GEOPHYSICAL
RESEARCH
LETTERS,
VOL.20,NO.2,PAGES
145-148,
JANUARY
22,1993
ONTHEVOLTAGE
ANDDISTANCE
ACROSS
THELOWLATITLrDE
BOUNDARY
LAYER
Mike HapgoodandMike Lockwood
Rutherford
Appleton
Laboratory
Abstract.
A passof the AMPTE-UKSsatellitethroughthelowlatitude
boundarylayer (LLBL) at 8:30 MLT is studiedin detail.
Themagnetosheath
fieldis predominantly
northward.
It is shown
thatmultipletransitionsthroughpart or all of the layer of
thelayer,AL, is theintegralof [(Y-s
- v•).n_]overtheresidence
time
of thesatellitewithinit, At. The voltageacrossthelayeris given
by integratingthe electricfield along the satellitetrack, both
considered
in therestframeof theboundary:
antisunward
flow leadto overestimation
of boththevoltageacross
thislayeranditswidth.Thevoltageis estimated
to beonlyabout
3 kV andthis impliesthat the full LLBL is about!200 km thick,
consistent
with previousstud/es.
V =+ []'•t•-
(Es-v_b)
x B__).•s-vb)
dt],
whereE is theelectricfield as measured
by the spacecraft.
The
plusor minusarisesfrom the senseof the integration:
the plus
appliesto a traversal
of theLLBL fromthemagnetosheath
intothe
magnetosphere,
the minusto a reversetraversal.Vectoralgebra
Introduction
Two types of mechanismhave been proposedfor driving
convection
in themagnetosphere
andionosphere.
Thefirstinvolves
yields
theproduction
of openflux by magnetic
reconnection:
thesefield
V = _.+[J'•E_..vs
dt- fatE.vb dr]
lines thread the magnetopauseand hence are transferred
antisunward
over the poles by the solar wind flow. All other
mechanismcan be classedas 'viscous-like'interactionsas they
involvethe antisunwardtransferof closedfield lines (which do not
threadthe magnetopause
and connectthe ionospheres
of the two
hemispheres).
Viscous-like
interactions
m9stproduceantisunward
(2)
The firsttermon theRHS of (2) is thevoltagededuced
directly
from the satellitedata,neglecting
any boundarymotions(=V•t).
Thus,weretheboundary
motionneglected,
whentheboundary
is
movinginwardfor an outbound
satellitepass(vb< 0; vs > 0), the
magnitude
of thetrueboundary
layervoltageis underestimated
(IVl
flows on northward-directed field lines within the low-latitude
> IV•d). However, the satellite may still emerge into the
boundary
layer, LLBL (see Cowley, 1982). Reconnection
could
magnetosheath
if theboundaryis movingoutward,but at a slower
produce
suchflows,evenon theflanksof the magnetosphere,
but
speedthanthe satellite(vs> vb > 0), thenthe potentialdifference
onlyif the pointwherethe field line threadsthe magnetopause is overestimated
(IVl < IV•l). Note that our definitionsmeanthat
remains
at very low latitudes.
positiveE and negativeV (and Vat) corrrespond
to antisunward
flow in the LLBL.
Observations
of the voltage acrossthe ionosphericpolar cap
duringnorthwardIMF, whenrecotmection
is not expected,indicate
Observations
thatlessthanabout30 kV is dueto viscous-likeinteractions
(e.g.
Reiffet al., 1981).However,Wygantet al. (1983) showedthatthis
voltagedecayedwith time elapsedsincethe IMF turnednorthward.
In this paperwe studyan outboundpassof the AMPTE-UKS
satellite on 10 November 1984 (orbit 47), which encounteredthe
Lockwoodand Cowley (1992) have shown how this, and the
ionospheric
flow patternsascribedto viscous-likeinteraction,are
boundarylayer and magnetopause
in the period08:35-10:00UT.
well explainedas resulting from continuingreconnectionof
At the nominal magnetopausecrossing, UKS was at GSE
residual
openflux in the tail. Hencethe observations
of transpolar coordinates
(X--5.26R•.,Y=-9.49RE,Z=0.23Rv_),
for whichtheMLT
was 08:30 and the magneticlatitudewas +14ø in SM coordinates
voltage
indicatethatthevoltagedueto viscous-like
interactions
are
verysmall(about5kV acrosseachflank of the magnetosphere).
