JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 93, NO. A8, PAGES 8502-8518, AUGUST
1, 1988
Plasma Bulk Flow in Jupiter'sDaysideMiddle Magnetosphere
MARK R. SANDS
1
Departmentof Nuclear Engineeringand Centerfor SpaceResearch,Massachusetts
Instituteof Technology,Cambridge
RALPH L. McNuTr,
JR.
Departmentof Physicsand Centerfor SpaceResearch,Massachusetts
Instituteof Technology,Cambridge
Using the plasmadataobtainedduringthe Voyager 1 encounterand the full responsefunctionof the Plasma Science(PLS) experiment,
convective
plasmavelocitieshavebeendetermined
in the daysidemiddlemag-
netosphere
of Jupiter(10 R• < r < 25 R•). We findthattemperature
anisotropies
haveverylittleeffecton
plasma velocity determinationand that the plasmadata are well approximatedby convected,isotropic
Maxwellian ion distributionfunctions.The insensitivityof the analysisto any thermalanisotropies
which
may exist allows a good determination
of the bulk plasmaflow velocity. In additionto the subcorotational
azimuthalflow thereexistsa substantial
nonazimuthalcomponentof plasmaflow. This nonazimuthal
flow is
mostly aligned (antialigned)with the local magneticfield but also exhibitsa cross-fieldcomponent.The
velocitypatternis inconsistent
with enhancedplasmaoutflowin the activesector,as suggested
by the corotatingconvectionmodelof plasmatransport.The contribution
of field-aligned
flow alongthe curvedmagnetic field linesto the stresson the magneticfield is evaluated.In the regionstudiedsuchflow contributes
up
to onehalf the stressproduced
by the azimuthalplasmaflow.
INTRODUCTION
alignedflow wasassumed.Boththisanalysisandtheanalysis
of
Pioneer
Observations
McDonald
et al. [1979]suggest
thatat leasta partof thisfieldaligned flow is directed away from the magneticequator.
From
observations
withthePioneer
spacecraft,
Smith
etal. Consequences
ofsuch
flows
forparticles
atthese
large
energies
[1975]
found
that
Jupiter's
magnetic
field
does
not
lie
in
are
discussed
by
Northrop
[1979]
and
Northrop
and
Schardt
meridional planes but instead exhibits a spiral structure. An
[1980].
explanationof this observationwas put forward by Northrop et
al. [1974]' slippageof magneticfield lineswith respectto the Voyager
Observations
planet
implying
thattheplasma
motion
deviates
fromrigid Following
theJupiter
flybyswiththeVoyager
1 and2
corotation.
McDonald
eta/. [1979]foundfromparticle
spacecraft,
plasma
flowinthedayside
middle
magnetosphere
has
anisotropies
measured
by Pioneer10 thatoutside
of 45 Rj (1 become
betterunderstood.
Initialresults
frombothencounters
R•--71,398
kin),energetic
protons
(0.5- 2.15MeV)exhibited
confirmed
thattheplasma
moves
primarily
in thecorotational
anisotropies
inconsistent
withrigidcorotation.
(azimuthal)
direction.
However,
outside
of-10Rjthedata
from
In addition
to partial
corotation,
plasma
streaming
alongthePlasma
Science
(PLS)
experiment
indicates
that
theazimuthal
magnetic
fieldlines
wasobserved
inthemiddle
magnetosphere
of component
ofvelocity
becomes
almost
constant,
i.e.,theplasma
Jupiter
[VanAllenetal.,1974;
McDonald
etal.,1979;
Northrop
does
notrigidly
corotate
withtheplanet
[Bridge
etal.,1979b;
etal.,1979].In looking
attheenergetic
proton
(0.2- 20MeV) McNutt
etal.,1979;
Belcher
etal.,1980;
McNutt
etal.,1981].In
datafromPioneers
10 and11,McDonald
et al. [1979]foundaddition
tothesubcorotational
flow,Belcher
andMcNutt
[1980]
largeanisotropies
which
theydetermined
wereduebothtothe and
McNutt
eta/. [1981]
qualitatively
showed
thatplasma
flowed
effects
of partial
corotation
andtheeffects
of magnetic-fieldaway
fromthemagnetic
equator
onthedayside
andtoward
the
aligned
streaming.
A muchsmaller
anisotropy
wasapparently
equator
on thenightside
during
theVoyager
flybys.These
duetospatial
gradients
in particle
intensity.
A detailed
analysis
observations
areconsistent
withinferences
of Northrop
et al.
of 1.8-to 2.15-MeVprotondatatakenby Pioneer
10 was [1979]andMcDonald
et al. [1979]regarding
themotion
of
performed
byNorthrop
etal. [1979].Inonecase
theyassumed
higher-energy
particles.
Atthattimenoquantitative
information
thattheiondistribution
function
fo wasisotropic,
allowed
no onthemagnitude
ofthese
flows
wasreadily
available.
field-aligned
flow,andassumed
theelectric
fieldto be due Anisotropy
measurements
athighparticle
energies
bytheLow
entirely
to corotation.
In a second
case,f0 wasallowed
to be Energy
Charged
Particle
(LECP)experiment
suggest
thatthetrue
anisotropic,
andfinally,in a thirdcase,f0 wasagainassumed
situation
maybeevenmorecomplicated.
Carbary
eta/. [1981]
isotropic,
butparallelflowwasallowed.Theonlycasewhich interpreted
first-order
particleflux anisotropies
in the0.57-to
wasableto account
formostof theanisotropy
wasthatwhich 1.78-MeV
proton
channel
asbeing
duetobulkflowoftheplasma
assumed
parallel
flow.Theothercases
required
density
gradients(Compton-Getting
effect)andderived
bothspeed
anddirection
whichwereorders
of magnitude
toolarge(andsometimes
in the (in theLECPscanplane)of plasma
bulkflow. Theirresults
are
wrongdirection),
whilealmostno gradientwasneededff field- in goodagreement
withthePLSresults
in locations
wheregood
determinations
are availablefrom bothexperiments.In particular,
' iN0Wat Science
Applications
International
Corporation,
McLean,
Carbary
eta/. [1981]
confirm
theobservation
ofsubcorotational
Virginia.
Copyright
1988
bythe
American
Geophysical
Union.
flow within --20 R• of Jupiter and in the crossingsof the cold
plasma
sheet
along
theinbound
legoftheVoyager
1trajectory
(within -45 Ra of the plane0. Outsideof-20 Ra and away from
Papernumber7A9255.
the cold plasma locations,unambiguousvelocity component
0148-0227/88/007A-9255505.00
determinations
at all locations
arenotpossible
usingthePLSdata
85O2
SANDS ANt) McNtrrr:
Pt. AS•,
Ft•ow AT JUPITER
8503
alone. Carbary eta/.
[1981] find anisotropyamplitudesmorequantitative
lookat theplasmaflow.Previousstudies
in this
indicative of corotation when the anisotropydirection is regionusingthe PLS datadeterminedonly onecomponent
of the
consistent
with corotation.Theseconditionsoccurredalongthe convective
velocity(primarilytheazimuthalcomponent,
see,e.g.,
Voyager1 inboundtrajectoryfourtimesbetweenthelastinbound McNuttet al. [1981]). This studyappliesthetechniques
usedby
magnetopause
crossing
and--25 R• (referto theirFigure18). At Barnettand[1986] in analyzingdataobtainedduringthe Io flux
times of nonazimuthalflow, as determinedby the first-order tubeflyby to dataobtainedduringthedaysidepassof Voyager1.
anisotropy
direction,the flow tendsto be in the sunwarddirection Althoughwe find mostof theflow to be in the azimuthaldirection
(asprojectedinto the LECP scanplane),but thereis a greatdeal (and subcorotational),
the flow componentaway from the
of scatterin the direction.The Voyager1 anisotropy
amplitudesmagneticequatorcan have a magnitudein excessof 35% of the
alsoshowa-10-hour periodicity.
corresponding
azimuthalflow component.The cross-fieldflow
The situationat the time of the Voyager2 encounter
is even component
in thedaysidemiddlemagnetosphere
is typically<15
lessclear. Plasmavelocitiesdeterminedfrom PLS dataacquired km/sin magnitude.
between-10 and 17 R• inboundare sometimessignificantly Analysisof theplasmadatawasconfined
to thedaysidemiddle
below corotation and exhibit fairly large field-alignedmagnetosphere
owingto spacecraft
orientation
andan effectof
(antialigned)components
[McNutt et al., 1987]. A single plasma"temperature."
Withrespecttoorientation,
ontheinbound
spectrum
obtainedfurtherout (-22 R•) alsoshowsa smallerleg of thetrajectory
azimuthal
flow is seenprimarilyby theD
velocitycomponent
into the PLS sidesensor
thanwouldbe cup,andanynonazimuthal
flowis reflected
in theB andC cup
expected
onthebasis
of rigidcorotation
[Bridge
et al., 1979b].data.Outbound,
thespacecraft
wasoriented
sothattheD cup
First-order
anisotropy
measurements
fromtheLECPexperiment
pointed
northward
of theequatorial
planeandthesymmeUy
axis
wereonly available
in to -30 R•. Boththe amplitudes
and of themainsensor
pointedearthward
andwell awayfromthe
directions
areconsistent
withazimuthal
flowat lessthanrigid direction
forviewing
corotating
plasma.
Thevarious
cups
exhibit
corotation
speedon average
but with a greatdealof scatter(see currents
abovethenoiselevelin thisregion,anda determination
Figure 19 of Carbary et al. [1981]). Outboundfrom Jupiter, of plasmaflow during the outboundpassmay be possiblewith
viewing geometriesfor both the PLS and LECP instruments more work. However, the viewing geometry makes such an
usuallywerenot favorablefor determiningbulk flow velocitiesor analysismuch more difficult than that presentedhere and lies
anyof theircomponents.
beyondthescopeof thiseffort.
