235
64/0936-64/1106
5.01-4.92
5.59-5.01
2b
64/1235-64/1405
4.92-5.36
3a
64/0842-64/0936
6.11-5.59
3b
64/1405-64/1443
5.36-5.68
4
5
6
190/2208-191/0136
190/1235-190/1450
190/0237-190/0514
10.12-10.40
12.60-11.65
17.77-16.31
TypicalDistance,
Rj TypicalB Field,*G
5.0
5.2
3.3 x 10-2
2.8 x 10-2
5.7
2.1 x 10-2
10.2
12.1
17.2
3.3 X 10-3
1.8X 10-3
6.0 X 10-4
* Magnetic
fieldvalues
fromN. F. Ness(private
communication,
1980).
8910
GEHRELS ET AL.: JOVIAN
200'
O AND S
creasingradial distanceout to at least 17 Rj, indicatinga positive radial gradientin the phasespacedensityin this region.
The Pioneer 10 and 11 points in Figure 8 are from the University of Chicago fissioncell detector [Simpsonet al., 1974,
1975]assumingthat its responseat L = 3.4 (Pioneer 10) and L
= 1.9 (Pioneer 11) wasdominatedby oxygennucleiof E > 75
REGIONS
1+2+3
.
ENERGETIC
MeV/nuc.Although
thedetector
wasprimarily
designed
to
measureproton fluxesin the presenceof high fluxesof energeticelectrons,it is alsosensitiveto nuclei with Z > 1. Signal
50- •"-:•• * ß '
characteristics
inside10Rj andcomparison
Withotherdetec-
'
o
0
I00
2•
300
400
500
600
•3 (MeV)
•cgio• 1 + 2 + 3 •oyagc• 1, •
•) fo• cac• pulse•cigM a•alyzcd
tor measurementsat 1.9 Rj were inconsistentwith a proton
dominated response,leading Simpsonet al. [1974, 1975] to
suggestthat energeticZ > 1 nuclei were contributingto the
fission cell measurementsin these regions. This suggestion
cannot be investigatedquantitatively by using CRS data,
sincethe observations
were made at differenttimes,but Fig-
ure 8 doesindicate that it is reasonableto interpret the measurement as oxygen. If the fission cell was respondingpredominantly to oxygen, and if energetic oxygen fluxes were
similar at all encounters,then there is little if any gradient in
1980].The 7.6 and 20.0 Rj pointswere obtainedwith LET B the phasespacedensityat •710 MeV/nuc-G between5.0 and
pointing •30 ø from the plane perpendicularto the magnetic 3.4 Rj. There is a gradient at ~ 130 MeV/nuc-G between 5.0
and 1.9 Rj, which is not surprisingconsideringthe absorption
field direction and are therefore not accurate measures of J,.
effect of Amalthea (2.5 Rj) on inwardly diffusingparticles.A
(If the fluxvariesin pitchangleassin4aasis thecasefor protons and electrons with E > 21 MeV between 5 and 12 Rj further analysisof the fissioncell data in light of the Voyager
[I/an Allen et al., 1974],then Jx at 7.6 and 20.0Rj wouldbe a findingscould provideusefulinformation about energeticoxfactor •2 higher than that plotted in Figure 8.) It is clear in ygen fluxesin the 1.6- to 4.9-Rj region where no other space-
t•at•g •2 (•d •1) •d stopp•g• •3. •vcntsin •c bottom
Figure8 that at a givenM, Jx/B2 increases
rapidlywith in-
craft has been.
In order to calculate the radial dependenceof the phase
spacedensityat constantmagneticmoment,Jx/B• wasdeterI
I
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I II
I
i
I
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I i I /I
mined
as a function
of L for discrete values of M from the
_
Oxygen
-
i0 a
spectrain Figure 8, and is shownfor a few representativevaluesin Figure 9. Sinceall measurements
were madenear magnetic equatorialplane crossings,
the L usedin this paper is defined to be equal to the radial distancein Rj. (TheseL values
may differ from the actual L valuesby up to ~0.1 due to the
dipoleoffset.)The data in Figure9 indicatea stee• outward
gradientin Jx/B•. In addition,althoughno singleconstantM
c-
I000
,
i
....
0
•
+
I0
_
REGIONS
1+2+3
S
500
ß
REGION
FLI
2
ß.-,5.2 R,•
A
REGION
4
ß-, 10.;:'R,•
dd
!
I
[
E-6.o
I ! II[
I
I0
0
I
!
[ ! ! I I
o
•
1
i
,
i
•
E1
i
200
(MeV)
I02
Fig. 6. Pulse-heighthistogramof the LI detectorin regionsI + 2
+ 3. The maxima correspondto oxygenand sulfur as shown. Since
Fig. 5. Differentialenergyspectraof oxygenionsin regions2 and only thoseeventssatisfyingthe equationE1 + 0.4E2 + 0.2E3 > 9.6
E (MeV/nuc)
4. A powerlaw of exponent6.0 is shownfor comparison
with the MeV havebeenplotted,the sharpdecrease
in the oxygenmaximum
measureddata in region4. It doesnot representa fit to the data.
below-•20 MeV is probablya thresholdeffect.
GEHRELS ET AL.: JOVIAN
TABLE
3.
Livetime
ENERGETIC
Corrections
O AND S
8911
for the Z > 2 Rate
Effective Oxygen Z > 2
Region MeasuredZ > 2 Rate,s-I
Oxygen Fraction
CorrectionFactor* Threshold,•MeV/nu½
of Z > 2 Rate•
1.2 x 104
1.0 x 104
1.3
1.2
1.4
1.4
0.52
0.53
1.3X
1.8X
1.4X
9.0 x
1.3
1.4
1.2
1.0ô
1.4
1.3
1.2
1.1
--0.5 õ
--'0.5 õ
--'0.5 õ
-•0.5 õ
104
104
104
102
* Typically +_0.1.
• 1.1 MeV/nu½ is the nominal oxygenthresholdlevel. Sulfur thresholdis 0.2 MeV/nu½ lower than oxygen threshold.
• Note: not abundancefraction.
ô 1.0 implies no correction.
{}Extrapolatedfrom spectraat higher energy.Typically + 0.1.
curve coversthe entire radial range, all measuredcurvesshow
the sametrend of increasingoutward gradient toward smaller
values of L between 17.2 and 5.7 R•. Inside 5.7 R•, however,
smaller gradients are seen at smaller values of L. The data
also show that the gradient in a given radial range is not the
samefor differentvaluesof M, but tendsto be larger for larger
valuesof M. This is due to the fact that the spectrain Figure 8
do not have the samespectralindex (slope)at a given value of
M. For example,the •5.7 R• spectrumis steeperat 500 MeV/
nuc-G than the spectrumat • 10.2R•, and thereforethe gradi-
I I I II
I
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I
i
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_
Oxygen
ent measured between 5.7 and 10.2 R• will increase toward
larger values of M. Hence, in the present analysisit is not a
good approximationto assume¾(M, L1) = ¾(M, L2) in (4).