(Z = 2.56Rv.).
Figure2 presents
the magneticfield andplasmaobservations
as
Similar conclusionswere reached by Mozer (1984) who
a function of time. When the satellite emergesfully into the
measured
the voltage acrossthe low-latitudeboundarylayer by
(at the time marked d), the field is pointing
integrating
the along-track
electricfield of a traversing
satellite. magnetosheath
northward(panel2) but is slightlyweakerthanin the boundary
Generallythe valuesobtainedwere as low as thoseinferredby
Wygantet al., but somelargervalues(as well as somenegative
valuesshowingnett sunwardflow) wereobtained.In thispaper,
we investigate
the LLBL voltageusinga similartechnique,
but
allowing
for thefactthattheboundary
is notstationary.
Vs?
Vb
/
! \
Method
-,
t
/ x
/
• x
Figure1 illustratesa traversalof the LLBL by a satellite.The
satellite
trajectory
is shownin therestframeoftheboundary
layer.
N
IntheEarth's
frametheboundary
ismoving
atvelocity
v_
bandthe
satellite
movesat velocityv_s(bothdefinedto be positivein the
I
LLBL
/ \\x
/
/
/
/
/
\
\\
/
\
/
/
"''/
/
outward
boundary
normaldirectionn_).Hencein therestframeof
theboundary
thesatellite
moves
at (X.s- _vb)
andthethickness
of
\
?
Copyright
1993by theAmerican
Geophysical
Union.
Papernumber93GL00063
1. Schematicillustrationof a satellitepath acrossthe boundary
layer, in its own restframe,when the boundaryis oscillatingin
0094-8534/93/93GL-00063503.
O0
location in the Earth's frame.
145
146
Hapgood
andLockwood:
Voltage
andthickness
of theLLBL
AMPTE-UKS
8O
ORBIT 47
10 NOV 1984
frame.Panel6 showsthe potential
distribution
obtained
by
integrating
this component
alongthe satelliteorbit (giving
a
08 35-10'00
voltageV•t).
Prior to the time t=a in figure 2, the field orientationwas
constant
andmagnetospheric
(panel2) andtheflow wassunward
m •o
(panels
6 and7). Thetransition
parameter
indicates
a number
of
partialboundary
transitions,
buttheflowat suchtimeswasstill
o
•oo
•
sunward and was, indeed, enhanced.Antisunward flow was
•oo
observed
in theboundary
layerbetween
timesa andd,marked
by
.•
the outermosttwo verticallines. In addition,a line hasbeendrawn
-100
100
at thetimeb whenN• andT.• (andhenceT) wereidenticaltotheir
m
8O
corresponding
valueat t=d. Similarly,the electron
gasat timee
.•
6O
was identical to that at t=a.
If we assumethat the boundarydid not vary in its electron
characteristics
in the 12 min.betweent=a andt=d, theN•, T•.and
T variations show that the satellite crossedthe antisunwardflow
channelof the boundarylayer three times. These threefull
traversals
arein the intervalsa - b, b - c ande - d. Frompanel6
we find thatthe voltagesobservedin theseintervals(V•t) are-2
kV, -8.5 kV and-3 kV. Considering
the intervalb - c, thesatellite
wasreturning
to moremagnetospheric-like
electroncharacteristics,
'•! 0
•o.s
z0.4
c70•
.a
0
,._,3 8
i.e. we infer that theboundarywas movingoutwardfasterthanthe
satellite(vb> vs> 0). Notethatthismeansthat-8.5 kV of thetotal
'-'32
Vs•t of-13.5kV wasduetothesecond
crossing
of theantisunward
flow layerandthata further-3 kV wasdueto a thirdcrossing.
Duringthe periodsa - b andc - d, the'boundary
mayhavebeen
movinginward,in which casethe
of 2 kV and 3 kV
c•2.8
(respectively)
wouldbeunderestimates.
However
at thetimes
b
40
50
60
70
80
90
100
110
I20
and c we know vb = vs > 0, and suchtimes act to makeIV•l
valuesoverestimates
of IVl. Given the similarity of the two
independent
Vs•t valuesfor thetwo outwardtraversals
of thelayer
(a-b; c-d), we estimatethe true voltage acrossthe antisunward
flowing layer was 3 + 1 kV, the uncertaintyarisingfromthe
boundary
motion.Thisvalueshouldbe compared
with the13.5kV
derivedif we assumethe boundaryto be static.In the following
sectionwe considersomeimplicationsof this estimate.