As longas the ionosphere
of Jupiteris not a perfectconductor With respectto "temperature,"
a spectrumis considered
"hot"
and plasmais flowing away from the planet,thereis a distance when the thermalvelocity is large enoughto yield an effective
beyond which the torque provided by the ionosphereis Mach numberM roughlylessthan5 (we defineeffectiveMach
insufficient
to impartenoughangularmomentum
to theplasmato numberas the ratio of the bulk flow into a particularcup to the
keepit corotating
with theplanet[Hill, 1979;Vasyliunas,
1983]. thermalspeedfor a given ionic component).In this case,the
The Voyager1 PLS observations
of deviations
from corotationindividualheavy ion peaksmakingup a spectrumbegin to
areconsistent
withinf•
ionospheric
conductivities
andplasma overlap,and,if the spectrum
is hot enough,onlyonelargebroad
production
ratesat Io [Hill, 1980].
peakis present(theprotonpeakremainsresolvedto lowervalues
Therehasbeenspeculation
aboutwhethertheLECP datafrom of M). Suchdata cannotnecessarily
be analyzedin a unique
the Voyager1 encounter
are alsoconsistent
with thispicture, fashion(the extentto whichthe parameter
determinations
are
considering
the apparent
"speeding
up" of the plasmato rigid uniqueis evendifficultto assess
in thiscase).However,if M > 5,
corotation
speedat largedistances
fromtheplanet.It is possiblethe individualion peaksaredistinguishable,
anduniqueplasma
thatthevariations
inferred
fromtheLECPanisotropies
aredueto parameters
caneasilybedetermined.
time-dependentvariations driven by changing solar wind
parameters
[McNuttet al., 1987] althoughthis is unlikelygiven
INST••
theperiodicities
notedin theinferred
flowspeed.Other ThePlasma
Science
(PLS)experiment
ontheVoyager
1 and
treatments
oftheLECPdatahave
tended
toconfirm
theresults
Voyager
2 spacecraft
consists
of twoplasma
detectors.
One
noted
above
[Brown
etal.,1985;
Paonessa,
1985],
although
the detector,
themainsensor,
ismade
upofthree
modulated-grid
details
aresketchy.
Thevariations
noted
by Carbary
et al. Faraday
cups,
theA,B,andC cups,
while
theside
sensor,
orD
[1981] could also be consistentwith the "inertial breakdown cup,consistsof one modulated-grid
Faradaycup. The symmetry
model"
ff thepoints
exhibiting
rigidcorotation
occur
at the axisof themainsensor
isparallel
totheaxisof thehigh-gain
magnetic
equator,
whileother
points
exhibiting
moredeviation
antenna
onthespacecraft
andthus
points
toward
theEarth,
except
correspond
tofieldlinescrossing
themagnetic
equator
atmuchforshort
periods
oftimeduring
some
spacecraft
maneuvers.
The
larger
distances
fromtheplanet,
duetothedistension
ofthefield normals
ofthethree
cups
ofthemain
sensor
aretilted
--20
øtothe
linesby the Joviancurrent
sheet(C. K. Goertz,privatesymmetry
axisandareequally
spaced--120
ø in azimuth
about
communication).
WhythePLSdatacorresponding
torelatively
thataxis.TheD cupnormal
is--88øtothesymmetry
axisandis
coldplasma
occurat locations
of intermediate
values
of the located
167ø
inazimuth
fromtheA cupnormal.
anisotropy-determined
speed
isnotexplained
bysuch
a scenario, Currents
duetopositive
ionsaremeasured
simultaneously
by
however.
Further
studyincorporating
detailed
comparisons
of allfourcups
in theenergy-per-charge
range
of 10- 5950V. In
flowparameters
determined
fromthePLSandLECPdatawillbe addition,
thesidesensor
measures
currents
dueto electrons
over
required
to determine
whether
thereis anobservational
versusthesame
energy-per-charge
range.
Thisrange
iscovered
byaset
theoretical
controversy,
and,if so,itsresolution.
Sucha studyofdiscrete,
contiguous
voltage
windows
which,
tofirstorder,
are
will involve
thedetailed
idiosyncracies
of bothinstruments
and spaced
logarithmically.
Whilemeasuring
positive
ions,thereare
theirrespectivedatasets;it is beyondthe scopeof thispaper.
two instrumentmodeswhich can be utilized. The low resolution
mode (L mode) breaks up the energy range into 16 voltage
Current
Study
windows,
each
withanenergy-per-charge
resolution
(AE/E)
of
The main result of the presentanalysisof the plasmadata -29%; the high-resolutionmode (M mode) has 128 voltage
obtainedby Voyager 1 in the daysidemiddlemagnetosphere
is a windows, each with an energy-per-charge
resolutionof -3.6%.
8504
Sn•)s •
McNtrrr:
I0
20
DISTANCE
(Rj)
25
20
i i i i i
.--
I5
I0
4.9
I
I
!
I
I
....
I....'....
i
i i i i i i i i i
15
1I
i i i i
4
In all, 44 spectralsetswere selectedfor analysis.Fourof these
were subjectedto slightly different initial guessesof the fit
parametersto verify the insensitivityof the final resultsto the
initial guessesin the nonlinearfitting procedure.Of the 44 sets,
11 were from the PLS L mode and 33 from the M mode.
In the
casesthat L modesetswere used,adjacentM modespectrafrom
the D cup were usedto determineinitial guessesfor the densities
and thermal speeds. In thesecases,the currentsin the B and C
cupsof the M mode were near the noise level, so the L mode
spectra,with their higher signal-to-noise
ratio, had to be usedto
determinethe flow velocities.Detailsaregivenby Sands[1987].
0.2
+
•
I•ASMA Fix)w AT JUPITER
o.o
'-" -0.2
MAXW•
0.4
-4
.........
I
1200
.....I •'.....
•..... II .....
I'1'1'1'
'
1400
LOCAL
TIME
1800
2400
VOYAGER
I
0200
I
]-IAN FITS
An indicationof plasmaflow can be foundfrom considering
the total particle flux into the variousPLS cups [Belcherand
McNutt, 1980]. For example, during the period of interestthe
currentsmeasuredin the B and C cups are not the same. In
Fig.1. Plotof thedifference
between
theB andC cupfluxdensities
FigureI thefractional
difference
in these
currents
(leftvertical
dividedby their sum from the Voyager1 encounter
with Jupiter. scale) is plotted against spacecraftevent time (SCET). The
Superimposed
onthisplotisthedistance
ofVoyager
1fromtheplane
of distance
indicated
atthetopof theplotistheradialdistance
from
the magneticequator. The samevariationin the observedion fluxe• as a
the centerof the planet,measuredin termsof Rj. Superimposed
functionof spacecraftmagneticlatitudewas foundduringthe Voyager2
encounter
halfayear
later.Reprinted
fromMcNuttetal.
[1981].
on thisplotis thelocation
of Voyager
1 withrespect
to the
magneticequatorialplane. Local time is shown on the bottom
scale. If one assumes the ion distribution functions are convected
During
theencounters
withJupiter
andSaturn
a complete
L mode Maxwellians,
the differences
in flux densities
can only be
takes3.84s to acquire,
whilea complete
M modemeasurement
accounted
for by a non-azimuthal
bulkplasma
flow.However,
takes30.72s. Eachmeasurement
sequence
lasts96 S,duringthese
differences
could
alsobeduetonon-Maxwellian
features,
a
whichcurrents
fromeitherthefirstorlast72energy
channels
of possibility
wediscuss
inthenextsection.
theM modearetelemetered
to Earth.Thusa complete
M mode Assuming
thedistribution
functions
of thevarious
ionspecies
spectralset is receivedat Earth every two measurement
are well approximated
by convected
isotropicMaxwellian
sequences,
i.e.,in 192s.Theconvention
adopted
hereforanalysisdistributions,
the spectraldatacan be analyzedin a manner
of M modesinvolves
producing
oneentiresetof M modespectrasimilarto thedatafromtheIo fluxtubepassage
[Barnett,1986].
(fromall fourcups)every192s by combining
channels
1 - 56 Onepositiveion spectxum
fromthisperiodwhichhasbeen
fromonemeasurement
sequence
withchannels
57-128 fromthe analyzedthis way is shownin Figure2; it was obtainedby
subsequent
sequence.
A moredetaileddescription
of the PLS Voyager1 on March4 at 2323 SCET. The spacecraft
was
experiment
isgivenbyBridge
etal. [1977].
ANALYSIS
TECHNIQUE
approximately
13.5Rj fromthemagnetic
dipoleaxisof Jupiter
and 1.06 R• abovethe magneticequator. The labelsA, B, C, and
D refer to the four cups of the PLS experiment. Currentsare
measured
in unitsof femtoamperes
(10
-•s ampere
=1
Once received,data from the PLS experimentduringthe femtoampere)
on the verticalaxis,whilechannelnumberon the
Voyager1 and 2 encounters
with Jupitercan be analyzedto horizontal
axisrefersto theenergy-per-charge
channels
discussed
determinecomposition,density,velocity,and otherpropertiesof above.
the plasma. Analysisof the data consistsof trying to duplicate The ions in the spectraare quite "cold;" i.e., three peaks
the currents measuredby the PLS experiment with currents representing
the heavypositiveions can be picked out as well as
calculatedusi.-.gan ,•,,.•o.o pro•ar.., given ....... n consffaints.the protonpeak. Five positiveion specieswere assumed(H+,
Thisanalysis
routineallowstheuserto choose
a modelfor the 0 +2,S+3,O+ (S+2),andS+) in the analysis;
the fit parameters
calculatedcurrentsand thenproceedsthrougha nonlinearleast includethethreecomponents
of theconvective
velocity(assumed
squares
fittingroutineto try to matchcalculated
currents
with thesamefor all of thevariousionicspecies)
VR, V,, and Vz,and
measuredcurrents.The algorithmusedis that due to Marquardt the five ion densities.The components
of velocityarereferredto
[Berington,1969].
a setof cylindricalcoordinates
in whichthe z axisis alignedwith
Even thoughmany spectracan be analyzedassumingthe the spinaxisof Jupiter.The protonthe•
speedwasalsoa fit
plasma distribution functions are convected isotropic parameter
withtheotherfourion thermalspeeds
determined
from
Maxwellians,thereare spectrawhichcannotbe duplicated
(i.e., the protonthermalspeed,assuminga commontemperature.
fit) using this assumption.For example,by assumingion Resultsof thefit are shownin Figure3. All thepeaksin theD
distributions
tobeisotropic
Maxwellians,
temperature
(pressure)
cuparefitquitew•ll,asarethelower
energy
channels
intheB
anisotropies
cannotbe taken into account.To investigatethe and C cups. We note that the assumptionof a common
possibilityof temperature
anisotropies
andtheireffecton fits to temperature
for the ions producesa good fit to the measured
the data, we modified and expandedupon the algorithm currentsin the D cup in whichthe variouspeaksare resolved.
developed
to analyzetheIo fluxtubedata[Barnett,1984;Barnett This sameassumption
hasbeenappliedthroughout
the analysis
and Olbert, 1986] to incorporate
the response
of the PLS presented
herein orderto (1) introduce
someconstraint
in the
detectors
to bimaxwellian
distributions.
