JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 104, NO. A12, PAGES 28,361-28,378, DECEMBER
1, 1999
A numerical study of solar wind - magnetosphereinteraction for
northward interplanetary magnetic field
P.Song,D.L. DeZeeuw,
T.I. Gombosi,andC. P.T. Groth
SpacePhysicsResearch
Laboratory,
Departmentof Atmospheric,
OceanicandSpaceSciences,
Universityof
Michigan, Ann Arbor
K.G. Powell
Departmentof Aerospace
Engineering,
Universityof Michigan,Ann Arbor
Abstract. The solarwind-magnetosphereinteractionfor northwardinterplanetarymagnetic field (IMF) is studiedusing a newly developedthree-dimensionaladaptivemesh
refinement(AMR) global MHD simulationmodel. The simulationsshow that for northward IMF the magnetosphere
is essentiallyclosed. Reconnectionbetween the IMF and
magnetospheric
field is limited to finite regionsnear the cusps. When the reconnection
processforms newly closedmagneticfield lines on the dayside,the solar wind plasma
trappedon thesereconnectedmagneticfield lines becomespart of the low-latitudeboundary layer (LLBL) plasmaandit convectsto the nightsidealongthe magnetopause.The last
closedmagneticfield line marksthe topologicalboundaryof the magnetospheric
domain.
When the last closedmagneticfield line disconnectsat the cuspsand reconnectsto the
IMF, its plasmacontentbecomespart of the solar wind. Plasmaconvectionin the outer
magnetosphere
doesnot directlycontributeto the reconnection
process.On the dayside
the topologicalboundarybetweenthe solar wind and the magnetosphere
is locatedat the
inner edge of the magnetopause
current layer. At the sametime, multiple currentlayers
are observedin the high-altitudecusp region. Our convergencestudy and diagnostic
analysisindicatethat the detailsof the diffusion and the viscousinteractiondo not play a
significantrole in controllingthe large-scaleconfigurationof the simulatedmagnetosphere.
It is sufficientthat thesedissipationmechanismsexist in the simulations.In our seriesof
simulationsthe length of the magnetotailis primarily determinedby the balancebetween
the boundarylayer drivingforcesand the drag forces.With a parametricstudy,we find that
the tail length is proportionalto the magnetosheathplasmabeta near the magnetopauseat
local noon. A higher solarwind density,weaker IMF, and larger solarwind Mach number
resultsin a longertail. On the nightsidedownstreamof the last closedmagneticfield line
the plasmacharacteristicsare similar to that in the magnetotail,posing an observational
challengefor identificationof the topologicalstatusof the corresponding
field lines.
1. Introduction
WhentheIMF is strictlynorthward,
it is parallelto the
Earth'sdipolemagneticfield. Dungey[1961] proposedthat
Thesteady
state
topology
ofthemagnetosphere
fordue reconnection
between
theIMFandthemagnetospheric
field
south
and
north
pointing
interplanetary
magnetic
field
(IMF) cantake
place
atcertain
points
along
thenightside
magneconditions
isofgreat
theoretical
interest
formagnetospheric
topause.
In theDungey
[1961]
model
themagnetosphere
physics.
In anidealized
situation
(assuming
a nonrotating
isclosed
except
atthetworeconnection
points.
In hispiplanet
witha strictly
southward
pointing
magnetic
dipoleoneering
work,Dungey
[1961]
concentrated
ontheglobal
moment)
such
configurations
exhibit
twoplanes
ofsymmemagnetospheric
configuration
andhedidnotprovide
the
try(theequatorial
plane
andthenoon-midnight
meridian).
ionospheric
convection
pattern
(even
though
hedidconsider
Theduesouth
andnorth
IMFconfigurations
have
been
the ionospheric
convection
patterns
forsouthward
IMF).
subjects
ofcountless
investigations
starting
withtheseminal Manyof thelatermodels
fornorthward
IMF haveas-
paperby Dungey [1961].
Copyright1999by the AmericanGeophysical
Union.
Paper number 1999JA900378.