Relative phase spacedensitiesat constantvalues of M can
now be calculatedby using (4) and the data in Figures 8 and
9. The f(L) for M = 680 MeV/nuc-G between5.7 and 17.2R•
is shownin Figure 10. The points at 5.7, 10.2, and 12.1 R• are
all basedon directmeasurements
of J•/B 2 and ¾.Thesequantities were not measured at 17.2 R• for M -- 680 MeV/nuc-G
but reasonablelimits can be placed on them by extrapolating
the 17.2 R• spectrumto this M value. The correspondinglimits on the phasespacedensityare shownas a bar at L -- 17.2
in the figure. The parametersusedto calculatef(L) are listed
in Table 4. Between5.7 and 10.2 R• the radial dependenceof
the phasespacedensityshownin Figure 10 is f(L) ocL 14.Al-
\
though there are no direct measurementsin this region at this
value of M to confirm a power law representation,the 7.6 R•
point at 160 MeV?nuc-G (Figure 8) and reasonableassumptions concerningthe spectrumindicate that f(L -- 7.6) at 680
103
MeV?nuc-G shouldbe between10-2 and 10-1. The powerlaw
representation
falls within thisintervalat f(7.6) •, 2 x 10-2.
REGION
2
DIFFUSION EQUATION SOLUTIONS
,--,5.2 Rj
102
The radial dependenceof f shownin Figure 10 is now compared with solutionsof the diffusion equation (1) to obtain
limits on the diffusion coefficientand the particle lossrate. It
is assumedthat the measured intensities represent a steady
statecondition and that there are no sourcesof energeticoxygen ionsbetween5.7 and 17.2R,. With a lossterm of the form
• = f/,r, where•-is the particlelosslifetime, equation(1) then
REGION
'--'10.2 Rj
becomes
Z 3-/ - - --o
(5)
A techniqueoften usedin solvingthis equation is to assume
D = DoLn
r = rOLm
(6)
_
_
_
_
_
J i
i i i J
i
i
i
I
i
i i iI
I
IO
E (MeV/nuc)
i
i
i
[Haerendel, 1968; Barbosa and Coroniti, 1976; Baker and
Goertz,1976;Goertzet al., 1979;Richardsonet al., 1980]where
Do, to, n, and rn are constantsto be determinedby fitting the
solution
to the data. Three
radial
diffusion
mechanisms
that
theoretically give a power law form for the diffusion coeffiFig. 7. Integral oxygenenergyspectrain regions2 and 4. J(E) is cient are fluctuating electric fields due to ionosphericturbuthe integral intensity above energy E. The solid parts of the curves lence (n -- 3 [Brice and McDonough, 1973]), disturbancesin
representthe samedata set as the differentialspectrain Figure 5. No
binninghasbeendoneto the data;eacheventis shownas a stepup in the convectionelectric field due to changesin the solar wind
integral intensity. The points at 1.4 MeV/nuc are basedon the Z > 2 interaction with the magnetosphere(n -- 6 [Birmingham,
rate.
1969]), and magnetic field disturbancesdue to solar wind
8912
GEHRELS ET AL.: JOVIAN ENERGETIC O AND S
in the strongpitch angle diffusion limit. In this case
Oxygen
q'strong
•' ao12/2
IO9
x\
(7)
[Kenneland Petschek,1966] where q-bis the particle bounce
period and ao• is the equatorial loss cone angle. For nonrelativisticparticlesat constantM in a dipolaf magneticfield,
•\ \\ 0
od
10e
R• MBs
m•'c2
•/2L•/2
4%trøas=
'•-
(8)
wherem• is the protonmassfor [• = MeV/nuc-G and Bs is
the equatorialsurfacefield of Jupiter,approx•ately equal to
T
107
4G. For largeL, •t•oas• L•/•.
As a prel•a•
step,(5) can be solvedfor the specialcase
of lossless
diffusion(• • •). Given the two bounda• conditionsf(LO and f(LO, the bsslessd•usion solutionfor n • 3 is
c•E
• • .....•
f
.•o io 6
=
%
_
-- f
--
__
(9)
The parameter Do doesnot appear • this equation becauseit
is a multip•cative constant • the general solution that disappearswhen the bounda• conditionsare •posed. A search
io 5
can now be madefor valuesof L•, L•, f(LO, f(L•), and n that
give acceptablefits to the measuredphasespacedensities.An
acceptablesolutionis de•ed as one that agreeswith the data
io 4
t],,, .... [ ......... ] .... ] .... [
•
•
I02
•
P•oneer
•
P•oneer II
I0•
[
I
....
I ....
I ....
I''"
680
-
Oxygen
o• • o
io3
[
I09 -
for
400
MeV
M=1800nu•
I0
108
160
3300
104
30
M (MeV/nuc-G)
Fig. 8. Voyager 1 and 2 measurements
of Jx/B 2 as a functionof
M for oxygenat differentradial positionsin the magnetosphere.
All
measurements
were made at, or near, magneticequatorialcrossings.
The telescopepointing directionwas within 20ø of the plane perpendicularto the local magneticfield directionfor the closedsymbols
and was,--30ø from the planefor the opensymbols.(The pitch angles
a of the measuredparticlesare on averageequal to the telescope
pointingdirection.)The dashedlinesrepresentinterpolationsbetween
--
107
67
E 06
the spectral
dataandthe Z > 2 ratepoints.The spectrum
at ,--5.0Ri
is dotted to distinguishit from the spectrumat ,--5.2 R•. The Pioneer
10 and 11 points are estimatesof the oxygenintensitybasedon data
from the University of Chicagofissioncell detector[Simpsonet al.,
1974, 1975].It was assumedthat the detectorwas respondingprimarily to oxygennuclei and that the spectralindex of the oxygenspectrum was ,•3 (approximatelythe value usedby the authors).For a
steeperassumedspectrum,the points could be as much as a factor of
I05
_
io 4
_
4 lower.
io3
pressurevariations(n ----10 [Nakada and Mead, 1965]). Another possiblediffusion mechanismis magnetic flux tube interchangedriven by centrifugalplasma forces.The L dependenceof D has not been fully specifiedtheoreticallyfor this
process,but indicationsare that D will not be a strict power
law in L [Siscoeand Summers,1981].Plasmaobservationsbetween6 and 8 R•, however,are consistentwith the approximation of a power law D with n = 5-8 [Froidevaux,1980; $iscoe
and Summers,1981].A power law q-cannotbe justified to the
sameextent as a power law D but is approximatelyobtained
s...........