Detailsof thealgorithm and(2) limit therequiredamountof computer
timefor doingthe
are given by Sands[1987]; a summaryis includedin the analysis.Whilewe havenot donea complete
mapping
of the
appendix.
consequences
of this assumption
in the corresponding
fit
SAI•S
Am) McNtrrr:
I•ASMA FCOW AT JUPITER
VO'fROEl=l
105
3PECTBRL
R-CUP
DR7R
105
B-CUP
•-10•I''
'I'''I'''I'''
•_ 10•1
z
z
••
8505
o
=
1 0•
102
lO p
0
lOs
•2
6•
96
CHANNEL NUMDE•
, I , , , I
0
128
32
6•
g6
CHRNNEL NUMBER
105
C-CUP
128
O-CUP
z
-•
03
•
1
• 03
_
102 i i i J i i mJ , i m J i i i
102
0
96
32
6q
CMRNNEL NUMBER
128
JUPITER
VOYRCER 1
CNRRGE DENSITY
ESTIMRTE
o
MAGNETOSPHERE
B = (33,997 , -22,288
=
(
[3.0302
32
6Lt
g6
CI-tRNNEL NUMBER
, -116,73q
128
> GAMMA
)
9?9 63 2323:t!.005
¾CUP = ( -1A.O?? , 59. 969 , 69.9q8
, 155.253
) KM/S
= t3,539
BHO(HRG) = t3,q97
Z(HRG) = [,063
R[O]D COROTRTION SPEEB = t69.915
Fig. 2. Spectraobtained
by Voyager1 onMarch4 at 2323 SCET. The spacecraft
wasapproximately
13.5R] fromthedipoleaxis
and1.06R] abovethe magneticequator.All the ion peaksarewell resolvedin theD cupallowinganunambiguous
determination
of thethermalcomponent
of theplasma.
parameterspace,we have done crosscheckson some spectra (only the lower energy-per-charge
channelswere usedin the B
whichindicate(1) thatthisis actuallya goodassumption
and(2) and C cups, althoughthe exact channelsused varied from
thatthevelocitydeterminations
areinsensitive
to thisassumption.spectrumto spectrum)nor "subtracting"
them out (their actual
We havealsobeenconservative
in our selectionof spectrato fit; contributionto the lower energychannelsis not known) should
i.e., we only usedspectrain which therewas at least a partial still result in a good velocity determination.
This is the most
resolutionof the heavyion peaksin the D cup. This approachconservative
approachknownat this time whichcan be usedin
allowedusto verifythatthecommontemperature
assumption
did thistypeof analysis.The signature
in the upperchannelsis the
indeedproduce
goodfitsto thedata.Furtherworkon theeffect subjectof an ongoingstudy;we do not anticipatea better
of suchassumptions
onlesswellresolved
spectra
thanthoseused understanding
of the originof thesecurrentsto changethe
in thisstudyis in progress.
analysis
results
presented
here,however.
Thesignalpresent
in theupperchannels
of theB andC cups Analysisof the spectral
setshownin Figure3 yieldsa bulk
andin theA cupmaybe dueto a hotionbackground;
it is also plasmaflow of V = -4.5 $R+ 139.7$, + 16.7$,. km/s (again
present
in thecurrents
in theD cupat highenergies
andbetweenreferred to a Jovicentriccylindricalcoordinatesystem).
the protonand heavyion signatures.
This background
ion Velocities
obtained
through
theanalysis
of similarspectra
from
population
was not fit for two reasons:First, it doesnot thisregionareshown
in Figure4, whereeachvelocity
component
significantly
affectthevelocitycalculation,
andsecond,
it is very (in kin/s) is plottedagainstspacecraft
eventtime (cylindrical
hardnumerically
to takethishotionbackground
intoaccount,
as radialdistance
fromthemagnetic
dipoleaxisis shownacross
the
its composition
anddistribution
functions
arenotknowna priori. top). There are two majorresults.First is the reconfirmafion
It is also possiblethat someof this signalmay be due to (usingthefull response
functionof thePLS instrument)that
the
contamination
by thehotelectron
population
present
at thistime. plasmadeparts
fromstrictcorotation
aboutJupiterasonemoves
Suchcontamination
is similar to that of the ions on the electron out from the planet. McNutt et al. [1981] originallynoted that
measurements
obtainedin the warm Io plasmatorus(see the the plasmastartsto departfrom corotationat leastas closeas
appendix
of SittlerandStrobel[1987]). A full discussion
of this -10 Rj to Jupiter,but thatanalysisusedonly D cupspectrafrom
effectis complexandbeyondthescopeof thispaper.Regardlesswhicha velocitycomponent
normalto the D cup wasobtained
of whichof theseis the sourceof the currentsin the higher and shownto be inconsistent
with the rigid corotationof the
channels,
weexpect
themto produce
currents
thatincrease
with plasma.Utilizingthefull response
function
to derivethefull
increasing
energy-per-charge
andto contribute
aboutequally
to convective
velocity
vectorleadsto thesecond
majorresultthat
all cups.Giventhatthepeakcurrents
in theB, C, andD cups thereis a substantial
nonazimuthal
plasmaflow component.
(whichcontribute
the mostto the determination
of the flow Againwe notethat this featurehad beenshownto exist
velocity)are abovethe measured
currentlevelsin the highest qualitatively[Belcherand McNutt, 1980;McNutt et al., 1981],
channels,simplyneitherincludingthe latter currentsin the fits butthemagnitude
remainedunknown.The observed
velocitiesof
8506
SA•n)S A•n) McNtrrr:
RB50:
1135
MRXNELLIRN
[
[
i
[
!
9IMULRTION
R-CUP
,
[
i
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]
,
I•ASMA
FLOW AT JUPITER
Vl
JUl =ITEM
RT
ON
105
[
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z
io
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102
32
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96
CI-IRNNEL NUMBER
0
0
128
32
6q
96
CHANNEL NUMBER
V:<-q,q6?,]39,673,16,G9q>
R.Z =
1.1
KM/S
t6.2
BCYL:(33,99?,-22,288.-Lt6,?3•>
32.3
[6, t
32, t
N(CM-3>
NPER =
1.4620
13.96
.9530
9.87
9.8?
NPRR =
=
1.2170
55.8•
55.8q
t3.96
8.8892
[3.96
[3,96
128
ORMMR
1.07tO
9.87
9.8?
Fig. 3. Currants
calculated
for the spectra
of Figure2, assuming
thatthe ion distribution
functions
am convected
isotropic
Maxwellians.
Thesimulated
currents
amsuperposed
onthespectral
dataforeasycomparison.
Calculated
currents
duetoeachion
species
am shownby the individual
peaks.Fit parameters
am shownin the lowerpanel(velocity
andthermalspeedin
kilometers/second,
densitiesin number/cubiccentimeter).
up to -50 km/s(20.5 km/s= 1 R•/h) suggest
thatthisflowcannot component.The magnitude
of thiscomponent
rangesfrom about
be ignoredin considering
magnetospheric
dynamics.
halfto all of themagnitude
of thetotalnonazimuthal
flow.
Insteadof usinga Jovicentric
cylindricalcoordinate
system,
the
A second
pointmadein Figure5 concerns
thedirection
of flow.
magneticfield(obtained
fromtheVoyagermagnetometer)
andthe From -13 R• to 18 R• the flow is consistently
away from the
plasmabulkflow velocitiescanbe transformed
to a tilteddipole magnetic
equator.Two spectral
setsanalyzed
in thevicinityof 20
cylindricalcoordinate
system(baseduponthe dipoleaxistilted R• andone at -25 R• alsofollow thistrend(the analysisresults
9.6ø to the rotationaxis and pointingtoward the systemIII from -25 R• are indicatedon Figure4 but not on Figure5).
longitude
of Xm= 201.7ø, thedipolefromtheOnmagnetic
field Generallyunfavorable
viewinggeometryand lack of resolved
model [Acuhaet al., 1983]). With the velocitiesand magnetic peaksandconstraints
on availablecomputation
•
precludeda
fieldgivenin thissystem,it is easierto visualizehowmuchof the moredetailedanalysisin the regionbetween25 R• and 18 R•,
nonazimuthal
flow is field-aligned
and how muchis cross-fieldalthoughthe spectrain this regionare qualitativelysimilarto
flow. To makecertainonlytheeffectof thenonazimuthal
flowis thosethreesetssubjected
to analysis.For the analyzedspectral
seen,a frameof reference
whichmoveswith theazimuthal
flow setswe foundthatwhenthe spacecraft
is above(northof) the
component
(i.e.,in whichV, = 0)is chosen.Usingtheradialand equator,flow is to the northand whenbelowthe magnetic
axial components
of the parallelandperpendicular
flows(i.e., equator,
observed
flowis in thesouthern
direction.
Thesimilarity
VliR,
Vii
' , V•n,Vt,) andtheradial
andaxialcomponents
ofB,we withthepattern
inFigure
1isobvious.
However,
inside
of13R•
constructed
Figure5. The wavy line is a projection
of the theflowis stilltowardthenorthandhencetowardtheequator,
Voyager1 spacecraft's
trajectoryonto magneticmeridionaleventhough
thespacecraft
is atsouthern
magnetic
latitudes.
Tbe
planes,with ZMAG beingthe distance
aboveor belowthe slightupward
deviation
at thistimein therelative
fluxshown
in
magnetic
equator
andRMAG thecylindrical
distance
fromthe FigureI mayreflectthischange
in theflowpattern,
although
it
dipoleaxis;bothdistances
are in unitsof Jovianradii. The emphasizes
thedifficulty
in tryingto derivea sense
of theflow
poloidal
(nonazimuthal)
component
of themagnetic
fieldforeach fromthedatashown
inFigure1 alone.
spectrum
is represented
by the dashedarrows.Solid arrows The cross-fieldcomponentof the flow also exhibits
represent
the nonazimuthal
component
of the bulkplasmaflow peculiarities.
Fromapproximately
15 R• to 25 R• thecross-field
obtained
foreachplasma
spectral
set.Thereareseveral
importantflowis awayfromJupiter,
whilebetween
11R] and13R] theflow
features
of Figure5 tonote.
is towardtheplanet.In therange13R• to 15R• thecross-field
An importantfeatureis the size of the field-aligned
flowisverysmallandoscillates
backandforthawayfromJupiter
(antialigned)
portionof the flow. Everyspectral
setanalyzedandinward
toward
theplanet.
givesa flowwhich
yields
a significant
field-aligned
(antialigned)Themagnitudes
ofthefield-aligned
andcross-field
components
SA•rDSA•rD McNtrrr: PLAs•
FLOWAT Jimm
8507
RMAG Rj
24
22
0
¾•
(•/,)
20
16
....................
14
12
'"-----'.......
--
-20
18
.....
•
•
•
'
•
i
••
t;'
'.
ß
ß. '
ß_
-•0 • •
_
300
•
--
_
V•
_
Z .
----
(•m/,) 200
Z
.....
'.
! ß '.
.
_
.....
--
....
ß
•
•
..
.
-
• •
50
.......... -
tl •
_
Vz
0
•..................
;........