0148-0227/99/1999J A900378509.00
sumedthat the magnetosphere
is open. One of the difficultiesfor an openmagnetospheric
modelfor northwardIMF is
thatit is difficultto disconnect
themagnetospheric
field from
the IMF in the distanttail (we note that for southwardIMF,
the two magneticfieldsbecomedisconnected
throughnightsidereconnection).In orderto solvethis problem,someof
28,361
28,362
SONG ET AL.' SOLAR WIND-MAGNETOSPHERE
INTERACTION
FOR NORTHWARD LMF
thesemodelsinvokedeithera finiteBy component
[Russell, in the distanttail region,andmorecomplicatedionospheric
1972; Reiff and Burch, 1985; Burch et al., 1992] or a finite
Bz component[Kan and Burke, 1985; Crooker,1992] (both
of whichbreakthe symmetryof the configuration)or require
quite complicatedmagnetic field geometries,while others
did not providea completethreedimensionalconfiguration.
Recently, Song et al. [1999] proposeda closedmagnetospheremodel for due northwardIMF, which is globally
consistentwith the Dungey [1961] reconnectionmodel. It
providesa self-consistent
frameworkencompassing
not only
magnetospheric
convectionbut alsoreverseionosphericcon-
currents[Fedderand Lyon, 1995;Mobarry et al., 1996].
Resultsfrom anotherrecentsimulationmodel were presentedby Berchemet al. [1995] and Raeder et al. [1995].
Similarto othermodels,thismodelalsoshowedcuspreconnection. Distinct from other models, however, in this model
the magnetosphere
is neverfully closed.Simulationsfor all
IMF
conditions started with a late-time solution for south-
ward IMF. An X-line type reconnectioncontinuesin the
near Earth magnetotail current sheet, even hours after the
IMF
was turned from south to north.
A channel of a few
vection cells and the northward Bz (NBZ) currents [Burke
et al., 1979; lijima et al., 1984; Zanetti et al., 1984; Clauer
and Friis-Christensen,1988; Taguchiand Hoffman, 1996].
These featuresare often difficult to model self-consistently
Earth radii wide is formed and persistsat the centerof the
magnetotaillinking nearthe Earthmagnetotailreconnection
regionto the solarwind. The simulationresultsdependon
in openmagnetosphere
models. One of the importantelementsof the Songet al. [ 1999] modelis the recognitionthat
distantclosedmagneticfield linescanmovetailwardinstead
of earthwardin the presenceof cuspreconnection.
The interactionbetweenthe magnetosphereand a purely
northwardIMF hasalsobeeninvestigatednumerically.Ogi-
IMF, the magnetospherewould be closed [Raeder, 1998].
initial conditions.
If the simulation starts with a northward
No ionospheric
convection
patternwasprovidedin thesepa-
pers [Berchemet al., 1995; Raeder et al., 1995].
Using yet anothermagnetosphere
model R. M. Winglee
and R. K. Elsen (unpublishedmanuscript1995) made several runs with due northwardIMF but different dynamic
no and Walker [1984] were the first to show reconnection pressureandmagnitudeof the IMF. In theserunsthe period
in the cuspregions. However, owing to the limitation of of steadynorthwardIMF lasted 1 to 2 hours. On the basis
the simulation domain, the distant tail could not be resolved of thesesimulations,R. M. Winglee and R. K. Elsen (unwell. The daysideconvectionin the equatorialplane ob- publishedmanuscript,1995) concludedthat for Bz _>$ nT
tained by Ogino and Walker [1984] is consistentwith the the lengthof the tail continuously
shrinksaslong asthe due
simulationresultsof the presentstudy.Anotherearly simu- northwardIMF is maintained.Eventually,shortmagnetotail
lationmodelfor northwardIMF waspresented
by Wu[ 1985]. configurationswere attained.
In his simulationan X-type geometryis formedat eachcusp
Gombosiet al. [ 1998] haverecentlypublisheda seriesof
region, although Wu [1985] suggestedthat it is a neutral magnetosphere
simulationswith steadynorthwardIMF conpoint and not a reconnectionpoint. Nevertheless,the sim- ditions. Thesesimulationsshowedclosedmagnetospheric
ulationsindicatedthat the magnetosphere
is closedand the configurationswith cuspreconnection.One of the interestlength of the tail decreasesas Bz varies from zero to a fi- ing resultsof theirparametricstudywastherelationship
that
nite positivevalue. This tendencyis also consistentwith the the lengthof the last closedmagnetospheric
field line (the
simulationsshownin the presentwork..
tail) variesas1/Bz for northward
IMF conditions
[Gombosi
Nearlya decadelater,Usadietal. [1993]presented
a sim- et al., 1998].
ulationmodel with a spatialcomputational
domainmuch
The presentwork usesthe MHD numericalmodel devellargerthanthe onesusedby the earlymodels.Theseresults opedat the Universityof Michigan [Gombosiet al., 1998]
againshoweda closedmagnetosphere
for northwardIMF, to providemoredetailedaccountof the processes
described
withreconnection
taking
placein thecuspregions.