';;........
, .... , ....
'
L (Rj)
Fig. 9. Measurements
of J•/B 2 asa functionof L for variousvaluesof M. The curvesrepresentcutsat constantM in Figure8. The
opensymbols
signifyJx/B2 valuesderivedprimarilyfromZ > 2 rate
measurements.
The errorson thesepointsare due mainly to uncertaintiesin the sulfur and oxygencontributionsto the rate and should
be consideredas systematicerrors.The errorson the pointswith
closedsymbolsare due to statisticaluncertaintiesassociatedwith the
numberof eventsin the spectrumand are thereforeuncorrelated.The
5.0 and 5.2 R• measurements
at 680 MeV/nuc-G were averagedtogetherto improve statistics.
GEHRELS ET AL.: JOVIAN ENERGETIC
Oxygen
O AND S
8913
now included in the diffusionequation.The general solution
in this casewith boundaryconditionsf(L]) and f(L2) is
_
IO
M-- 680 nuc
MeV
G
f (L) = f (L,)
_
_
_
4- f(L2)
_
_
[see,e.g., Goertz et al., 1979] where L(x) and K•(x) are the
modifiedBesselfunctionsof order v, v = (3 - n)/(n + m - 2),
andxi = xoL,-p,wherep = (n + rn - 2)/2 andXo= (p2Doro)
-•/•.
There is alsoa specialsolutionfor n + rn = 2 (p = 0), but it
_
_
_
_
_
_
_
_
does not apply here since, as will be shown below, the data
_
_
_
_
_
_
_
_
_
_
_
_
io-5
(10)
I
I
4
I
6
I
I
8
I
I I t • • I III1[
I0
15
I I II
20
30
L (Rj)
Fig. 10. The phase spacedensity of oxygen ions with M -- 680
MeV/nuc-G betweenL = 5.7 and L = 17.2.f(L) is normalizedto be
1.0 at 10.2R/. For L > 12.1,f(L) was estimatedby extrapolationof
measurementsat larger values of M. The uncertainty in this extrapolation is indicated by the error bar at L = 17.2.
at 5.7, 10.2,and 12.1R/and with the limits at 17.2 R/(Figure
10) and has an essentiallymonotonicradial dependence(i.e.,
no large local maxima or minima). Figure 1la shows three
losslessdiffusion solutions.None of these solutions,or any
other onestried, is acceptableas defined above. Solution 1 is
the closestto an acceptablefit over the entire radial range, but
it, as well as solution2, has negativevaluesfor n while theory
and other observationsindicate that positive values are more
likely. Solution 3 has n = 0, but fits (approximately) only the
measurementsbetween•8 and 17.2R/. Although no solution
with non-negativen was found to fit the data over the entire
radial range, solution 3, which is our best effort in terms of
finding a solution with non-negative n that fits the data to the
smallestpossibleradial distance,showsthat losslessdiffusion
may be occurring outside •8 R/. Thus, there is evidence that
lossprocesses
must be occurringinside of •8 R/and may be
occurringat larger radial distances.It is not surprisingthat
lossesare occurring inside •8 R/since both the plasma density [Bagenal and Sullivan, 1981] and the electromagnetic
wave activity [Scarf et al., 1979] are enhanced in this region.
The wave enhancementcontinuesout to • 10 R/, indicating
that lossesare also likely in the 8-10 R/region.
As a preliminary investigationof the effectof lossprocesses
on the phasespacedensity,lossesof the form given by (6) are
specifyn + rn = 5-6. Equation(10) is usuallysimplifiedconsiderablyby choosingf(L = 1) = 0 or f(L = O) = O. In the
presentanalysis,however, the inner boundary condition was
chosento be the measureddensityat L = 5.7, f(5.7) = 2.4 x
10-4, becauseit is likely that the diffusioncoefficientand lifetime are muchdifferentinsideIo's orbit than outsidegiventhe
abrupt changein plasma density and temperatureat L = 5.7
[Bagenal and Sullivan, 1981; Richardsonand Siscoe, 1981].
The other conditionapplied was f(L = 10.2) = 1.0.
The method usedin searchingfor acceptablesolutionsfor a
given rn and n was to find the Xosuchthat the solutiongives
the correctvalue at 12.1 R/and then examine the solution to
seeif it liesbetweenthe limitsat 17.2R/and hasan essentially
monotonicradial dependence.Of the three sample solutions
shownin Figure 1lb, only solution2 is acceptable.Solution 1
lies outsideof the range of the data at 17.2R/, while solution3
has a pronouncedminimum at -6.5 R/. The valuesof n and rn
for which acceptablesolutionswere found are shownin Figure 12. There are no acceptablesolutionsfor n < 3, but for n
> 14the band of solutionscontinues.Althoughthe acceptable
l0 2
' i I i •i
T-'"'
cOno
losses
.//11..
•
MeV ,'1"'•/]
- M:
680
:
M = 680 MeV/nuc-G
L,
L2
5.7
10.2
5.7
10.2
12.1
12.1
17.2
between L -- 5.7 and L = 17.2
¾(M,L2) J•.(M,L:)/B • (L:)
f (L:)/f (L,)
-
finite
r
_
MeV
-M:680n--•--•--•
-
•.
-
_
_
..!
///
/!
:
-
n
i
'1I
-5.5
:•2
2
0.0
-
n= 6
'/I'#m
-
-3.3
0
/•/ 32ß
EL. I0 -4
_
_
ß
k"3
[0-5
i
i
i
]
IIl[Illll
L (Rj)
TABLE 4. QuantitiesUsed to Calculatethe PhaseSpaceDensity at
(bl i i • [ [ • , ,,,i,,,,/i,, ,,
/
I
iJ
4
i
i
i
i
•11,,,,
L (Ro)
Fig. 11. Solutions of the diffusion equation compared with the
measuredf(L) at 680 MeV/nuc-G. (a) Losslessdiffusion; equation
(9). The valuesof n for eachsolutionare listed.For solutions1 and 2,
f(L2) -- 12.0,L• -- 8.0,andf(LO -- 3.1 x 10-2 (i.e.,thevalueat 8 R/of
and L• -- 5.7 and L 2 -- 12.1, respectively.For solution 3, L 2 •- 17.2,
4.8
2.2
1.7
1.2 X 104
1.1 x 108
6.1 x 108
upperlimit
1.7
3.9x 109
6.5
lower limit
0.8
1.6 x 109
1.2
4200.