-50
-I
I
I
I
I
I
I
I
I
I
I
I
I
I
[
1300
I
I
I
I
I
t
1800
I
I
•
I
I
0000
63
64
SCET
Fig. 4. Plas• b•k flow vel•ifi•
(in cyliMfical c••tes),
•in•
••
•e analysisplowedag•nst s•cmff
•e d•t• linein•e plotof •imu•al vel•ity,Ve,•pr•ents•e 1•1 •gid•fional
andV, •p•nt
•
vel•ity •m•nent. •e e•r ba• iMi•te •e f•l
1• e•
dis•n• f•m •e dixie •s •AG is •o•
a•ss •e topin u• of Jovi• •ii;
owingto •e s•c•fi
s•
a• •e w•bling m•i• • •e •gnetic •is.
vel•ity,while•
eventtime.
in•e plusof V•
in •e• •me•.
•e cylin•c• •dial
s•ing •tw•n •e dis•n• •e•
v•es
are comparableto thosefound by McNutt et al. [1987] for the fit, it is not clear a priori what would be the effect of a thermal
Voyager2 encounter.The regioninvestigated
for theVoyager2 anisotropy
on theotherfit parameters.
encounter
(10.1 R• to 16.7R•) is similarto thatstudiedhere,but
To determine
whetherthededuced
nonazimuthal
component
of
that analysiswas less detailedand was performedon fewer plasmaflowis, in reality,a manifestation
of a thermalanisotropy,
spectra
owingto limitations
of thedata.
selected spectra were reanalyzed,allowing parallel and
perpendicular
thermalspeedsto vary independently.One of these
reanalyzedsets of spectrais that one shown in Figure I (the
Although our simulationsof the data indicate that the Maxwellian simulationto this set was presentedin the previous
suprathermalions (and/or electron contamination)should not section).
affectthedetermination
of the convectivevelocityfor the spectra In this analysis,the simulationalgorithm outlined in the
BIMAXWEU.IAN
FiTS
30
20
-30
12 o
13 o
140
150
160
170
180
190
20 0
RMAG( Rd)
Fig. 5. A vectorplotof thecalculated
nonazimuthal
component
of theplasmabulkflow andassociated
magnetic
field. A tilted
dipolecoordinate
system
is used,whereZMAO is thedistance
thespacecraft
is aboveorbelowthemagnetic
equator
andRMAO
thecylindrical
radialdistance
fromthedipoleaxis. Theplacement
of thevectors
corresponds
tothespacecraft
location
atthetimes
of theassociated
spectra.Magneticfieldis represented
by thedashed
arrows,whilethesolidarrowsindicatethenonazimuthal
bulk
plasmaflow.
210
8508
SAtes At• McNtrrr: Pt.ASMAFLOWAT Jm'rrw
BILRB:
105
BIMRXNELLIRN BIMULRTION •
,
i
!
i
i
R-CUP
i
i
i
i
!
ON 1979
105
l
z
••
V1 RT JUPITE•
1 0•
z
10
%
•
103
83
2323:11.005
B-CUP
lO2
0
lo s
32
6u•
96
CHRNNEL NUMBER
126
c-cuP
o
32
6•
96
CHRNNEL NUHOER
1oS
128
D-CUP
10q•'
''I'''I'
lO2
0
102
32
6•
96
CWRNNEL NUMBER
128
o
32
6q
CHANNEL
96
128
NUHBER
Fig.6. Result
ofafit,assuming
theiondistribution
functions
arebimaxwellian,
tothespectral
setshown
inFigure
2. There
isvery
little difference
betweenthis fit and the fit assuming
convected
isotropic
Maxwellianion distribution
functions.Totaland
individual
ioncurrents
aresuperposed
onthespectra.
Thecorresponding
fit parameters
are,forH+,O++,S+•, O+ (S•), andS+,
density
(cm-3):
1.63,
1.39,
0.91,
8.34,
and
0.93;
perpendicular
thermal
speed
(knVs):
56.89,
13.59,
9.61,13.59,
and9.61;
parallel
thermalspeed
(kin/s):190.97,40.87,28.9,40.87,and28.9,respectively.
appendix
wasemployed.
The samefit parameters
as in the velocity
of V=-4.8 •R+140.10++16.9t•,km/s.These
values
Maxwellian
casewereused,butnowtheprotonparalleland canbe compared
withthosefromtheisotropic
MaxwellJan
fit
perpendicular
thermal
speeds
areallowed
tovaryindependently
shown
in Figure3 for whichV =-4.5 $R+ 139.7•, + 16.76,
andarefit independently
of theheavyions,whichareassumed
to km/s.Thedifferences
in thesetwosetsof components
arewithin
havecommon
values
of TllandTñ. Thischoice
wasmadetolimit the1-sigma
formalerrors
forthefits.
the numberof fit parameters
while still allowingfor an Thisresultis typical.Theorientation
of thecupnormals
with
assessment
of the effectof an anisotropy
in theplasma.Results respectto themagneticfieldis suchthatfor mostof theencounter
of thisfit areshownin Figure6. The fit currents,
assuming
a periodthe distribution
functionsare being "sliced"mostly
convectedbimaxwellian,are practicallyidenticalto those perpendicular
to themagnetic
field. As a consequence,
boththe
obtained
in theconveered
Maxwellian
fit. Theonlydifferencesconvective
velocityand w1 are well determined
if the ion
showup in thelastfewchannels
of theB cupandasa slightlyconvective
flow into at leastone of the cupsis large in
largersignalin theA cup.Otherspectra
analyzed,
assuming
both comparison
to thethermal
widthtowhichthecupis sensitive.
As
a Maxwellian
anda bimaxwellian
iondistribution
function,
yield thisunambiguously
fixesonevelocity
component,
a combination
similarresults.
Thisexample
is shownbecause
it exhibits
the of thethermal
speeds
(mostly
wñ)andthedensities,
theallowed
largestdeviation
between
thetwocasesandthusprovides
an variation
in theothervelocity
components
withrespect
to the
upperlimit to anisotropies
in thethermal
plasma
in theregionmeasured
currents
in theothercupsis severely
constrained.
The
investigated.
Because
thehotionbackground
wasnotsimulated,spectralsets fit were selectedto take advantageof these
the effectof the fittingprocedure
is to increase
the parallel constraints
soasto yielda gooddetermination
of theconvective
temperature
to account
for thesignalin theupperchannels
of the velocityvector.
B andC cups.However,
owingtotheorientation
of thecups,
the Of all thespectra
sentbackby Voyagers
1 and2 duringthe
currentcalculated
in theA cupserves
asa checkonthemaximum Jupiterencounters,
only one spectralset to date has been
anisotropy
allowed.
A further
increase
inTiIcauses
thecalculated
identified
aspossibly
exhibiting
a truetemperature
anisotropy
in
current
intheA cuptoovershoot
theactual
measured
values,
thus an unambiguous
way. Thespectral
setshown
in Figure7 was
limitingthe anisotropy.This "simulated"
anisotropy
givesan obtained
by Voyager2 on July9, 1979,at 0720 SCETwiththe
upperlimitof theratioTII/T1 = 9.0 for theheavyions(herethe spacecraft
14.9R.•from the dipoleaxisand2.9 R.•belowthe
thermalspeedsfor the protons,fit separately,
yieldeda higher magnetic
equator(in theregionof theplasma"voids;"seeMcNutt
ratioof 11.3). An important
pointto noteis thattheformalerrors et al. [1987]). Becausethe spectraare so hot, the individual
in w1 aresmall,-1.8%, whilethosein w, arelarge,-14% (1- peaksof theheavyionsall mergeintoonebroadpeak.The
sigmalevel;formalerrorsin theprotonfitsarehigher).The proton
peak,however,
is stilldiscernible
in allfourcupsandcan
computed
valueforTIIITñranges
between
12.1and6.5at theI- thusbeused
toyielda bulkplasma
flow.Fitparameters
consisted
sigma
level.At thesametime,thecalculated
bulkplasma
flow of theproton
density,
thermal
speed,
andallthreecomponents
of
waspractically
identical
tothatfound
intheMaxwellian
case;for thebulkplasma
flow.All fourcups
wereused
intheanalysis,
as
theconvex:ted
bimaxwellian
distribution
weobtained
aconvective
theproton
signature
iseasily
discernible
ineachcup.Thebestfit
SAbreS
•
McN•:
PLASMAFLOWnT JtwrmR
VOYAGER SPECTRAL
10•
A-CUP
8509
DATA
10•
,
, , i ,
B-CUP
, , i , , , i , ,•-•:
_
_
•!iiIiiii,iiIiiiI
L• 103•
z
• •o•
102
0
102:
32
6•
CHRNNEL
10•
96
128
C-CUP
I
10• z,
I
, , I '
'
D-CUP
' I ' '
'
I '
128
'-•
_
z
•
32
6q
96
CHRNNEL NUMBER
0
NUMBER
z
103
•
102
0
103
102
32
6q
96
128
•,
0
CNRNNEL NUHBE•
JUPITER
VOYt4C,
EIB 2
• I ,,,
I,,,
1,,,
32
6q
96
CHRNNEL NUMBEF•
128
MRGNETOSPHERE
B = (-8q.807
CHRBC,
E DENSITY ESTIMRTE = ( 2.716 )
, 1•.083
, -85. 681 ) C,RMMR
1979 190 0720:10.078
VCUP = ( 32.516 , 102.926 , 117.136 , 155.665 ) KM/S
lB = 1S.177 BHO(MFtGNETIC)
= lq.893
Z(MRGNET1C)=-2.92•
FIIGID COFIOTRTION
SPEED= 190
Fig.7. A spectral
setobtained
ontheinbound
portion
oftheVoyager
2 encounter
withJupiter.
Voyager
isabout
14.9R•fromthe
dipole
axisand2.9Rffbelow
themagnetic
equator.
Because
theplasma
temperature
ishigh,onlytheproton
peak
isresolved
inthe
fourcups(indicated
bythearrows).
Reprint
fromMcNuttetal. [1987].
from the analysis,assuming
a convected
MaxwellJan
ion i.e., thedetermination
of theflowvelocityis decoupled
from
distribution,
cannotsimulate
the currents
corresponding
to the thermal
anisotropy
in thedistribution
function.
protonpeakin all fourcupssimultaneously.
Results
of thisfit are
shownin Figure8. Thisinabilityto fit thesignatures
in all of the
cupssuggests
thata convected
bimaxwellian
distribution
might
DISCUSSION
yield a betterdescription
of the data. Usingthe samefit FlowDirections
parametersas before but now allowing the parallel and Most of the nonazimuthal
velocityis field aligned.The most
perpendicular
thermalspeeds
to varyindependently
givesthefit notable
exceptions
to thisareexhibited
bythespectra
fromearly
shownin Figure 9. Allowing the paralleland perpendicular
onday64 andthespectra
duringhour18onday63. Buteven
temperatures
to floatindependently
greatlyimproves
thefit in all
thesespectra
generally
showa Viicomponent
whichis greater
fourcupsandgivesananisotropy
of Tll/Tñ= 3.08+ 0.4. Thebulk
than
the
V
1
component.