Usadiandrequired
in themodelof Songetal. [1999].Herewe
etal. [1993]alsoconfirmed
thatthemagnetotail
becomes
concentrate
onthephysical
understanding
ofsimulation
reshorter
asthenorthward
IMF increases
fromzero.In addi- sults.
In section
2,webriefly
describe
thenumerical
scheme
tion,theflowin theequatorial
planein thedistant
tailshowsusedin thesimulations.
In section
3, wediscuss
theresults
bothearthward
andtailward
convection,
although
theflow ofsimulations
andtheirphysical
implications.
Then,insecpattern
becomes
noisier
asthesimulation
timeincreases. tion4, wefocus
onthecoupling
processes
between
thesoMorerecently,
Fedder
andLyon[1995]andMobarry
etal. larwindandmagnetosphere.
Specific
topics
discussed
in[1996]published
theresults
obtained
froma significantly
clude
themagnetopause,
theformation
oftheLLBL,andthe
improved
model.It includes
a muchlargersimulation
do- length
ofthemagnetotail.
main,improved
ionospheric
boundary
conditions,
anda highresolutionupwindnumericalscheme.In additionto the fea-
turesshown
in previous
models,
such
ascusp
reconnection
2. Numerical Solutionof Ideal MHD
andclosed
magnetosphere,
theresults
alsoshowed
NBZcur- Equations
rents,ionosphericreverseconvectioncells,anda flow diver2.1. Description of BATS-R-US
gencein the equatorialplane near95/•E from the Earth in
themidnight.Amongthemajordifferences
betweenthese The codeusedin thisstudyemploysa BlockAdaptiveresultsandthosepresented
in ourpaperare a muchlonger Tree Solar-windRoe-typeUpwindScheme(BATS-R-US).
tail (thelengthof thetail is 155/•E, whiletheentiremag- It solvesthegoverning
equations
of idealmagnetohydrodynetosphere
is 165 /•E long), very smallLLBL/tail region namics,whicharewrittenin conservation
form as
SONG ET AL.: SOLAR WIND-MAGNETOSPHERE INTERACTION FOR NORTHWARD IMF
0U
Ot
+ (V-F)T- SB,
(1)
where the eight dimensionalsolutionand sourcevectorsU
andSB are givenby
p
pu
u-
B
V.B.
So--
(2)
28,363
The basicdatastructureusedin the BATS-R-US approach
is an adaptive-blocksscheme[Powell et al., 1999]. Each
blockis a Cartesiangrid of cells, and all blocksare identical
in structure.Adaptiveblockspartitionspaceinto regionsaccordingto the gradientsin solutionsof physicalquantities.
In a region where large gradientsexist, the resolutionswill
needto be refined.The blockis replacedby eightchild subblocks(one for eachoctantof the parentblock). Likewise,
if coarseningis needed,the eight childrenare replacedby a
parentblock. The blocksin the grid, at their variouslevels
of refinement, are stored in a tree-like data structure.
We note that the sourceterm SB arises solely from the
Galilean invariantform of Faraday'slaw [Jackson,1975].
It equalszero whenthe magneticfield is divergencefree and
the conventionalform of idealMHD equationsis recovered.
The divergence-free
conditioncanbe easilyspecifiedin the
solar wind, and it then convectsinto the simulation domain
accordingto the conservation
of the divergenceof the magneticfield which is obtainedby takingthe divergenceof the
thirdequationin equation(1). Finally,F is a flux tensorhaving the form
-T
BATS-R-US wasspeciallydesignedto handleobjectswith
strongintrinsicmagneticfields. In this case,there is often
a large spatialgradient associatedwith the intrinsic magnetic field. The schemesolves for only the deviation of
the magneticfield from the intrinsicmagneticfield, namely,
B1 = B - Bo, where Bo is the intrinsicmagnetic field
correspondingto a dipole magneticfield with a strengthof
0.31 G at the equatorialsurfaceof the Earth. We notethat in
this formulation B 1 does not have to be small; therefore this
decomposition
is completelygeneral.