4.3
f(L2) -- 12.0,L• -- 8.0,andf(LO -- 3.1 x 10-2 (i.e.,thevalueat 8 R/of
the power law interpolation between measurementsat 5.7 and 10.2
R/). No curvegivesan acceptablefit to the measuredvaluesover the
entire radial range. (b) Lossydiffusion;equation (10). The measured
valuesof f(L) were usedfor f(L•) and f(L2) with L• -- 5.7 and L2 •10.2. Only curve 2 is an acceptablefit.
8914
GEHRELS
I
I
I
I
I
ET AL.: JOVIAN
I
ENERGETIC
O AND
S
lower limit, there are no solutions with reasonable diffusion
_
/
occeptoble
coefficientsthat fit all the data from 5.7 to 17.2 R• given the
powerlaw formsof the diffusioncoefficient
andlifetimein (6).
However, if lossesoccur only inside 8 R•, the strongpitch
angle diffusion lifetime at 17.2 R• will not be a constrainton
rm• and Dmaxat 6 R•. If, for example,we assumethe above
lossy-diffusionsolution inside 8 R•, with n + m • 6, Do,o •,
_
10-6, and%t•o.s
(L -- 8) -- 2.5 x 104s,whichlimits*Omi•
to 8-m
2.5 X 104 S,thenthe equivalentof (11) becomes
Dmax(g
) --' 1.1X l0-5
T•TO
Lm
-IO
0
I
2
I
4
I
(5.7_<L _<8)
(12)
At L = 6, Dm•x(6)rangesfrom 4 x l0 -6 s-• to 2 X l0 -6 s-• asn
I
6
s-'
8
I
I
I0
12
4
n
Fig. 12. The region in the n-m plane where acceptablesolutions
were obtained for the caseof lossydiffusion. Calculationswere done
only at integer n. The band of solutionscontinuesfor n > 14.
n and m's individuallyvary by about 12 unitsin the figure,the
sumn + m is relativelyconstant,rangingfrom --,6 at n = 3 to
-•5 at n = 14. This is due to the fact that all parameters except
rangesfrom 3 to 6.
ß
Sinceboth the solutionwith lossydiffusionbetween5.7 and
17.2R• and that with lossydiffusionbetween5.7 and 8 R• and
losslessdiffusionbetween8 and 17.2 R• give valuesof the diffusion coefficient
that are consistent with
earlier
work
and
give reasonablefits to the data, this data set alone cannot be
usedto choosebetweenthem. The reasonfor this inadequacy
is that the data set has been restrictedto magnetic equatorial
crossingsto simplify the analysis,and therefore doesnot have
the necessaryradial resolutionto further specifythe extent of
the lossyregion. More information can be obtained about the
particle lossesby an analysisthat includesthe nonequatorial
data (work in progress)and by direct comparisonwith plasma
and electromagnetic
wave data. However,the presentanalysis
does demonstratethe inward flow of the energeticions and
doesshowthat the measurementscan be describedby a diffu-
v dependon n and m in sum.Sincethe solutiondependsonly
weaklyon v, its n dependence
is a smalleffect.Also note that
Do and ,o enter the solutionas a product.No informationcan
be gainedabouteitherof themindividuallyfrom thisanalysis
alone. This is physicallyreasonablesince,for a given radial
dependenceof f, D, and ,, the larger Do becomes,the larger
the net diffusiveflux into a region becomes,and, therefore, sion model with diffusion coefficients similar to those derived
the higherthe lossrate (smaller,o) mustbe to maintaina con- by othersfor electrons,protons,and plasma. Therefore, a reastant densityin the region.
sonable value for the diffusion coefficient can be chosen for
The acceptablevaluesof Do,owere found to range from --,5 the sourcestrengthanalysisthat follows.
X 10-7 at n = 3 to -•5 x 10-6 at n = 14. Given Do,o, n, and m,
lower limits on, can be imposedto determine the maximum
DISCUSSION
allowable
diffusion
coefficient
as a function
of L. The mini-
mum ß, *m•, dictatedby the strongpitch angle diffusionlimit,
is given by (8). Since all acceptablesolutionswere found to
have m < 11/2, the strongestrestrictionthat can be placed on
ß between5.7 and 17.2 R• occursat 17.2 R• (i.e., if a given so-
lution with m < 11/2 has ,(5.7) = *stro.g
(5.7), then ,(17.2) <
ßstrong
(17.2), whichis impossible).
At 17.2R•, (8) gives
(17.2) = 1.7 x 106s, and thereforethe minimum,o is *Omin
=
17.2-m 1.7 X 106S.The maximum diffusion coefficient,D .... is
then
Having establishedthe inward diffusive flow of the energetic oxygenions, we can now use the measuredion number
densities (as determined from the spectra), the measured
phasespacedensitygradients,and the calculateddiffusioncoefficientsto estimatethe inward diffusiveflow rate of energetic
oxygen ions acrossa given radius. This can then be compared
with the Io sourcestrength of oxygen and sulfur ions.
The diffusiveflow I of ions'with magnetic moment greater
than M acrossradius r is given by
I>• = n>•2,rr. 2hvo ions s-•
Dm•x(L)-Do*o
Ln=1.5X10
-5
TOmin
(13)
s-•(5.7
__<
L_<17.2)wheren>•t is the numberdensityof oxygenionswith mag(11)
netic momentgreaterthan M, h is the scaleheight of the particle distribution relative to the magnetic equatorial plane,
and vo is the radial diffusionvelocitydefinedas vo -- D. [(1/
f)(Of/OL)] [Schulzand Lanzerotti,1974].For the specificcase
of r = 10 Rj and M = 400 MeV/nuc-G, the oxygen number
assumingn + m • 6 and Do,o •, 10-6. For L = 6, Dma
x is a
steeplydecreasing
functionof n, rangingfrom -•6 x 10-7 S-•
fromthe 10.2Rj spectrum
to be
at n = 3 to <3 x 10-8 s-• for n > 6. Previousproton,electron, densitycanbe estimated
and plasmameasurements
give typical valuesof 3 • 10-8 - 4 • 8 x 10-6 cm-3. We use10Rj ratherthan a largerradialdisx 10-6 for the radial diffusioncoefficientat 6 Ra [Thomsenet tance in this calculationto allow comparisonwith other diffual., 1977; Goertz et al., 1979; Froidevaux, 1980; Siscoe and sioncoefficientdeterminations.The diffusioncoefficientupper
Summers, 1981]. These other measurementssuggestthat the
mostlikely solutionsin the presentanalysisare thosewith n <
6 (m > 0).