Except
for
the
magnetic
equator
crossing
velocity is V = - 44.2•s + 151.44, - 48.1$, kin/s, which
includes
anonazimuthal
component
offlow
much
larger
than
in just
before
day
64,thesign
change
ontheparallel
velocity
the
Maxwellian
case.
However,
the
formal
errors
are
much
larger
component
seems
tobeagood
indicator
ofthe
spacecraft
crossing
intheformer
case,
reflecting
theobviously
"bad"
fittothethe
magnetic
equator.
Asnoted
above,
prior
tothe
crossing
ofthe
magnetic
equatorial
plane
near-13R•wefindthatwhen
Voyager
spectra.
is above
themagnetic
equator,
theflowis anti-field-aligned,
i.e.,
It is important
to notethatanother
explanation
of thissignature
towardthenorthmagnetic
pole,and,whilebelowthemagnetic
could be an isotropicMaxwelliancombinedwith a negative
theobserved
flowis fieldaligned.
Thistrenddoes
not
spacecraft
potential
accelerating
ionsintoall fourcups.Fromthe equator,
holdwithin-13 R• butdoesholdfortheisolated
pointnear25R•.
position
of theprotonpeakin theA cupa potential
of lessthan
oftheparallel
flowcomponent
isshown
inFigure
100V in magnitude
maybe capableof producing
thesignature,Themagnitude
10;
the
component
of
plasma
flow
along
the
magnetic
fieldis
but full consideration
of this possibilityis beyondthe scopeof
thispaper.
plotted
versus
thetotalnonazimuthal
flow. Forreference,
a
dottedlinehasbeendrawnrepresenting
thelocusof pointswhere
Two important
resultsfollowfromthebimaxwellian
analysis:
the
magnitude
of
Vii
equals
the
magnitude
of the total
(1) the thermalcomponents
of the magnetospheric
plasmaare
nonazimuthal
plasma
velocity.
The
magnitude
of this
well approximated
assuming
a convected,
isotropic
MaxwellJan
flow reachesalmost50 kin/s,whichtranslates
to
distribution
for the ions,and(2) the nonazimuthal
flowsobtained nonazimuthal
2.5 R•/h.Theisolated
pointnear25 R• (not
usinga Maxwelliandistribution
are real and are accuratelyapproximately
exhibits
a parallel
velocity
component
of 68km/sanda
determined.As a final note, for the spectraof Figure 7 the shown)
component
of 74km/s.It isinteresting
tonote
nonazimuthal
flow component
occursalongwith the anisotropy, totalnonazimuthal
8510
SAntOsA•rO McNtrrr:
AB50'
MAXNELLIRN
lO•
SIMULATION
,
PLASMA FLOW AT JUPIT!•R
V2
FIT
JUPITER
ON
1979
10•:
lq-CUP
190
0'720:10.078
B-CUP
_
_
_
_
z
z
lB
• 103
lO2
102
%
_
0
:32
5LJ,
CHANNEL
tO•
96
0
128
32
6L•
CHANNEL
NUMBER
lBt
C-CUP
'
'
'
I
'
'
95
B-CUP
'
128
NUIdBEB
I
'
'
'
I
'
'
'-_
_
_
_
z
1o2
lO2
0
32
BE,
96
CI-IlqNNEL NUMBER
V=<-t9,660,1q?,390,-3t,ttl)
0
1_28
128
32
6d,
98
CHANNEL NUMBER
KM/S BCYL=(-8•.8O?,tq.083,-85,681)
ORMMR
A,Z =
N(CM-3)
=
.8700
NPER =
NPRR =
8•.g?
84.97
Fig.8.Result
ofafittothespectra
ofFigure
7,assuming
theiondistribution
functions
tobeconvected
isotropic
Maxwellians.
The
analysis
iscarried
outfortheprotons
only.Currents
from
allthecups
could
notbewellsimulated
simultaneously.
thatthe largestnonazimuthal
flowsalsotendto be the mostfield
aligned. The ratio of the plasmaflow alongthe magneticfield to
the azimuthal flow is plotted againstcylindrical radius (tilted
dipole coordinates)in Figure 11. Parallel flow is seen to
BILFIB:
BIMRXNELLIRN
10u
5IHULRTION
,
contribute
significantly
to theoverallplasmaflow (azimuthalplus
nonazimuthal)throughoutthe middle magnetosphere.
Ratiosof
0.2 and over are not uncommon.By contrast,the magnitudeof
the perpendicular
flow component
is muchsmaller. Figure 12
V2
FIT JUPITER
lq-CUP
ON
1979
190
0'720:10.078
B-CUP
10•
'''
I'''
I
'
'
'
I
'
'
'
z
lO2
lO2
0
:32
BLl
CHRNNEL
lOq
-i
i
i
I
'
'
96
o
NUMBER
C-CUP
'
128
I
I
I
I
I
'
'
32
6Ll
96
CHANNEL NUMBER
lO,j.
'-
128
D-CUP
_
_
_
z
z
,,, 102
lo
lO2
lO2
o
32
BE,
96
CI-IIqNNEL NUMBER
V=<-qq,233,15t,q36,-gB,
A,Z =
],•
N(CM-3)
NPER =
NPRR :
=
t21)
128
KM/S BCYL=<-8K.807,
o
32
6'..1
96
CHANNEL NUMBER
tq.083o-85,681)
128
GRMMR
.8•00
78.22
]37. t9
Fig.9. Result
ofafittothespectrum
ofFigure
7, assuming
theproton
distribution
function
tobeabimaxwellian.
Onlytheprotons
arefit, and,unlikethosein theMaxwelliancase,thecurrents
fromall fourcupscouldbe simulated.
SANDS AND MCNUTr: PLASMA FLOW AT JuPrml•
8511
5O
•
•
40
30
ß
ß
--
o
_
>
Eo
ß
--
--
ß
--
--
ß
-
....
....- ß
--
ß
-
_
•
ß
lo
ß
ß
__
ß
ß
ße
_
...
10
20
non-azimukhal
30
40
50
ß
o
veloeiky (km/see)
12
lO
14
16
magnetAc cylindrical
18
20
radius
Fig. 10. Plasmaflow along the magneticfield is plottedversustotal
nonazimuthal
flow. Sinceparallelflow is contained
withinthe Fig.12.Ratiobetween
perpendicular
plasma
flowandazimuthal
flow
nonazimuthal
flow,
Viican
never
exceed
themagnitude
ofthenonazimuthal
versus
cylindrical
radial
distance.
Perpendicular
flowdoes
notcontribute
flowcomponent;
thedotted
linerepresents
thiscutoff.
significantly
totheoverall
plasma
flow(azimuthal
plus
nonazimuthal).
Implicationsfor CorotatingConvection
showsthat the ratio of this componentto the azimuthalflow never
At Jupitera convectionsystemhasbeenproposedby Hill et al.
exceeds-0.2 andaveragesonly -0.06.
opticalobservations
Radial transportof plasmathroughthe magnetosphere
can be [1981] which would explainthe Earth-based
inferredby consideringthe radial componentof the cross-field of a significantlongitudinal asymmetryin the plasma torus
flow,Vi•. Thedatashowtheoccurrence
of bothinflowand associatedwith Io. This asymmetryis in the form of enhanced
collisionally excited emission lines of singly ionized sulfur
outflow. For the mostpart, spectraduringday 63 exhibitoutflow,
[Pilcher and Morgan, 1980; Trauger et al., 1980]. This
while duringday 64 thereis a substantial
inflow. Time-dependent
convection system hinges on the magnetic anomaly in the
upstreamsolar wind conditionscould accountfor this effect.
northernhemisphereof Jupiter centerednear the System III
Duringa periodof increasedsolarwind ram pressure,
the dayside
magnetosphere
would compress,giving rise to inward plasma
flow. Subsequently,outflow would follow as the ram pressure
decreased. McNutt et al. [1987] found by extrapolating
measurements
madeupstream
by Voyager2 to Voyager1 thatthe
ram pressurewas at a maximumon March 2 (day 61) and
generallydecreasedafterward. Voyager was deep within the
magnetosphere
duringday 64, so the effectof a decreased
solar
wind ram pressuremay not havebeen"felt" yet (thusthe inward
flow), while furtherout,themagnetosphere
wasinflatingowingto
the decreasein ram pressure.
longitude•n = 260ø [Acuhaet al., 1983].
The proposedconvectionsystemis fixed in the Jovianframe
of reference becausethe magnetic anomaly, which drives the
system,corotateswith Jupiter.The regionof the magnetosphere
connectedto this anomaly is known as the active sector, and
spansabout 100ø in longitudecenterednear Im= 225ø [Hill et
al., 1981; Vasylitomsand Dessler, 1981, andreferencestherein].
Using plasma velocitiesobtainedthrough this analysis,the
corotafingconvectionmodel for plasmatransportcan be directly
tested. The plasmadata which were analyzedcover a period of
time duringwhich the spacecrafttraversedthe activesectortwice.
The first crossingof the active sector began shortly after the
spectralseton day 63 at 0841 SCET andendedbeforethe spectral
seton day 63 at 1527 SCET. The secondtraversalcorresponds
to
the spectraacquiredfrom day 63, 2103 SCET to day 64, 0025
SCET.
oo
e el ß
ß e
ß
ß
ß
ß
ß
ß
ß
ß
ß
ß
ß
ß
10
ß
12
14
16
ß
ß
18
No
definite
conclusion
can be made
about the radial
outflow during the time of the first active sectorcrossing;no
spectrawere analyzedduring this time owing to the lack of
identifiablepeaks and/or sufficientflux in at least three of the
cups. Many spectrawere analyzedduringthe secondtraversalof
the activesector,however,and a surveyof the resultsshowsthat
both outflow and radial inflow occurred. Also, the spectrawith
the largestradial outflow (betweenday 63, 1819 SCET and 1903
2O
SCET) do not lie within the active sector.
Theseresultsare contraryto thoseof Hairstonand Hill [ 1985]
(see also Hairston [1986]), who derived radial velocity
componentsfrom magneticfield signaturesand the basic MHD
equations.Their cleanestresultswere obtainedfor the samethree
magnekic cylindrical radius (Rj)
inboundmagneticequatorialcrossings
coveredby thedatausedin
this
study.
Table
1
lists
the
radial
plasma
flows obtainedat each
Fig. 11. Ratio betweenparallelplasmaflow and azimuthalflow versus
cylindrical
radial
distance.