2.2. Boundary Conditions
At the upstreamboundarya free streamingsolarwind enters
the computationaldomain. The otherfive outerboundF •
,
(3)
aries
contain free-streamingsolar wind conditions. Since
uBBu
theseboundariesarefar enoughawaysothattheplasmaflow
is supersonic
and superalfv6nicat theselocations,the effects
_ u e+p+Tfi-guo
]-•
of the boundaryconditionson the solutionsare minimal.
The inner boundaryof the simulationdomainis at 3 RE.
wherethetotalplasmaenergydensitye is givenby
At the inner boundary the boundary conditionsallow no
massflux acrossthe boundary. Reflective boundarycon1
p
1 B2
3' -- I
2po
ditionsare usedfor the massdensityand thermalpressure.
Neumannconditionsare applied to the tangentialcompoand 7 and p0 are the ratio of specificheatsand the perme- nentsof the deviativemagneticfield (the differencebetween
ability in vacuum,respectively.Represented
in the equation the dipolemagneticfield and the actualmagneticfield) and
set are four equationsfor the conservationof mass,momen- Dirichlet conditionfor the normalcomponent.The velocity
tum, and total plasmaenergy,as well as the inducedelec- at the inner boundaryis specifiedby the couplingwith the
tric field as describedby Faraday'slaw. The variablesp, u, ionosphereas to be discussed
below.
p, and B correspondto the density,velocity,pressure,and
The coupling betweenthe magnetosphereand the ionomagneticfield, respectively.
sphereis taken into accountin a conventionalway. It asWe describebrieflyherethe BATS-R-US code.A detailed sumesthat magnetospheric
field-alignedcurrentsflow from
descriptionof the code can be found in the work of Pow- the magnetospheric
inner boundaryinto a height-integrated
ell et al. [1999]. In this code, the hydrodynamicand elec- electrostaticionosphere.UnderMHD conditions,V' ßj = 0.
tromagneticeffects are solvedin a fully three-dimensional This means that the normal componentof the magnetotightly coupledmanner,ratherthanin separatesteps[Gom- sphericcurrent jn at the interface betweenthe magnetobosiet al., 1996; Powell et al., 1995, 1999]. The tight cou- sphereandionosphere(i.e., the currentthatdownwardenters
pling betweenthe hydrodynamicandelectromagnetic
quan- the ionosphere
from the magnetosphere
is positive)mustbe
tities makesthe schemework equally well acrossa range divertedinto horizontalcurrentsin the height-integrated
thin
of severalorders of magnitudein plasma /3 where /3 is ionosphere.With the help of Ohm's law appliedin the ionthe ratio of the thermal and magneticpressures.A high- sphereat R0 this can be written as
resolutionfinite volume solutionupwind schemeis used
basedon two accurateapproximateRiemannsolvers,Roe's
j,• (R0,0,•b)- -[Vt. (E ßV'•P)t]r=no,
(5)
puu
+ (p
+ 2p'•
Po
1B2)
i- _I__BB
(
1B2• 1(B.u)S
e- •pu2+
+
,
(4)
[1981] scheme [Powell, 1994] and Linde's [1998] solver.
where •p is the ionosphericelectrostaticpotentialand E is
order accuracyaway from discontinuities,while simultane- the height integratedconductivitytensor. The symbol
The code uses a limited reconstruction
that ensures second-
ouslyproviding
thestabilitythatensures
tomaintain
nonoscil-denotes
thetangential
component
of thegradient
operator
in
latorysolutions.
theionosphere
surface,
thesubscript
"t" refersto thetangen-
28,364
SONGET AL.: SOLARWIND-MAGNETOSPHEREINTERACTION FOR NORTHWARDIMF
tial components
at the magnetospheric
boundary,and 0 and
½denotelatitudeandlongitude,respectively.Oncetheionosphericelectrostatic
potentialis derived,it is mappedalong
the magneticfield linesto the magnetospheric
innerboundary assumingthe magneticfield lines to be equipotential.
One can then calculatethe convectionvelocity,
Plate 1a showsthe noon-midnightmeridianfor the northern hemisphere.The white lines with arrowheadsare magnetic field lines. The color codingrepresentsthe logarithm
of thethermalpressure.The thick red linesindicatetopological boundarieswhich separateflows of distinctcharacteristics. Plate lb showsthe equatorialplane for the morningside.
ui--
BiB•
xV•b)
t'
2.3. Simulation
Parameters
The solarwind and terrestrialparametersusedin the pre-
lines with arrowheads
are streamlines
and the
color codingrepresents
the sonicMach number.