For the caseof finite lifetime, all acceptablesolutionswith n
< 6 give valuesof the phasespacedensityat 17.2 R• near the
upper limit allowed by the data. If the actual value is near the
limit at L -- 10 obtained for the case of lossy diffusion between5.7 and 17.2Rj (equation(11)) rangesfrom 6 X 10-7 to 3
X 10-6 s-• for 6 _>n _>3, while that obtainedfor lossydiffusion between 5.7 and 8 Rj (equation (12)) rangesfrom 2 X
10-5 to 10-4 s-• for 3 _< n _< 10. The results of other diffusion
coefficientdeterminations [Thomsenet al., 1977; Goertz et al.,
OEHRELS ET AL.: JOVIAN ENERGETIC
1979; Froidevaux, 1980; Siscoe and Summers, 1981] can be
O AND S
8915
particle lossesare due to wave-particle interactions rather
represented
by D(L = 10)= 10-5ñ•s-• (in somecases
we have than geometric absorptionby Io.
used a formula quoted only for 6 _<L _<8) which is approximately consistentwith our values.With (1/f)(Of/OL) • 1.4
(Figure 10) and h = 1 Rj, estimatedfrom the magneticlati-'
tude dependenceof the Z > 2 fluxes, the energetic oxygen
flow rate in acrossr = 10 Rj is then I>st = 5 x 1021ñ'ions s-•
for M = 400 MeV/nuc-G. Thus, sincethe energeticion abundancesimply an Io source,and, sincethe Io sourcestrengthof
oxygenand sulfur ions is estimatedto be 1027-1029
ions s-•
[Eviatar and Siscoe, 1980; Shemansky, 1980], we find that
3. There is a steep positive radial gradient in the phase
spacedensity of the energeticoxygen ions between 6 and 17
Rj. The diffusiveflow of the energeticions is therefore inward
in this region,indicatingthat the accelerationregionis outside
17 Rj.
4. Steady-statesolutionsof the diffusion equation with
diffusion coefficient and loss lifetime of the forms D -- DoLn
and r -- T0Lm were fit to the measuredphasespacedensitiesat
M -- 680 MeV/nuc-G between 5.7 and 17.2 Rj. For the case
'• 10-7ñ2of the ionssuppliedby Io to the torusat • 10-n MeV/
of losslessdiffusion(r --> oo), no solutionswith reasonable
nuc-G must be accelerated to >400 MeV/nuc-G
values of n could be found to fit the data over the entire radial
in some re-
gion outside17 Rj and then diffuseback in to 10 Rj.
range. However, solutionswere found that fit outside 8 Rj. It
Oxygenions with magneticmomentsin the range 102-104 is thereforepossiblethat the high-energyions are undergoing
MeV/nuc-G have also been observed by the low energy losslessdiffusion from 17.2 to -•8 Rj and then 1ossydiffusion
chargedparticle (LECP) instrumentjust inside the magnet- from 8 to 5.7 Rj. Another possibilityis that there are lossesof
osphereat 65 Rj inboundon Voyager 1 [Krimigiset al., 1979], the power law form given above throughoutthe region. For
and in the magnetospheric
wind region(r > 150Rj outbound) this case, solutions were found that fit the data over the entire
on both Voyagers1 and 2 [Krimigiset al., 1981].The J/B •- range 5.7-17.2 Rj, with n + m = 6 and n > 3. The upper limit
calculated from the 65 Rj measurementis two to three orders on the diffusioncoefficientat L = 6, as determinedby the soof magnitudelarger, at the samevalue of M, than that at 17.2 lutions,fallsin the rangeof othermeasurements
(3 x 10-8 - 4
Rj in Figure 8. This observationdoes not necessarilyimply x 10-6 s-l) for n between6 and 3.
5. On the basisof the diffusioncoefficientupper limits obparticleflow directlyin from 65 to 17 Rj sincethere may be a
maximum in the phase space density at some intermediate tained from the phasespacedensityfits, the upper limit on the
distance,but it doesrequire an accelerationregion outside17 number of oxygen ions with magnetic moment greater than
400 MeV/nuc-G diffusingin across10 Rj is -•5 x 1021ñ'ions
The observationssuggestthat plasma ions diffuse outward s-l, indicatingthat -• 10-7ñ2of the ionsfrom Io are accelerated
from the Io toms, are nonadiabaticallyacceleratedin somere- to >400 MeV/nuc-G and diffusein to 10Rj.
gion outside17 Rj, and then diffuseinward and outward from
APPENDIX
the acceleration region. The radial diffusion process will
The high radiation levels of Jupiter'sinner magnetosphere
changeparticle energiesbut is assumedto conservemagnetic
moments. The LECP measurementsjust describedand the causethree instrumentaleffectsin the LET systemthat must
CRS measurementsreported here both require an accelera- be correctedfor before absoluteparticle fluxes and energies
tion mechanismthat is capableof increasingparticle magnetic can be determined:
1. Discriminator retrigger times. Finite retrigger times for
momentsfrom that of the plasmanear Io, -• 10-n MeV/nuc-G,
discriminator circuits cause a dead time in the circuits that reup to -• 10n MeV/nuc-G.
One possiblemechanismis that proposedby Eviatar et al. sults in observed rates that are lower than the true rates. For
[1976] to predict the observedenergeticsodiumcomponentin the CRS instrument,the effectbecomessignificantabove rates
the magnetosphere.
In that model,fastneutral particles,possi- of 10n s-•.
2. Discriminator threshold shifts. High counting rates
bly producedby chargeexchangebetweenneutralsand corotating plasmanear Io, escapethe magnetosphereand become cause shifts in the baseline voltage level at the output of the
ionized in the solar wind. The ions are then accelerated to the
detectoramplifiers. Since discriminatorthresholdsare set for
•400 km s-! solar wind speed and re-enter the magnet- a specifiedlevel above the nominal baseline,the baselineshift
osphere.This mechanism,will, however, result in magnetic producesan increasein the effectivethreshold,so that, for inmomentsof not more than •20 MeV/nuc-G. Two other pos- stance,at high counting rates it takes a larger energy deposit
sibilitiesare stochasticaccelerationby cyclotronwavesin the to triggera giventhresholdthan at low countingrates.The efplasmaof the outer magnetosphere[Papadopoulos
et al., 1980], fect becomessignificantabovean energylossdepositionrate
or the application of recirculation models (Sentman et al. in the detectorof • 105MeV s-•. For regions1, 2, and 3, the
[1975] (radial recirculation)and Goertz[1978] (azimuthal re- L 1 energylossdistributionshownin Figure 6 producessignificantbaselineshiftsfor Z > 2 ratesabove103s-•. In regions4,
circulation)) to heavy ions.