TIME (MINS) FROM 08:00UT
2. Plasmaand magneticfield datafrom AMPTE-UKSfrom an
outbound
magnetopause
crossing
on 10November1984(orbit47):
(1) magneticfield strength,Bror and (2) direction,4)• (in the
estimated
LM planeof the boundary- positivevaluesdenote
northwardfield); (3) the transitionparameter,
T; (4) the electron
density,
N,; (5) theperpendicular
electron
temperature,
T•.;(6) the
voltage,
Vsat;
and(7)theelectric
fieldcomponent
alongthesatellite
track,-[2.x B__]11.
Thetimesa - d arediscussed
in thetext.
Transition Parameter and Thickness
Figure3 showsthe samedataas figure2, but plottedasa
functionof the transitionparameter,T, ratherthan observatiort
time.Theideabehindsuchplotsis thatrepetitive
encounters
ofthe
samepartof theboundary,
duetoboundary
motions,
areallplotted
at the sameT. Panel1 showsthat the transitionparameter
oders
the field orientationwell, showingonly magnetospheric
field
directions at all values above about 20. Below T = 20 there is a
rangeof values,reflecting
variability
in themagnetosheath
field
level of the field fluctuation,indicativeof the moreturbulentfields
orientation.
Panel3 showsthat the magnetosheath
flow direction
is maintained
up to T of about40, andPanel2 showsthattheflow
of the magnetosheath,
and the field-perpendicular
electron
speedin thisantisunward-moving
boundary
layeris onlyslightly
temperature,
T_•,becomes
constant
andlow (panel5). As the
lessthanin the magnetosheath
proper,At T above40, theflow
directionis variablebut its speedis low. Panel4 showsthe
layer(panel1). Moreover,
at thetimed thereis anincrease
in the
satellitemovesfurtherintothemagnetosheath,
theplasmadensity,
anisotropy,
defined
to be (Tii - Tz)/(Tii+ Tz).Thisis
N•, (panel4) growsandthemagnetic
fielddecays,
in accordance electron
withpressure
balance.
Halletal. (1991)identify
theabrupt
change alsowell orderedby T. The featurewe wishto highlightis the
in field orientationat 9:50 with the magnetopause.
However,we
clearonsetof loss-cone
typedistributions
at T > 90 whichdefines
notethatthis doesnot correspond
to any changein any plasma
clearlymagnetospheric
plasma.
parameter
norin thetotalfieldstrength
or fluctuation
andwe
Hence
wedefinetheboundary
layertobebetween
T of20and
90. Panel(5) of figure3 presents
thealong-track
electric
field,
showing
an antisunward
flow charmel
in therange20 < T < 40
therefore
consider
thisto be a temporalchange
in the sheath
field
orientation.
Panel$ of figure2 shows
thetransition
parameter,
T, asdevised
by Hapgood
andBryant(1990,1992).Thisparameter
is settobe
0 wherethe electrontemperature
and densityclearlydefinethe
andweaksunwardflow at 40 < T < 90. No significantflowwas
detected
in the purelymagnetospheric
population
at T > 90.
Panel(6) investigates
the voltageacrossthe boundarylayer
usingT. In orderto dothis,wehaveassumed
thatT varieslinearly
with distanceacrossthe bo•.mdary
and we thenadoptvarious
valuesfor the spatialthicknessof the boundarylayer,AL,
Panel7 showsthealongtrackcomponent
of theelectricfield [-_v
to theboundary
layerrangein T, AT = (90-20).
x B_..]11,
where
v istheplasma
velocity
measured
in thespacecraft corresponding
plasma
tobemagnetosheath
andto 100wheretheplasma
isclearly
magnetospheric.
At anyonetimeT is thendefined
byN• andTz.
Hapgood
andLockwood:
Voltage
andthickness
oftheLLBL
AMPTE-UKS
ORBIT 47
10 NOV 1984
08 35-10
O0
ORBIT 47
147
DA'f 84,'315
08-35
-
10:00
UT
200
lOO
I
I
o
-lOO
T=20
/
T=/+O
I
I
'""300
I
I
200
• 1oo
•-' -I
0 ?