(6)
wherethesubscript"i" denotesthevaluesat theinnerboundary. This convectionvelocity is usedas the boundarycondition for the magnetospheric
simulation. This procedure
has been summarizedby Goodman [1995], whoseresults
were modified by Amm [1996]. In the presentsimulation
we solvedthe equationsgivenby Amm [1996].
White
It can be seen in Plate 1 that a bow shock is formed
in
front of the magnetosphere.This fast magnetosonicshock
decelerates,deflects,and heatsthe solar wind plasma. The
magnetosphere
is essentiallyclosedwith the exceptionof a
small region near the cuspwhere reconnectiontakesplace
betweenthe IMF andthe magnetospheric
field.
3.1. Planesof Symmetry
Thesimulation
results
arepresented
onthreesurfaces:
the equatorialand noon-midnightmeridianplanesand the
sent
simulations
arebased
onthecommunity
reference
bench-height-integrated
ionosphere
(seePlate2).Boththeequatoplanesare planesof symmetry
mark suite. The elementsof the ionosphericconductance rial and the noon-midnight
tensorare constantin time and spatiallyuniform (E•, = 5 for the particularsituationconsideredin this paper, This
S, E•t = 0 S, Eo = 5000 S, where E r, E•t, and Eo are meansthat the solutionmust exhibit certainpropertiesin
ionosphericPedersen,Hall, and field-alignedconductances, theseplanes.
In the noon-midnightmeridianplane, both the magnetic
respectively.The specificheat ratio is 5/3. The reference
run usesan undisturbedsolar wind velocity u = 400 km/s,
field and the velocityhave no componentnormal to the
in thelastsection,in themagnetosphere,
density
n = 5 cm-a, andacoustic
Machnumber
of 8. The plane.As discussed
the governingequationsare ideal MHD. In ideal MHD, the
magneticfield linesavd streamlinesare equipotentials
becausethe electricfield is perpendicularto both magnetic
field and velocity. The magneticfield lines in the noontionalcellis0.125x 0.125x 0.125Ra•andsixlevels
ofre- midnightmeridianplanecanbe of thesamepotentialif they
finementare used. The total numberof computationalcells are on the same streamline. The red thick lines in Plate l a
is around1 million. The height-integrated
electrostaticiono- separateregionsof differentflowsandhenceregionsof difsphereis locatedon a sphericalsurfacewith a radiusof 1.08 ferentpotentials.
For symmetryreasonsthe magneticfield hasno compoR•.
The codehas beencarefully validatedfor northwardIMF nent in the equatorialplane,thereforethe magneticfield is
runs.The validationstudieshavebeenpresentedin an earlier alwaysverticalto the Z = 0 plane and pointsnorthward
paper[Gombosiet al., 1998]. Here we only mentionthatthe everywherein our case. In contrast,plasmastreamlinesdo
solutionsaregridconvergedandall steadystatesolutionsare not leavethe equatorialplane. An immediateconsequence
of thesefactsis thatthemotionalelectricfieldis in theequaindependentof the initial conditions.
torial planeandit is normalto the streamlines.The potential differencebetweentwo givenstreamlines
in the equato3. Results: Qualitative Analysis
rial planeremainsthe samethroughout
the plane.MagnetoPlate 1 shows results of our reference run. The results
sphericelectriccurrentsare associatedwith the distortionof
presentedare the steadystate solution. This result can be the magneticfield from the dipolemagneticfield. Stretchobtained from either northward IMF and southward IMF as ing of the magneticfield generates
currentsin theclockwise
the initial condition.The dynamicprocesses
from the initial directionwhile a compression
of the magneticfield results
conditionsto the steadystatesolutionsseemto follow a large in a counterclockwise
currentin the equatorialplane. The
scale monotonic evolution. Little evidence for turbulence or
Lorentz force associatedwith thesecurrentsalwaystends
burstybulk flows, suchas thosereportedby Angelopoulos to restorethe dipolemagneticfield geometryin the closed
et al. [1994], has been observed.The solarwind input pa- magneticfield line region. The divergenceor convergence
rameters used are as described in the last section. Later in
of thesecurrentswithin the closedmagneticfield line rethepaperwe will discussresultsof simulationrunswith dif- gion generatesthe field-alignedcurrentsflowingout of the
ferentinputparameters.Theserunswill be usedto examine equatorialplane. Thesefield-alignedcurrentsmap into the
the globalmagnetospheric
responseto differentsolarwind ionosphere.However,we notethatthe majorcomponent
of
conditions.
the currentin theequatorialregionof the distanttail doesnot
interplanetary
magneticfield is 5 nT andduenorth.