5, and 6, the bulk of the particleshave energylossesin L 1 •<10
CONCLUSIONS
MeV, requiringZ > 2 ratesof at least104s-• beforebaseline
The principal conclusionsof this studyof oxygenand sulfur shiftsbecomeimportant.
ionswith energiesin the range 1-20 MeV/nuc between5 and
3. Pulsepileup effects.As fluxesincrease,the probablility
20 Rj in the Jovian magnetosphereare as follows:
that two particleswill be coincidentin a detectorwithin the
1. The Voyager I oxygenand suffur fluxesinside •18 Rj instrumental resolving time increases,degrading the pulse
were the sameas thoseof Voyager2 to within a factor of-•2.
height data from that detector.For large oxygenpulsesin the
2. The minima in the oxygenand sulfurfluxesnear Io oc- detector,the effect of a high rate of coincidentsmall proton
curred at L -- 5.6 inbound and L -- 5.4 outbound. These pulsesis to broadenthe oxygenpulseheight distribution.Oxradial positionsare more closelycorrelatedwith changesin ygen eventsin coincidencewith other large pulses,however,
plasmaand electromagnetic
waveconditionsthan with the or- will be displacedcompletelyout of the normal oxygendistribital positionof Io itself.The indicationis, therefore,that the bution. The fractiondisplacedis rpHARZ>2,where Rz>2is the
8916
GEHRELS ET AL.: JOVIAN ENERGETIC O AND S
TABLE 5. Livetime Correctionsfor Event Analysis
EnergyRange,
Region
I
2
3
4
5
6
Livetime
PulsePileup
Total
MeV/nuc
Correction Factor
Correction Factor
Correction Factor
3.7-7.1 *
1.5
1.4
2.0
7.1-23.5T
1.5
1.0
1.5
3.7-7.0*
1.5
1.4
2.0
7.0-23.5T
1.5
1.0
1.5
3.7-6.3'
1.5
1.5
2.2
6.3-23.5T
6.3-23.5•
4.8-5.3*
5.3-23.5•
4.3-5.5*
1.5
1.6
3. l:l:
1.6
4.8:l:
1.0
1.0
1.0
1.0
1.0
1.5
1.6
3.1
1.6
4.8
5.5-23.5•
1.7
1.0
1.7
Correctionfactorsin the table aboveare typically+_0.1 exceptas noted.
* Z estimatefrom L 1 versusL2 plot.
• Z estimatefrom L2 versusL3 plot.
•+ o.5.
countingrate of large pulses,and the effectiveresolvingtime,
*PH^,for pulse height analysisis -20/•s. Therefore, for example, in regions1, 2, and 3 the Z > 2 rate (large pulses)of
Cobserved
Ctru½
•--(1- z•R•)(1
- z2R•2)(1
- T3RL3
)
(15)
-1.4 x 104s-1 (Figure2a;Table 3) will cause-30% of the ox- whereR,.i is the singlesrate in detectorLi, •'1is the L1 retrigygen pulseheightsin the front detector(L1) to be displaced ger time, and z2 and z3 are the discriminatordeadtimesof L2
by up to -100 MeV.
and L3, respectively,Here, discriminatordeadtime refers to
In orderto correctfor the discriminatorretriggertime and
thresholdshifts,a spareCRS instrumentwascalibratedby using light pulsesfrom light emittingdiodes(LEDs) situated
abovethe detectors.As far as the detectoramplifiersand electronics are concerned,the detectorpulse output is the same
the time after the discriminator
for ionization created by the photons as that created by a
charged particle, assumingthe light pulse is short in comparisonwith the amplifiershapingtime. In our case,the amplifier shapingtime is approximately2/•s and the light pulses
were alwaysshorterthan 100 ns. The countingrate in the detector was controlledby the frequencyof the random pulse
generatordriving the LED, and the pulse height was controlled by the intensityand duration of the light pulse.The effect of different particle species,energies,and fluxes incident
at the same time on a detectorwas simulatedby having several independentLEDs above it.
The standard livetime
correction formula
for rate R is
has returned to its zero state
beforeit can be retriggered.r2 and r3 are defineddifferently
thanZlbecause
theLETcoincidence
logicisa strobed
system
triggeredby L 1. Equation (15) is exactonly in high flux environmentswhere all detectorsinglescountingrates are much
larger than the observed coincidence rate. The calibration
showed that there is almost no discriminator
deadtime
in L2
and L3 for a heavy ion following a proton event and therefore, that the L2 and L3 termsin equation(15) are negligible.
(There is a discriminatordeadtime on the order of tens of microseconds
for a heavy ion following another heavy ion, but
theheavyratein L2 andL3 is nevergreaterthan ~ 103s-l). As
in the caseof the Z > 2 rate, zt was found to dependon rate
and pulse-heightdistributionand rangesfrom ~ 13 to -•15/•s
in the sixregionsof interest.The measured
livet'tmecorrection
factorsfor the coincidencerate in theseregionsare listed in
Table 5. The first line of each region is for L 1 ßL2 eventsand
the second
line is for L 1 ßL2-L3 events.Onlyparticlesstopping in L3 were used in region 4. In regions1, 2, and 3, the
Robserved
Rtru½
= (1--*Rob
....a)
instrument was in its L1. L2 command state, which means
(14)
that a particle is requiredto trigger L1 and L2 in order to be
countedin the coincidencerate; no requirementis made on
where z is the retriggertime of the discriminators,often as- L3. In regions5 and 6 the instrumentwas configuredin a
sumedto be a constant.The calibrationshowed,however, L1. L2. L3 commandstate to maximize backgroundrejecthat r is a functionboth of rate and pulseheightdistribution tion. In this state,a coincidentpulseis alsorequiredin L3. In
in the detectorand rangesfrom -12 to -19/•s in the six re- orderfor a Z > 2 particlestoppingin L2 to be analyzedin this
gionsof interest(Table 2). Thereforerate corrections
werede- commandstate,theremustbe a pulsein L3 due to, say,an acterminedfor eachregionby simulatingthe measured
pulse cidentallycoincidentproton. There is thereforean additional
heightdistributions
and matchingthe observedrate. The live- livetime correctionfactor for particlesstoppingin L2 in retime correction,[1/(1 - rRob..... a)], and the effectivethresh- gions5 and 6, which dependson the L3 countingrate.