8OO
lO0
0
-t
-100
4 -
I
' ss
SPH
1
• 02
-!
8 ,-
-2 0
'EtO
x
I
-•4•
5
T= 90
I
I
i
0
I
-
I
/-
1
_30 [
,
-400
-•00
0
200
400
600
800
I000
1200
1400
D[STANC'E
FROMMAGNETOSHEATH
EDGE(KM)
0
20
40
80
80
100
3. The datashownin fig. 2, as a functionof transitionparameter,
4. Locusof thesatellite
in theN, M planeof theboundary-normal
co-ordinates,
basedon a linearspatialvariationof T and the
T: (1) themagnetic
field direction,qbB;
(2) theplasmaspeedin the
LM plane,Vm; (3) theplasmaflow directionin theLM plane,qb,;
flowchannels
areshownbetween
themagnetosphere
(SP)andthe
(4)theelectron
anisotropy,
(TII ~ Tz)/(TIi+ Tz); (5) theelectric
fieldcomponent
alongthesatellite
track,-• x B_B_]II;
and(6) the
potential
distributionfor AL = 1200 km.
derived thicknessAL = 1200km. The sunward and antisunward
magnetosheath
(SH).
Analysis of the electron characteristicsindicatesthat the antisunward flow channel was crossed three times as the satellite
Hencefor eachelementof T, dT, we canestimatea lengthd!,
which
wethencombine
withtheaverage
along-track
electricfield
(fordT)andsoderivethevoltagedrop.It shouldbenotedthatthe
assumption
thatT varieslinearlywithdistance
across
theboundary
(initsownrestframe)is employed
hereonlybecause
it is the
simplest.
However,
figure3 shows
thatthevalueof thealong-track
electric
fieldis relativelyconstant
in boththeouter,antisunward-
movedoutbound,
dueto magnetopause
motions.As a result,both
thevoltageandthickness
oftheboundary
layerwereprobably
less
thana thirdof thevalueestimated
by assuming
theboundary
tobe
stationary.Note that the results are very dependenton the
identification
of the edgesof the boundarylayer:we believethat
it is muchmoresatisfactory
to examineseveralplasmaandfield
characteristics.
Use of a singleparameteris morelikely to cause
confusion
betweentemporalchanges
andspatialstructure.
flowing
layerandin theinner,sunward-flowing
layer.Thisbeing
Figure 4 summarises
the inferredtrajectoryof the satellite
thecase,
theerrorsintroduced
by theassumed
formof thespatial throughthe boundary,basedon a linear spatialvariationof the
variation of T are small.
transition
parameter,
T, withtheinferredAL of 1200km (=0.2RF.).
In figure3, wehavetakenAL = 1200kin. Thisfigurehasbeen
The distancealong the boundaryis almostexactlyin the -M
chosen
because
it produces
a voltageacross
the antisunward (sunward)directionfor this case.Also shownare the boundary
channel
of 3 kV,asestimated
in theprevious
section.
Hencefrom layerflow channels,
deduced
fromthe transitionparameter.
It can
thisargument,
wefindthatthewholeboundary
layer(including
be seen that the satellite travelled a considerable distance inside the
sunward
flowinginner portionand antisunward
flowingouter
portion)
is only1200_+400 km wide.Furthermore,
we findthat
sunward-flowingportion, before traversing the anti-sunward
theantisunward
flowingportion
between
T of 20and40isjust
430+ 140kmwide.Thisfigureis roughly
fivegyroradii
fora l
keVproton
andshould
becompared
toavalue
of1500km
derived
if weassume
theantisunward
flowchannel
tobestationary.
direction)
wasabout
2 kms't, andthethickness
derived
hereyields
an average
outward
boundary
speedof <%> = 1.6km s'I during
channelthreetimesand thenenteringthe sheath.The outward
velocity of the satellite (in the estimatedboundarynormal
the intersection
periodAt = 53 min. However,the fluctuationsin
% aboutthismeanareupto about40 kms't in amplitude.
Discussion and Conclusions
The voltagederivedhereis within the range,but smallerthan
theaverage,reported
by Mozer(1984).The low valuesupports
the
A crossing
of the boundary
layerby AMPTE-UKS
with suggestion
by Wygantet al. (1983)and LockwoodandCowley
flow observed
generally
northward
magnetosheath
field hasbeenpresented. (1992) thatmuchof the so-called'viscously-driven'
148
Hapgood
andLockwood:
Voltage
andthickness
oftheLLBL
in theionosphere
whentheIMF is northward
is, in fact,theeffect
of reconnection
in the magnetospheric
tail.
in considering
previousestimates
of the voltageandthickness
of the LLBL, the biasescausedby boundarymotionmustbe
considered.