The computationaldomainextendsfrom a: = 192 R• to
a: = -384 R• alongthe Sun-Earthline and from -192 to
192 R• in the •/and z directions. The smallestcomputa-
SONG ET AL.' SOLAR WIND-MAGNETOSPHERE
INTERACTION
FOR NORTHWARD
IMF
28,365
a)
IogP
'I.6
'1.42
4O
'1.24
'1.o6
IllHi
o.88
0.7
IN
ml
0.52
o.34
o.'16
..0.02
-0.2
N
Ism
2O
mlnllll
[][]llnl[]11nl
III1
III
Illl
I[]t
20
0
-20
-40
-60
i
x
b)
M
8
[]
7.2
6.4
4O
5.6
4.8
4
3.2
2.4
1.6
0.8
0
2O
m
%
20
0
-20
-40
-60
-80
x
Plate 1. Simulationresultsfor the referencerun with northwardIMF. The upstreamconditionsare n = 5
cm-3, u = 400km/s,acoustic
Machnumber
- 8, specific
heatratio= 5/3, andIMF magnitude
= 5
nT. The two panelsare the following: (a) Noon-midnightmeridian for the northernhemisphere. The
white lines with arrowheadsare magneticfield lines. The color codingrepresentsthe logarithm of the
thermalpressure.The thick red linesindicatethe topologicalboundarieswhich separateflows of distinct
characteristics.(b) Equatorialplane for the morningside. White lines with arrowheadsare streamlines
and the color codingrepresentsthe Mach number. The two red lines indicatethe boundariesbetween
distinctflow regions.The dashedsegmentindicateswhere streamlinesare difficult to define becauseof
theextremelylow velocityin the region.The redhalf-dotindicatesthe locationof thelastclosedmagnetic
field line in the midnight.
28,366
SONG ET AL.' SOLAR WIND-MAGNETOSPHEREINTERACTION FOR NORTHWARD IMF
'"• o o o o
ooooooooooo
o
o
o
I
o
I
o
I
o
I
I
i
\
/
-•
/
/
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\
/
\
/
\
/
.
/
/
/
x,
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/
/
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/
SONG ET AL.: SOLAR WIND-MAGNETOSPHERE
INTERACTION
FOR NORTHWARD IMF
28,367
converge/diverge
within the magnetosphere.
It is closedvia
In our simulation model in regions of closed magnetic
field lines the forces that directly affect the flow are the
the "magnetopause"
currentin the tail region.
pressuregradientforce and the Lorentzforce. The pressure
3.2. Global Topology and Coupling
differencebetweenthe subsolarmagnetopauseand the last
Inspectionof Plate 1 revealsthatthereare threetopologi- closedmagneticfield line on the nightsideis an important
cally distinctregionsin themagnetosphere:
theinnercoreor driving force for the plasma flow. This pressuregradient
plasmasphere,
the outermagnetosphere,
andthe low-latitude force is further enhancedby the pressurebuildupupstream
and the low-pressureregion
boundarylayer (LLBL)/tail region.Theseregionsare sepa- of the daysidemagnetopause
ratedby boundarieswhich are markedin Plate 1 by thick red immediatelydownstreamof the last closedmagneticfield
lines. In Plate lb in a largeregion,from -10 to -30RE, the line in the distant tail, as seen in Plate l a.
An importantfeaturein an idealMHD flow is thatthe moflow velocityis very small. Errorsin both computationand
streamlinetracing are significant.Streamlinesin this region tions of different streamlinesare related through the induchave not been drawn. However, qualitatively,one can see tion equationwithout invokinga viscousforce. The electric
potentialdifferencebetweentwo givenstreamlinescan couregionsof different flows. The red line near X -- -20 RE
to the ionosphereand the solarwind
at local midnight is picked up by a changein the Y com- ple the magnetosphere
ponentof the electricfield, which is not shown. The night- alongmagneticfield lines and can affectplasmatransportin
sideboundarybetweenthe plasmasphere
and outer magne- theseregions. It shouldbe further noticedthat this effect is
tospherecannotbe clearly resolvedin the simulation. The not in the directionof the velocity vector,and henceit can
physicsof theseregionswill be discussedlater in this sec- causeshearsin the plasmaflow. Sincein ideal MHD thereis
tion.