old for the Z > 2 rate, as determinedby the calibration,are
All particlesstoppingin L3 wereanalyzedby usingtheir L2
listed for the six regionsin Table 3.
andL3 pulseheightinformation.The maximumcountingrate,
Livetimecorrections
werealsoincludedin theenergyspectra of large oxygen and sulfur pulsesin thesetwo detectorsis on
calculations.Sinceonly a small fraction of the valid two-de- the orderof 103s-1 (L2 in regions1, 2, and 3), sothat pulse
tector (L1.L2) and three-detector(L1. L2.L3) eventsare pileupaffects<2% of the Z > 2 particlesstoppingin L3. For
pulse height analyzed, a coincidencerate is used to convert particlesstoppingin L2, however,the L1 pulseheightis rethe numberof analyzedeventsof a givenelementalspecies quiredfor elementalidentification.The countingrate of large
and energy into a flux measurement.The livetime correction pulsesin L1 is the Z > 2 rate, which is on the order of 104s-l
formula for the L 1 ßL2. L3 coincidence rate C is
in regions1, 2, 3, and 5 (particlesstoppingin L2 werenot used
GEHRELS
ET AL.: JOVIAN
in region 4). The resultingamount of pulse pileup can be determined from the data by comparinga spectrumfor particles
stoppingin L3 usingL 1 in the elementalidentificationprocess
with one in which only L2 and L3 were used. The ratio between the resulting spectrais fairly energy independent over
this energyrange and indicateswhat fraction of the eventsin
L 1 are displacedout of the oxygendistribution.The ratio was
thereforeused as a correctionfactor for the L 1 ßL2 part of the
spectrum.The pulsepileup correctionfactor is listed in Table
5. It was found that no correctionfactorswere required in regions5 and 6, eventhoughthe Z > 2 rate in region 5 was -1.7
ENERGETIC
O AND
S
8917
Johnson,T. V., A. F. Cook II, C. Sagan, and L. A. Soderblom, Volcanic resurfacingratesand implicationsfor volatileson Io, Nature,
280, 746, 1979.
Kennel, C. F., and H. E. Petschek,Limit on stably trapped particle
fluxes, J. Geophys.Res., 71, 1, 1966.
Krimigis, S. M., T. P. Armstrong W. I. Axford, C. O. Bostrom, C. Y.
Fan, G. Gloeckler, L. J. Lanzerotti, E. P. Keath, R. D. Zwickl, J. F.
Carbary, and D.C. Hamilton, Low-energy chargedparticle environment at Jupiter: A first look, Science,204, 998, 1979.
Krimigis, S. M., J. F. Carbary, E. P. Keath, C. O. Bostrom,W. I. Axford, G. Gloeckler, L. J. Lanzerotti, and T. P. Armstrong,Characteristicsof hot plasma in the Jovian magnetosphere:
Resultsfrom
the Voyager spacecraft,J. Geophys.Res., 86, 8227, 1981.
Kumar, S., The stability of an SO2 atmosphereon Io, Nature, 280,
x 104 s-l. The reasonis that the Z > 2 rate in this regionwas
758, 1979.
dominated by -10 MeV pulseswhich do not seriouslycon- Nakada, M.P., and G. D. Mead, Diffusion of protonsin the outer rataminate oxygen signals.
diation belt, J. Geophys.Res., 70, 4777, 1965.
Ness,N. F., M. H. Acufia, R. P. Lepping, L. F. Burlaga, K. W. Behannon,and F. M. Neubauer,Magneticfield studiesat Jupiter by
Voyager 1: Preliminary results,Science,204, 982, 1979a.
Ness, N. F., M. H. Acufia, R. P. Lepping, L. F. Burlaga, K. W. Behannon,and F. M. Neubauer,Magneticfield studiesat Jupiter by
Voyager 2: Preliminary results,Science,206, 966, 1979b.
Cook, and D. E. Stilwell. We also thank D. L. Chenette, A. C. CumPapadopoulos,K., J. D. Gaffey, Jr., and P. J. Palmadesso,Stochastic
mings,and T. L. Garrard for helpful discussions.
N. Nessand his colaccelerationof large M/Q ions by hydrogencyclotronwavesin the
leagueson the Voyager magnetometerteam provided the magnetic
magnetosphere,Geophys.Res. Lett., 7, 1014, 1980.
field data usedin this analysis,which we gratefully acknowledge.We
Pearl, J., R. Hanel, V. Kunde, W. Maguire, K. Fox, S. Gupta, C. Ponare alsograteful to A. W. Schardtfor providing a specialformatting
nampemma, and F. Raulin, Identification of gaseousSO2 and new
of the magnetic field data and for useful discussions.We thank A.
upper limits for other gaseson Io, Nature, 280, 755, 1979.
Eviatar for sharing with us new ideas about accelerationprocesses. Richardson,J. D., and G. L. Siscoe,Factorsgoverningthe ratio of inSupported by NASA under NAS7-100, NGR 05-002-160, and
ward-to-outwarddiffusingflux of satelliteions,J. Geophys.Res., 86,
Acknowledgments.We greatly appreciatethe effortsof R. E. Vogt,
both in his capacityas CRS Principal Investigatorand as a colleague
who has provided useful discussions.
We are also grateful to the Caltech and Goddard groupswho have supportedthis investigation,with
specialthanks to W. E. Althouse, M. F. Beazley, R. Burrell, W. R.
NAGW-200.
8485, 1981.
The Editor thanks T. G. Northrop and R. B. McKibben for their
assistancein evaluatingthis paper.
REFERENCES
Bagenal,F., and J. D. Sullivan, Direct plasmameasurementsin the Io
toms and inner magnetosphereof Jupiter, J. Geophys.Res., 86,
8447, 1981.
Richardson,J. D., G. L. Siscoe,F. Bagenal,and J. D. Sullivan, Time
dependentplasma injection by Io, Geophys.Res. Lett., 7, 37, 1980.
Sandel,B. R., D. E. Shemansky,A. L. Broadfoot,J. L. Bertaux, J. E.
Blamont,M. J. S. Belton,J. M. Ajello, J. B. Holberg, S. K. Atreya,
T. M. Donahue, H. W. Moos, D. F.Strobel, J. C. McConnell, A.
Dalgarno, R. Goody, M. B. McElroy, and P. Z. Takacs, Extreme
ultraviolet observationsfrom Voyager 2 encounterwith Jupiter,
Science, 206, 962, 1979.
Baker, D. N., and C. K. Goertz, Radial diffusionin Jupiter'smagnetosphere,J. Geophys.Res., 81, 5215, 1976.