Parallel
flowisseen
tocontribute
significanfiy
of thecrossings
andthecorresponding
values
determined
from
totheoverall
plasma
flow(azimuthal
plusnonazimuthal).
thisanalysis.Crossings
A andC arein the activesectorwith the
8512
SnNos •
McN•:
TABLE 1.
Crossing
A
Time,
Day of Year,
SCET
Time Range,
Day of Year,
SCET
63 1408
PL•MA
FLOW AT Jta, rma
Compari•n of RadialVelocities
Hairstonand Hill [1985] Values
AverageVelocity,km/s
Velocity Range,km/s
63 1201
PLS Measurements
AverageVelocity, km/s
Pointsin Range
0.052 4- 0.38
2
11.28 4- 7.08
12
-2.18 4- 7.86
26
26.4
to
B
63 1914
63 1633
(17.4- 35.2)
63 1754
12.9
to
63 2059
C
64 0005
(9.1-
63 2154
15.0)
33.6
to
64 0213
(22.5 - 47.9)
corresponding
timeslisted. The samplingtime intervalfor each
crossingis also shown. The range of velocitiesobtainedby
Hairston and Hill [1985] are given in parentheses,
while the
preferredvalueis listedabovethem.For the two crossings
inside
theactivesectorthe flowsareradiallyoutwardandlargerthanthe
value obtainedat crossingB (which is not within the active
other two crossingsclearly are not (althoughour determination
for crossingA is probablynot well determined;see discussion
above).
During the outboundleg of the encounter,Hairstonand Hill
[1986] identifiedregionsin which an inflow of supercorotafing
plasmais expected.This expectation
is basedupontheobserved
sector).The valuesquotedfrom thisanalysiswereobtainedby progradespiral in the magneticfield lines [Hairston,1986;
takingthevaluesof Vi• andaveraging
themoverthesamerange HairstonandHill, 1986].Although
almostall of thePLSspectra
for eachcrossing
(for thespectralsetswith severalfits,thevalue obtainedoutbound
cannotbe fully analyzedin an unambiguous
of the velocitycomponentfrom the best fit was used). The way, therewasone spectralsetfrom whicha velocitycouldbe
averagevalueobtained,standarddeviation,andnumberof points obtained.This set was obtainedon day 64 at 1942 SCET at
usedin computingthe averageare alsoshown. While thedirectly which time the spacecraftwas 9.3 Rj from the planetand about
measuredvaluefrom crossingB is consistent
with thoseobtained 0.3 Rj below the magneticequator;it is shownin Figure 13.
from the analysisof the magneticfield data,the valuesfrom the When analyzed, this set did yield an inward radial flow
¾O'fACEI•
108
,
,
,
i
,
,
R-cuP
,
i
,
,
,
i
,
,
3PECTBRL
105
105
z
m 1 Dq
c_)
•
lo •
103
lO 3
32
Bgl
96
CHANNEL NUMBEB
o
o
128
-,•,,I•,
1oB
-
32
6LI
CHRNNEL
C-CUP
lO6
lOS
B-CUP
1oB
,
z
z
OA7A
I---
!
g6
128
NUMBER
D-CUP
'''
l'''l
'''
I'''
1oS_
z
.
-•
c•
i
•
0•
104
z
_
lO3 ,,,
103
0
32
C•NN•L
Bq
96
NUMB[g
o
128
1,,,
32
1,,,
6q
CNRNNEL
1,,,
9B
128
NUMBER
JUP I'I'ER MFtGNE'TOSPHERE
B = (-68.,.t53
VOYIqCER I
CHRRC.,E DENSITY
ESTIMI::ITE :
( 9q.8182
, ?,J,.,.tlO , -q09. ?29 > OAMMfl
)
]9?9
6q ]9q2:30.N]]
VCUP = ( -?•.85q
, -39.99q
, -2].562
. 88.9?5
) KM/5
R = 9.3q3
RHO(MRG) = 9.339
Z(MAG) : -.280
RIGID COROTRTION SPEED : 117.259
Fig. 13.A spectral
setobtained
on day64 at 1942$CET duringtheoutbound
legof theVoyager1 encounter
withJupiter.At this
timethe spacecraft
was9.3 Rfffromtheplanetandabout0.3 Rffbelowthemagnetic
equator.Thissetis uniquefromtheoutbound
passin thatresolved
peaksarepresent
in theD cup.
SANDS A•D McNoTr:
Pt,AS•
Ftx)w AT luPrm.•
8513
(Va=-7.4 kin/s),however,the azimuthal
velocityof V, = 115 estimatedfrom pressurevaluesat severalcrossings
of the
km/s is slightlyless than the local corotationalvelocityof (assumed)symmetry
surfaceof themagnetic
field[McNutt,1983;
V,= 117 lcm/s. This one set of spectrayields an azimuthal McNutt,1984;MaukandKrimigis,1987].
velocitycomponent
closerto corotationthan thoseobtainedat
One possibleexplanationfor the lack of agreementbetween
similar distances inbound; however, the plasma is not inward and outwardstressesis the neglectof possiblefieldsupercorotating.
A hybridmodelproposedby Hill et al. [1982] aligned flows [McNutt, 1984; Mauk and Krimigis, 1987]. If
which combinescorotatingconvectionwith radial diffusion,is field-alignedflow is assumedto exist, it will contributeto the
also not consistent with the observed velocities. In this case the
outward stress in a manner similar to the azimuthal flow.
The
netmasstransport
is outward
at all longitudes
butlargerin the forcedensity
dueto thisparallel
flowViiis pV•,/R•,
whereRcis
active sector, and the azimuthal flow is subcorotationalthe 1ocalradiusof curvatureof the magneticfield line. A parallel
everywhere.Eventhoughtheproblemof lack of supercorotationcomponentto the plasmaflow is present,so the questionof the
canbe resolvedin thisfashion,theproblemof observed
plasma extentto whichfield-alignedflow playsa role in the cross-field
inflow remains.The latestversionof the corotatingconvection stress balance can be answered. Unfortunately, reliable,
model[Hill and Liu, 1987]can simulatethe longitudinal
mass unambiguous
resultsfor the amountof field-aligned
flow have
symmetry
associated
with theline emissions
fromhighercharge beendetermined
hereonly for distances
within20 Rj of Jupiter
states
of sulfurandoxygen
in theoutertorus[Brown
etal., 1983], (withtheexception
of the singlepointin thevicinityof 25 Rj
butit stilldoesnotexplaintheobserved
inflowof thethermal mentioned
previously)
wherethereis no majorproblem[Mauk
plasma
onthedayside.
andKrimigis,
1987].Giventhemodeling
inherent
intheprevious
Theresults
of thisanalysis
castsomedoubtasto thevalidityof calculations
of theLorentzstresses,
it is stillrelevant
to consider
thecorotating
convection
modelas currently
formulated
and possible
contributions
tostress
balance
duetofield-aligned
flows
appliedto the Jovianmagnetosphere
duringthe Voyager 1 flyby. for the sake of checkingconsistencywith the previous stress
At best,it would seemthat ff the convectionmodel is valid, it is balance results.
not an importantpart of the overall dynamicalpicture of the
We emphasizethat this contributionto the balanceof stresses
Jovianmagnetosphere
and may be radically disturbedby time- from a field-alignedflow can be calculateddirectlyfrom the data
dependent
changesproducedby, e.g., the solarwind.
without making global assumptionsabout the magnetospheric
geometry.Here, we carefullyfollow a procedureto minimizethe
Consequences
for StressBalance
assumptions
foldedintothedata.The datasuggest
thatVii= 0 at
Jupiter is a rapid rotator, so, in a steady state situation, the symmetryplane of the magneticfield configurationnear 17
Newton'ssecond
law requires
theinwardLoreritzforcefromthe Rj; however,thisdoesnotholdnear13Rj (cf. Figure5). Onlya
currentsheetto balancetheoutwardcomponent
of thepressurenonzeroflow at the(assumed)
symmetry
planecancontribute
to
gradientandcentrifugal
forces(as seenin a localrestframe). the distension
of the magnetic
field suchas thatconsidered
by
McNutt[1984]found,however,
thatthestresses
didnotmatchup; McNutt,[1984]. On theotherhand,flowsawayfromthissurface
theLoreritzforcewasmuchtoolarge.Themagnetic
fieldmodel cancontribute
to a general"inflation"
of thecurrentsheetwhich
usedwasa tilteddipolepluscurrentsheet,whichassumes
an wouldnormallybe associated
onlywithpressure
gradients.In
azimuthal
currentof strength
J = Io/R flowingin an annulus
of what followswe determine
quantitative
contributions
to both
inner radius a, outer radius b, and half thicknessD. The phenomena.
dimensions
of theannulus
aswellasI0 areparameters
whichare The radiusof curvatureRc, and the magneticfield line
adjustedto optimal valuesby comparison
with in situ curvature
vector,
•c,aregivenby
magnetometer
data[Connerney
etal.,1981].
Using
alocal
modeling
technique
todetermine
the
Loreritz
stressas well as betterestimatesof the pressuregradientdue to
1 _
R'-•
=I•cl--1(6'
V)61
(1)
thehotplasma
population,
Mauk
and
Krimigis
[1987]
found
thatwhere
• isthemagnetic
field
unit
vector.
Byexplicitly
writing
they
could
match
upthe
particle
and
field
stresses
within
-22Rj the
unit
vector
6=BIB
and
using
vector
identifies,
(1)can
becast
oftheplanet.
Outside
ofthis
distance
they
also
found
that
there
is intothefollowing
form:
4n JxB
a "missing"componentto the particle-produced
stress.
c
lc= ---B2"+ Vl(ln
B)
(2)
In theseanalysesthe particle stresseswere assumedto come
from two sources:centrifugalforce and pressuregradientforce.
V). Usingthe current
density
profile
The centrifugal force results primarily from the high-density whereVi--V-•(•.
obtained from the magnetic field model, the field curvature
"cold" plasma (detectedby the PLS experiment),whereasthe becomes
pressuregradient resultsprimarily from the low-density"hot"
4•0
1
plasma(detectedby the Low Energy ChargedParticle (LECP)
r = c RB 2 (B.• - B.,•.) + V,(ln B)
(3)
experiment). This is simply a consequenceof the plasma
[I(--8np/B
2)forthe"cold"
plasma,
being
only
a fewpercent,
The
current
density
profile
isvalid
forIzl-<2.5Rjand
5Rj<R<
while
the"hot"
plasma
I•isoften
greater
than
1 [McNutt,
1983;50 Rj. FromConnerney
et al. [1981]a valueof
McNutt,
1984;
Mauk
andKrimigis,
1987].
Thecentrifugal
force4•J0/c=4.5x 10-• G gives
thebest
simulation
oftheobserved
can
beestimated
themost
reliably
asitdepends
only
upon
localfield
during
theVoyager
1encounter.
Except
fortheVl(lnB)
measurements.