no functionalrelationshipbetweenelectricfield andelectric
Plate 2 shows the results of the reference run for the
current,they are not necessarilyparallel to each other. In
height-integratedionosphere.One can see that three pairs regionswherethey are parallel,the plasmagainsenergyand
of field-alignedcurrentsconnectthe magnetosphere
and the the fields lose energy. These regions are sometimesconsideredanalogousto loads in electric circuits. In the reionosphere.Closestto the magneticpole is the pair of NBZ
currents,followed by the regionI and region II currentsas gionswhere the currentand electric field are antiparallel,
one movesequatorwardin the ionosphere.Associatedwith the plasmalosesenergyand the fields gain energy. These
the NBZ currentsis a pair of sunwardconvectioncells in regionsare sometimesreferredto asdynamos.For example,
the samesenseas the reverseconvectioncells. Equatorward as shownin Plate lb, sincethe magneticfield is northward
from the reversecells is a pair of antisunwardconvection and the flow in the LLBL/tail region is antisunward,the eleccells with a sense consistent with viscous convection cells.
tric field pointsdawnward.Becausethe magnetotailcurrent,
The field-alignedcurrentswith the same senseas region whichis not shown,is from dawnto dusk,it is antiparallelto
II currents shown in Plate 2 must be treated with considerthe electricfield. Thereforethe LLBL/tail region functions
able caution.It shouldbe emphasized
that eventhoughour as a dynamo.
In our model, the governingequationused in the ionoMHD simulationshowsa pressuremaximumin thering current region,it is not a realisticring current,sincethe model sphereis not ideal MHD, but Ohm's law which directly redoesnot includeadequatelyphysicalprocesses
that generate lates the current density to electric fields. There are two
the ring current.Furthermore,in our presentruns,the iono- major mechanismsthat drive the ionosphericplasma:fieldsphericconductances
havebeenassumedto be uniform. Re- alignedcurrentsandelectricfields.They operateself-consisgion II currentsare so weak that they are not able to drive a tently throughOhm's law. Since in our ionosphericmodel
separatepair of cells. In reality,an importantdriver of con- we do not directly solve the momentumequation,the two
vectioncells associatedwith regionII currentsmay be the mechanismsaffect the flow in different ways. (1) Fieldgradientsin the conductances,as to be discussedin section alignedcurrentsclose in the ionospherethroughhorizon5.4, which are not includedin the presentruns. In addition, tal ionosphericcurrents. These horizontal currentsgenersincethe dipolemagneticfield usedin our modelis nonrotat- ate ionosphericelectric fields throughOhm's law. In the
ing, the corotatingelectricfield is not includedin the model. presenceof the Earth's intrinsic magneticfield this elecWe recognizethe incompletenatureof ourmodel,andthere- tric field causesan E x B drift motion of the plasma. (2)
fore we will not discussanyphenomenaassociated
with re- The magnetospheric
electricpotentialmapsdirectlyto the
gionII currentsandin the innermagnetosphere
in thispaper. ionosphere(sincein MHD magneticfield lines are equipoMoreover, we note that in the absenseof realisticregion II
tenrials). The potentialdifferencebetweenmagneticfield
currentsonecannotaddressthe issueof field-alignedcurrent lines resultsin the ionosphericelectric field. This ionoclosurein themagnetosphere
in anyquantitatively
consistent sphericelectricfield needsto be consistentwith that derived
manner,sincea very importantcomponentof the globalcur- from the field-alignedcurrents,or additional Petersencurrentsystemis missing.In spiteof the limitations,whenused rentswill be generatedandneedto be closedin someways.
with appropriatecaution,globalMHD simulationsprovide In addition,whengradientsin conductances
are allowed,the
importantinsightsinto solarwind-magnetosphere
coupling gradientsin the conductances
will be built up to modulate
processes.
the abovetwo processes.
28,368
SONG ET AL.: SOLAR WIND-MAGNETOSPHERE
INTERACTION
FOR NORTHWARD IMF
discussion
of thiscouplingprocess,oneis referredto Song
3.3. Interpretation
et al. [ 1999].