Barbosa,D. D., and F. V. Coroniti, Lossy radial diffusion of relativistic Jovian electrons,J. Geophys.Res., 81, 4553, 1976.
Birmingham, T. J., Convection electric fields and the diffusion of
trappedmagnetosphericradiation, J. Geophys.Res., 74, 2169, 1969.
Brice, N., and T. R. McDonough, Jupiter'sradiation belts, Icarus, 18,
Scarf,F. L., D. A. Gurnett, and W. S. Kurth, Jupiterplasmawave observations:An initial Voyager 1 overview, Science,204, 991, 1979.
Schardt,A. W., F. B. McDonald, and J. H. Trainor, Energeticparticles in the pre-dawn magnetotailof Jupiter, J. Geophys.Res., 86,
206, 1973.
Broadfoot, A. L., M. J. S. Belton, P. Z. Takacs, B. R. Sandel, D. E.
Shemansky,J. B. Holberg, J. M. Ajello, S. K. Atreya, T. M. Donahue, H. W. Moos, J. L. Bertaux, J. E. Blamont D. F. Strobel, J. C.
McConnell, A. Dalgarno, R. Goody, and M. B. McElroy, Extreme
Sentman, D. D., J. A. Van Allen, and C. K. Goertz, Recirculation of
8413, 1981.
Schulz, M., and L. J. Lanzerotti, Particle Diffusionin the Radiation
Belts, Springer, New York, 1974.
energeticparticlesin Jupiter'smagnetosphere,Geophys.Res. Lett.,
2, 465, 1975.
Shemansky,D. E., Mass-loadingand the diffusion-loss
ratesof the Io
plasma toms, Astrophys.J., 242, 1266, 1980.
Simpson,J. A., D.C. Hamilton, R. B. McKibben, A. Mogro-CampScience, 204, 979, 1979
ero, K. R. Pyle, and A. J. Tuzzolino, The protons and electrons
trappedin the Jovian dipole magneticfield region and their interBrown, R. A., Optical line emissionfrom Io, Symp.Int. Astron. Union,
action with Io, J. Geophys.Res., 79, 3522, 1974.
65, 527, 1974.
Brown, R. A., and Y. L. Yung, Io, its atmosphereand optical emis- Simpson,J. A., D.C. Hamilton, G. A. Lentz, R. B. McKibben, M.
sions,in Jupiter,edited by T. Gehrels,University of Arizona Press,
Perkins,K. R. Pyle, A. J. Tuzzolino,and J. J. O'Gallagher,Jupiter
Tucson, 1976.
revisited:First resultsfrom the University of ChicagochargedparEviatar, A., and G. L. Siscoe,Limit on rotationalenergyavailableto
ticle experiment on Pioneer 11, Science,188, 455, 1975.
exciteJovianaurora, Geophys.
Res.Lett., 7, 1085, 1980.
Siscoe,G. L., and D. Summers,Centrifugally driven diffusion of IoEviatar, A., Yu Mekler and, F. V. Coroniti, Jovian sodium plasma,
genic plasma,J. Geophys.Res., 86, 8471, 1981.
Smith, B. A., E. M. Shoemaker, S. W. Kieffer, and A. F. Cook II, The
Astrophys.
J. , 205, 622, 1976.
role of SO2 in volcanism on Io, Nature, 280, 738, 1979.
Froidevaux,L., Radial diffusionin Io's toms:Someimplicationsfrom
Voyager 1, Geophys.Res. Lett., 7, 33, 1980.
Stilwell, D. E., W. D. Davis, R. M. Joyce, F. B. McDonald, J. H.
Goertz, C. K., Energization of charged particles in Jupiter's outer
Trainor, W. E. Althouse, A. C. Cummings, T. L. Garrard, E. C.
magnetosphere,J. Geophys.Res., 83, 3145, 1978.
Stone,and R. E. Vogt, The Voyager cosmicray experiment,IEEE
ultraviolet observationsfrom Voyager 1 encounterwith Jupiter,
Goertz, C. K., J. A. Van Allen, and M. F. Thomsen, Further observa-
Trans. Nucl. Sci. NS-26, 513, 1979.
tional supportfor the lossyradial diffusionmodel of the inner Jo- Stone, E. C., R. E. Vogt, F. B. McDonald, B. J. Teegarden, J. H.
vian magnetosphere,J. Geophys.Res., 84, 87, 1979.
Trainor, J. R. Jokipii, and W. R. Webber, Cosmicray investigation
Haerendel, G., Diffusion theory of trapped particlesand the observed
for the Voyager missions:Energeticparticle studiesin the outer heproton distribution,in Earth's Particlesand Fields,edited by B. M.
liosphere•and beyond, Space Sci. Rev., 21, 355, 1977.
McCormac, Reinhold, New York, 1968.
Hamilton, D.C., G. Gloeckler, S. M. Krimigis, and L. J. Lanzerotti,
Composition of nonthermal ions in the Jovian magnetosphere,J.
Geophys.Res., 86, 8301, 1981.
Thomsen, M. F., C. K. Goertz, and J. A. Van Allen, A determination
of the L dependenceof the radial diffusioncoefficientfor protonsin
Jupiter's inner magnetosphere,J. Geophys.Res., 82, 3655, 1977.
Trainor,J. H., F. B. McDonald,B. J. Teegarden,W. R. Webber,and
8918
GEHRELS ET AL..' JOVIAN ENERGETIC O AND S
E. C. Roelof, Energeticparticlesin the Jovian magnetosphere,
J.
Geophys.Res., 79, 3600, 1974.
Van Allen, J. A., D. N. Baker, B. A. Randall, and D. D. Sentman,The
magnetosphereof Jupiter as observed with Pioneer 10, 1, Instrumentand principal findings,J. Geophys.
Res., 79, 3559, 1974.
Vogt, R. E., W. R. Cook, A. C. Cummings,T. L. Garrard, N. Gehrels,
E. C. Stone,J. H. Trainor, A. W. Schardt,T. Cordon,N. Lal, and F.
B. McDonald, Voyager 1: Energeticions and electronsin the Jovian magnetosphere,Science,204, 1003, 1979a.
Vogt, R. E., A. C. Cummings,T. L. Garrard, N. Gehr½ls,E. C. Stone,
J. H. Trainor, A. W. Schardt,T. F. Cordon, and F. B. McDonald,
Voyager 2.' Energeticions and electronsin the Jovian magnetosphere,Science,206, 984, 1979b.
(Received March 11, 1981;
revised June 2, 1981;
acceptedJune 2, 1981.)