Boththic•kness
andvoltagewill be overestimated
if the
Eastman,T.E., and E.W. Hones, Jr., Characteristics
of the
magnetospheric
boundary
layerandmagnetopause
layeras
observedby IMP6, J.Geophys.
Res.,84, 2019-2028, 1979.
Hall, D.S. et al., Electronsin the boundarylayersnear the
dayside
magnetopause•
J. Geophys.
Res.,96,7869-7891,
1991.
boundary
is movingin the samedirectionas the spacecraft, Hapgood,M.A. andBryant,D.A., Re-ordered
electrondata
in the low-latitudeboundarylayer, Geophys.Res. Lett.,
whereas
theywill beunderestimated
if it is moving
in theopposite
direction.
I7, 2043-2046, 1990.
Both Eastmanand Hones(1979) and Mitchellet al. (1987)
reportedthat the LLBL thicknessincreasedwith distancefrom
noon. In their survey,Eastmanand Hones found that the 12
crossingsof the boundarylayer by IMP-6 with GSM X in the
range5-6Re gaveth.ickness
ranging
between
0.08REand0.98Re
witha meanvalueof 0.34RE.Hencethevalueof 0.2 REderived
hereis withintheirrangebuta bit smallerthantheaverage.
In the
absence
of anybiasin theaverage
boundary
motion,thisaverage
wouldreflectthe true widthof the boundary
layer.Honesand
Eastmandid not find a dependence
of thickness
on the orientation
of the magnetosheath
field, howeverMitchell et al. foundthatthe
ISEE-1satellitetendedto remainlongerin low-latitude
boundary
layer if the !MF was northward.
Hapgood,M.A. andBryant,D.A., Exploringthe magnetosphericboundarylayer,Planet.SpaceSci.,40, 1431
-1459, 1992.
Lockwood,M. andS.W.H. Cowley,Ionospheric
convection
andthesubstorm
cycle,in S•bstorms-1,
Proceedi•gsof the
First !nrer•mtionalCo•fere•ceo• Substorms
(ICS-]), ESA
SP 335, pp. 96-107, EuropeanSpaceAgencyPublication_s,
ESTEC, Nordvijk, The Netherlands,1992.
Mitchell, D.D. et al., An extendedstudyof the low-latitude
boundarylayer on dawnand duskflanks of
the magnetosphere,
J.Geophys.
Res., 92, 7394-7404, 1987.
Mozer, ES., Electric field evidencefor viscousinteraction
at the magnetopause,
Geophys.
Res.Lett.,]], 981-984, 1984
Hencethe boundarylayer thicknessderivedhere is in good
Reiff, P.H.,R.W. Spiro,andT.W. Hill, Dependence
of
agreementwith previousestimates,supporting
the low derived
polarcappotentialdropon interplanetary
parameters,
J.
voltageof 3kV across
theanti-sunward
flowingboundary
layer.A
Geophys.Res., 86, 7639-7651, !981.
surveyof all theAMPTE datais nowunderway,
usingthemethod Wygant,J.R., R.B. Torbertand F.S. Mozer, Comparisonof
described
hereto determine
thevariationof thisvoltagewithMLT.
S3-2 polarcap potentialdropswith the interplanetary
Acknowledgements
WethankDr A. Johnstone
of MullardSpace
magneticfield andmodelsof magnetopause
reconnection,
ScienceLaboratory
andProf.D.J. Southwood
of ImperialCollege,
J. Geophys.Res., 88, 5727-5736, 1983.
Londonfor provisionof, respectively,
the ion and magnetometer
data from the AMPTE-UKS
satellite.
M.A. Hapgood and M. Lockwood, RutherfordAppleton
Laboratory,Chilton,Didcot, OXll 0QX, UK.
References
Cowley, S. W. H., The causesof convectionin the Earth's
(Received
September
21, 1992;
magnetosphere:
A reviewof developments
duringIMS,
revised: November 18, 1992;
Rev. Geophys.,20, 531-565, 1982.
accepted:December2, 1992.)