Theoutward
cenUifugal
forcedensity
hasa termandJ, all quantities
aredetermined
fromin situ
magnitude
pga,/r.
Here
theplasma
mass
density
isgiven
byp measurements.
From
Figure
5,atabout
17.5
Rjand
14Rj,itcan
with
r
being
the
cylindrical
radial
distance
from
the
spin
axis
of
be
seen
that
the
spacecraft
trajectory
is
approximately
the systemandV, the local azimuthalvelocitycomponent
of the
plasma(for the periodconsidered,Voyager 1 movedfrom-1 o to
perpendicular
to the magneticfield direction.Thus
-2
øin
system
III
latitude,
so
r iseffectively
the
radial
distance
from
Jupiter).
On
theother
hand,
thepressure
gradient
must
be
Vl(ln
B)= Aln
B= In
- InB2
As
. B1
As.
(4)
8514
SnsrDsnSrDMcNcrrr: PLASMAPLOWAT Juerm•
A plot of f versusmagneticcylindricalradiusis shownin
Figure14. Thecurvature
stress
generally
contributes
20- 50%to
the total inertialstress,a significantcontribution.However,the
contributions
atthetwocrossings
of themagnetic
equatorial
plane
arestillsmallcompared
to thecentrifugal
stress.
The isolated
pointat 25 Rj is locatedonly0.22Rj belowthe
nominalmagnetic
equator,
yettheparallelvelocitycomponent
is
ß
ß
L
ß
ß
ß
ß
•e ee
ß
high, -68 km/s, as mentionedabove. If the inferred radius of
curvatureof-1.23 Ra is conect, then the ratio of curvatureto
ee
ße
centrifugalstressfor thispointis -3.0. On the basisof thisone
point,it isnotpossible
toconclude
thatfield-aligned
streaming
is
thesource
of themissing
particlestress;
indeedthisrelatively
largevaluewouldappear
notto be largeenough
to satisfythe
balance
condition
near
-30
Ra
[Mauk
and
Krimigis,
1987].
o
However,this one analyzedpointdoeskeep openthe latter
lO
12
14
16
18
20
possibility.
As modeling
effortsontheplasma
datafromJupiter
magnetic cylindrical radius
continue,
more
work
will
be
done
in
this
region
in
anattempt
toat
Fig. 14. Ratioof outward
components
of curvature
to centrifugal
stress
versus
magnetic
cylindrical
radius.Thecurvature
termis seento leastsetsomelimitsonthiseffect.In passing,
it should
benoted
ß
ß
ß
ß
-
ß
©©
ß
contribute
asmuchas-45•to thetotalstress
duetothecentrifugal
force thatin theregioncoveredby thisanalysis,
bidirectional
flowsand
resulting
fromtheazimuthalplasmaflow.
"missed
flows"nearthemagnetic
equator
canberuledout;
outsidethis regionmore work mustbe doneto assessthe limits
that can be placedon flow parameters
versusviewingangle
where
limitations
ofthePLS
sensors.
More
progress
may
bepossible;
As2--(R•- R2)2 + (z•- z2)2
(5) the situation
is not as hopeless
as suggested
by Maukand
Krimigis[ 1987].
which
allows
one
toestimate
Vi(lnB
) atapoint,
byknowing
the AsMauk
and
Krirnigis
[1987]
point
out,
anexact
balance
may
spacecraft
position
(inmagnetic
cylindrical
coordinates)
andnotoccur
owing
tothedynamical
effects
ofradial
transport
of
magnetic
fieldonboth
sides
ofthatpoint.
Theperpendicular
plasma.
In addition,
time-dependent
effects
could
also
have
a
gradient
term
was
estimated
for10spectra
and
added
tothefirstsignificant
effect.
Ontheother
hand,
it isdisquieting
that
the
term
of(3)tocalculate
aradius
ofcurvature.
This
value
was
thenapparent
discrepancy
is aslarge
asit iswithout
some
other
compared
to thevalue
of Rewhich
neglected
thegradient
obvious
signature
inthefields
and
particles
data.
Intheregion
contribution.
Forallcases,
theeffect
oftheVi(lnB
) term
is covered
bythisanalysis
wehave
shown
that
theobserved
fieldnegligible.
Thelargest
contribution
is associated
withthealigned
(antialigned)
flows
arenotresponsible
fora significant
spectrum
at1819
SCET
onday63,where
Re= 2.18
Rjwithout
contribution
to theradial
distension
of themagnetosphere;
theVi(InB
) piece
and
Re= 1.94
Rjwiththeadded
term
(an11%however,
they
docontribute
totheinflation
ofthemagnetosphere
decrease
inthesize
ofRe).Alltheother
cases
showed
adecrease
perpendicular
to thesymmetry
plane
in thisregion.
A full
in theradius
of curvature
of lessthan1%.Thus,
neglecting
assessment
ofthis
latter
effect
requires
adetailed
comparison
with
Vi(InB)
and
substituting
(3)into
(1)gives
inferred
hotplasma
gradients
offtheequator
and
isbeyond
the
1
c
Re-- • =
RB
I•:l 4rd0
(6)
scope
ofthisstudy.
SUMMARY
Wehaveassumed
thatB2= B•
2+ B:2(i.e.,B, = 0). Withtheradius An in-depth
studyof theplasma
dataobtained
fromthe
of curvatureknown, the ratio of the curvaturestressto the Voyager1 spacecraft
encounter
withJupiterhasbeenperformed.
centrifugal
stresscan be calculated.
The component
of the The knowledge
anduseof thefull response
function
of the
centrifugal
forceperpendicular
to thefieldlineis needed;
hence, PlasmaScience
experiment
hasmadeaccurate
determination
of
itsprojection
intothe-f: direction
is required.
Thecentrifugalplasma
bulkflowvelocities
possible
in themiddle
magnetosphere
forceunitvector
I•c(theunitcylindrical
radialvector
withrespectof Jupiter.
Thefirstresult
of thisanalysis
isthereconfirmation
of
to thespinaxis)canbewrittenas
subcorotational
plasmaflow. However,the majorresultis the
confirmationand quantificationof the substantialnonazimuthal
•c= R• + _z•,
r
r
component
ofthe
plasma
flow.
The
magnitude
ofthis
component
is as large as -40% of the local azimuthalspeed,with 20% a
•,herer:= R:+ z: because
thespacecraft
liesin therotational
typical
value.
Resolving
thenonazimuthal
flowintoparallel
and
equatorial
plane.Thustheratioof thecomponents
of thetwo perpendicular
components
(withrespect
to themagnetic
field)
stresses
in the-t: direction
is
f=• r
where
• = -it ßI•
showsthatmostof the flow is field-aligned
(anti-field-aligned).
On thedaysidein muchof theregiontreated,plasmaabovethe
magneticequatormovesin an anti-field-aligned
direction,while
(7)direction,
below
the
equator,
plasma
tends
tomove
inafield-align
i.e., away from the magneticequator.This resultis
similar
tothatfound
atmuch
higher
energies
during
thePioneer
(8) 10encounter
withJupiter.
The cross-field
component
of the bulkplasmamotionexhibits
with•t a unitvector
inthedirection
of•c;• isknown
because
t: both
inflow
andoutflow.
Thisresult
isveryinteresting
inthatthe
canbedetermined
using
(3)and(4).
presumed
dominance
of Jupiter's
rotation
on magnetospheric
S•s
•
McNtrrr:
PLASMA Ft.ow AT JuPrmt•
8515
motionat thesedistances
combined
with theplasmaoutputof Io thestresses
shouldbezero. However,theinwardlydirected
JxB
suggeststhat, to lowest order, the systemis azimuthallyforcefromthemodelis muchlargerthantheoutwardly
directed
symmetric
in thisregion,furtherimplyingthat only outflowof centrifugaland pressure
gradientforcesin someregions.The
plasmawouldbe observed.A modification
to thissimplepicture plasmaflow exhibitsa largefield-alignedcomponent,
so a stress
by the corotating
convection
modelcan alsobe ruledout (see, due to magneticfield line curvaturemustbe considered.By
e.g.,Vasyliunas
[1983]andHill et al. [1983]).
calculating
the radiusof curvatureof the magneticfield (at the
To obtainall the components
of the convectivevelocity,a point of observation)
and usingVii, the relativeimportance
of
nonlinearleast squaresanalysiswas performed.Assumingthe curvaturestressto the overallmissingstresscan be ascertained.
ion distribution
functionto be a convected
Maxwellian,a plasma In mostof theregionof theJovianmagnetosphere
investigated
in
velocityis calculated
whichis consistent
withthedata. However, thisstudytheforceimbalance
is notserious.Thecurvature
stress
thesederivedvelocitiescould, in principle,dependupon the can be as large as 50% of the usualcentrifugalstressfrom
thermalanisotropy
if the latteris largeenough.The viewing azimuthalflow, andthe additionaloutwardstressis sufficiently
geometry
of the instrument
is suchthat mostof the observedsmallnotto bein conflictwithapproximate
balance
in thisregion
signalis dueto flowand/orplasmatemperature
perpendicular
to [McNutt, 1984; Mauk and Krimigis, 1987]. One point
themagnetic
field. However,
theB andC cupsalsosample,
to a investigated
suggests
a largercontribution
to thestress
by fieldlesserextent,field-aligned
flow and/orplasmatemperature
along alignedflow, but the natureof the apparently
missingoutward
thefieldlines. Thusa largethermalanisotropy
is requiredfor it stress
remainsa mystery.
to be "seen"by the PLS instrument.To quantifythis effect,we
developed
ananalysis
algorithm
which
uses
thefullresponse
APPENDIX
function
of theinstrument
andallowsthemodeliondistribution Currentmeasured
by thePLSexperiment,
for a givenenergy-
function
to be a convected
bimaxwellian.
Several
spectra
were per-charge
channel
k,isgivenbytherelation
then reanalyzedand the resultscomparedto the simulations,
assuming
a Maxwelliandistribution.
The assumption
of
bimaxwellian versus Maxwellian
distribution is found to have
little effecton the velocitydeterminations.In fact, noneof the
lk(x,t}=•(x,t}-•+•(x,t}
(A1)
where•(x, t) and•+•(x, 0 arethetotalcurrents
measured
by the
instrument(at location x and time t) due to positive ions with
spectra
analyzed
from
theVoyager
1encounter
show
aunique
velocities
greater
than
thethreshold
velocities
forchannels
kand
signature
of a thermalanisotropy.
A temperature
anisotropy
is k+l, respectively.Thesethresholdvelocitiesaredefinedby
fairlyindependent
of theflowfor thespectra
considered,
and
well. Maxwellians
convected
simulate
the
measured
currents
quite
Aset
ofspectra
from
the
Voyager
2encounter
with
Jupiter
was
v, =
(A2)
analyzed
byassuming
botha Maxwellian
anda bimaxwellian
ion withe andmr beingtheprotoncharge
andmass,
respectively.
distributionfunction. This set could only be simulatedif a For ionicspecies
i themassnumberandchargestatearedenoted
convected
bimaxwellian
distribution
is assumed
for the ions. by Ai andZ•/, respectively.
The set of contiguous
potentials
Both a significantthermalanisotropy(Tll/T1= 3.08) and provided
by themodulator
gridof a givenFaraday
cupto select
nonazimuthal
flowwerededuced.
the energy-per-charge
channels
is •,, wherek goesfrom 1 to N
The derivedplasma
velocities
wereusedto investigate
their andN is 16fortheL modeand128fortheM mode[seeBridge
implications
forplasma
transport
andstress
balance.
Onemodelet al., 1977].Thusthecurrent
measured
for thekthchannel
is
ofplasma
transport
hypothesizes
thatalocalized
depression
ofthe principally
dueto particles
withvelocities
whichfall intothe
surfacemagnetic
field strength
of Jupiterenhances
radiallyvelocity
window
ofwidthAv,,
where
outwardplasmaflow (corotating
convection
model)for a
particular
range
oflongitudes
[Hill
eta/.,
1981].
The
plasma
data
Av•
=vk+•
- vk
(A3)
analyzed
covered
a period
oftimeduring
which
Voyager
wentalthough
particles
outside
of thisrange
canalsocontribute
through
theassociated
active
sector
twice.
Examination
ofthesignificantly
duetothenature
oftheresponse
discussed
below.
velocities
showed
nosuch
enhanced
flowinside
theactive
sector.
This
extra
contribution
constitutes
the"feedthrough"
current.
Infact,
during
one
traversal
most
oftheradial
flow
was
inward,Thetotal
measured
currents
making
uptheterms
ontheright
not outward(as required
by this model).Hairstonand Hill handsideof (A1) aregiven by
[1986]havesuggested
thatsupercorotational
flowwaspresent
on
the nightsideof Jupiterduringthe Voyager1 encounter,
supporting
thecorotating
convection
hypothesis.
However,
the
(A4)
analyzed
spectral
setfromthisregionshows
no significant
departure
from corotation
in eithera subc.
orotational
or
supercorotational
sense.Theresults
of theanalysis
castsomewhereft is a unitvector
in thedirection
normal
to thePLScup
doubt
asto thevalidity
of thecorotating
convection
model,
at being
considered.
Thus
leastascurrenfiy
formulated,
andpossibly
introduce
a problem
in
reconciling
theplasma
andmagnetic
signatures
during
some
of
--
the
current
sheet
crossings.
Atbest,
itappears
that
ifthe •(x,O=Z*eIdv.
ldv,•dv.v.f(x,v,t)
R(v,v•)
(AS)
corotating
convection
model
isvalid,it wasnotanoverriding
part
..•
-.•
of theoveralldynamical
pictureof theJovianmagnetosphere
at
theepoch
of theVoyager
1 encounter.
wherej•x, v, t) is the ion distribution
function
andR(v,vO is
Using
thecurrently
accepted
magnetic
fieldmodel
oftheJoviandefined
astheinstrument
response
function
andis analyzed
in
magnetosphere,
a stress
balance
analysis
can be performed.
greatdetailby Barnett[1984]andBarnett
andOlbert[1986].
Assuming
themagnetosphere
is in equilibrium,
thesumtotalof Symbolically,
R(v,v,)canbewritten
asaproduct
oftwoterms,
8516
Sns-Ds ns-D McNtrrr:
R(v, vO = T(v, vO A(v, v•)
PLaSMa FLOW AT JUPITER
(A6)
with
where
T(v,
vO
is
defined
the
transparency
function
and
A(v,
v•)[lx-the "sensitive"
area
of theas
collector.
+
The transparency
of a given grid within the cup is definedas
1
1
+[.
w•
the
probability
ofan
incident
particle
passing,
unobstructed,
[_.•]2
[.•}
probabilities.
This
final
probability
can
beparameterized
interms
[lz--- +
.•
probabilities;
the
side
sensor
has
eight
grids,
hence,
eight
such
1 [.1
1]
offour
gaussians
[Barnett,
1984;
Barnett
and
Olbert,
1986].
The w}
• w}
through
the
grid
plane.
Since
each
cup
ofthe
main
sensor
has
nine
[ly
-such grids, T(v,v•) is a product of the nine associated
sensitivearea is defined to be the area overlap of the collector
(AlO)
with
the
projected
image
of
the
aperture
onto
the
collector.
The
[-'•]
{•1['
product
ofthetransparency
function
and
sensitive
area,
atnormal
ht
•=
incidence,
isdefined
astheeffective
area,where
AoT0
= 67.3cm2
ux
_
1
w•
for each of the three cups making up the main sensorand
AoTo
= 56.2cm2forthesidesensor.
To completely
specify
thecurrents
•(x, t), wemustspecify
an
Twodifferent
iondistributions
have
been
used
toexplicitly
-u•_ 1
analytic
form
of
the
distribution
function
of
the
ions,
f(x,
v,
t).ht•(X)
[_.•]
evaluate(A5): a convectedisotropicMaxwelliandistributionand
a convected bimaxwellian
distribution.
The case of a convected
allfourcups
of thePLS
instrument.
Thebimaxwellian
case
is T,= •uz
+ 1
isotropic
Maxwellian
distribution
is
covered
by
Barnett
[1984]
for
w• fw•
discussed
below.
z,,
(uß
In general,a bimaxwelliandistributionfunctioncan be written and
in the followingform (see,e.g.,Rossiand Olbert [ 1970]),
f(x,v,0=
expI
Iv-ul
Z'enToAo
c• cj
gx,0--
(A7)
The x andy componentsof the sensitiveareaare denotedby A•
where
and A•, respectively[Barnettand Olbert, 1986], while the
variablesof integration,X and Y, are definedin the following
wll(x,t) -- ion parallelthermalspeed
manner
Wl(X,t) -=ionperpendicular
thermalspeed
u(x, t) -= ion bulk velocity
5(X,
t)--magnetic
field
unit
vector
(All)
The shift functions is definedby
s*[-•]
=s
h
(A12)
n(x,
t)-=ion
number
density
where
histhe
distance
between
the
aperture
and
collector
and
sø
v--particle
velocity
is
theshift
vector.
Thisshift
vector
isthen
defined
asthe
displacementof the aperture image from a perpendicular
projectionof the apertureonto the plane of the collector. This
Insertingthe above expressionof f(x,v,t) into (A5) and shiftresultsfrom the refractionof the ion trajectorywithinthe
knowingtheresponse
functionyieldsfor thetotalcurrent,
instrument
dueto theelectricfieldsbetweenthevariousgrids. In
practice, s is a complicated function of the modulator and
suppressor
voltagesand is storedin tabular form. Finally, the
(A8) constants
a•, a2, c•, and c2 are usedin the parameterized
where
expressionof the transparencyfunction; they were found from
fitting the true transparency
functionto the sumof two gaussians
and are also stored in tabular form for doing computations
[Barnett and Olbert, 1986].
A nonzerotemperatureanisotropyshowsup via the expression
(A9)which
(w•
2-w•2).
This
factor
can
dominate
terms
intheexpressions
contain it. This temperature anisotropy factor greatly
increasesthe mathematicalcomplexityrequired to evaluatethe
modelcurrents.This occursbecause¾•has an X dependence
SANDSAND McNw•:
PLASMAPLOW AT JUPITER
which adds considerable analytical complexity over the
Maxwellian
case.
Since there is an X dependencein the integrandof the Y
8517
gg(v•)-gu(vz)
G(v,)
= Z,,-Z• -
g•vz)-ga(v,)
Z,t-Z•
(A18)
integral,
weevaluate
thelatterintegral
first.Looking
onlyatthe Subscripts
ontheg functions
indicate
which
Yisbeing
used.The
Y integral
in (AS)andcompleting
thesquare
in theexponentialfunction
g is a verycomplicated
function
of v, andcanhaveone
terminly, weobtain
of 10 possible
forms(thesearegivenby Sands[1987]).This
complexity is a result of the facts that the empirical
•(x) azA,e-z•(A13)
has
been
parameterized.
[]i
approximation
of
•(Z)
isafunction
of
IZI
and
the
sensitiv
area
K(X)
--fdY
I•(X,
Y)=_L
[5'•
exp
•
The
total
current
can
then
be
written
as
where
(A19)
i,j=-I Vk
(A14)
anduponintegrating,gives
(A15)
z•,)
-•(z,,)
- •(z,,,,)
-•(z,•)
]
xfer.
with
1
½(Z)
-=Zerf(Z)+• e-z2
(A16)
anderr (Z) beingtheerrorfunction,namely,
z
erf (Z) --
+2v,
u.,
+ 51•w•
The final integration over vz, in (A19), must be done
numerically.The integrandis so convolutedthat no analytical
solutionis possibleunlessmany assumptionsare made which
result in a seriouslimitation to the usefulnessof the analysis.
Once•(x,0 is foundnumerically,
the currentmeasured
in any
given channelk, due to a given set of plasmaparameters,can be
calculatedusing(A1).
Acknowledgments.
Theauthors
thank
H. S.Bridge
andJ.W.Belcher
dt
foraccess
totheplasma
dataandfortheirsupport
overthecourse
ofthis
study. They thankT. G. Northropfor pointingout furtherpublished
work
on the field-aligned streamingof high-energyparticlesmeasuredby
The subscripts
on Z in (A15) refer to constants
which are values Pioneer
10. TheyalsothankJ. D. Richardson
andthereferees
forhelpful
of Y corresponding
to five contiguous
rangesoverwhichdifferent comments
andN. F. Nessfor access
to theVoyager
magnetic
fielddata.
parameterized
expressions
of thesensitive
areaareusedin the Thisworkwassupported
byNASAunder
contracts
953733
and957781
integral
of(A13).Thisdeparts
somewhat
fromthetreatment
of fromtheJetPropulsion
Laboratory
totheMassachusetts
Institute
of
Barnett
andOlbert
[1986],
who
retain
anX dependence
oftheseTechnology.
The Editor thanks A. Nishida
and another referee for their assistance in
values
of Y. Weighted
constants
mustbeused
hereowingtothe evaluating
thispaper.
difficultiesintroducedinto the next integrationby the anisotropy.
Detailsof the differencesaregivenby Sands[ 1987].
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Magnetosphere,
editedA. J. Dessler,chap. 1, CambridgeUniversity
Press,New York, 1983.
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=•Zl
+le-z2
+IZI[ce
-•z2
2z2](A17)
+ce-'
where
a• = 1.3
a2 = 7.0
c• = -0.6
c2 = -0.3
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