Plate 3 summarizesour physical understandingof the
In the following,we will providemore detailsof the solar
global convectionand mapping patternsin the magnetowind-magnetosphere
interactionportionof thisglobalphyssphereand ionosphere[Songet al., 1999]. There are three
ical picture. The detailsof the ionosphere-magnetosphere
major topologicalregions in the magnetosphere:the incouplingwill be discussed
in a laterpaper.
ner core or plasmasphere,the outermagnetosphere,
and the
LLBL/tail region. Theseregionsare separatedby separatrix
surfaces.They correspondto the magnetopause,
the bound- 4. Results: In-depth Analysis
ary betweenthe outermagnetosphere
andLLBL/tail, andthe
4.1. Bow Shockand MagnetopausePosition
plasmapause.Under ideal MHD approximation,thereis no
In the referencerun, the bow shockis locatedat 14.3/t•
massflux acrossa separatrixsurfaceunlessthereis a toporegion,23/t• at thenoon-midnight
terminalogical changeat the surface.The inner two separatrixsur- in the subsolar
facesare magneticsurfaces.However,becauseof reconnec- tors,and26.3/t• at the equatorialterminators.If onefitsthe
is 0.84 in
tion at the cusps,the outermostsurface,the magnetopause, daysidebowshockwithanellipse,theeccentricity
meridundergoesa topologicalchange in certain areas. Conse- the equatorialplaneand 0.61 in the noon-midnight
quently,the solarwindflux entersthroughthemagnetopause ian plane. The simulationresultsare in generalagreement
The averageobserved
eccentricity
in the
on the daysideand magnetosphericflux exits throughthe with observations.
equatorialplaneis 0.81 [Farris et al., 1991].
nightsidemagnetopause.
In the referencerun the last closedmagneticfield line
The LLBL/tail region consistsof a pair of convection
channelsfrom the subsolarmagnetopause
to the last closed is locatedat 10.7 /t• in the subsolarregion, 14.8 /t• at
magnetic field line in the distant tail. The convectionin the noon-midnight
terminators
and 15.0/t• at the equatothis region is directlydrivenby the entry of the solarwind rial terminators,
indicatingthatthe daysidemagnetosphere
plasma. In the ionospherethis region mapsto the region is slightlyelongated
in thedawn-dusk
direction.Theempirlocationusingthegivenvaluesof Bz and
within the polar caps. This is the regionwhereone expects ical magnetopause
precipitationof particlesof solarwind origin. Few particles solarwinddynamicpressure
is 11.1/t• atthesubsolar
point
from the steadilytrappedmagnetospheric
populationwould and 15.5/t• at the equatorialterminator[Shueet al., 1998].
be observedin the polar cap at ionosphericaltitudes. The The difference is within the resolution of the simulation and
distortionof the magneticfield in this regiongeneratescur- theuncertainty
of the observations.
It is worthmentioning
rentsthat map to the ionosphereand correspondto the NBZ thatthesubsolar
magnetopause
is definedin ourcaseby the
lastclosedmagneticfieldline, namely,pointA in Plates3a
The convectionin the outermagnetosphere
forms a pair and 3b. If one followsthe streamlinealongthe Sun-Earth
of closedcells. Becauseparticlescan be trappedin thisre- line,it splitsat pointB in Plate3b, whichis theinneredge
gion for a long time, the plasmaexhibitsthe characteristics of theLLBL, insteadof themagnetopause.
of a steadilytrappedpopulation.The ionosphericfootprint
Reconnection
betweenthe IMF and the magnetospheric
of thisregionis in theregionequatorwardof the polarcaps. fieldtakesplaceat (1.6, 0, 13.2)/t• in the noon-midnight
a few/t• tailwardof thecusps.Themagnetotall
is
Any precipitationin thisregionshouldshowmagnetospheric meridian,
theresults
fordifferent
upstream
type plasma. The convectionin the outermagnetosphere
is 56/t• long.Table1 shows
TheBz = 10 nT runkeepsall otherparameters
not directly driven in the magnetospherebecausein ideal conditions.
currents.
MHD
there is no momentum
transfer across streamlines.
It
is drivenin the ionosphere
by Pedersencurrents.ThesePetersencurrentsare associatedwith the equatorwardcurrents
producedby the NBZ currentswhentheyflow into andout
of the ionosphere.In the ionosphere
thesecurrentscango
underthroughthe topologicalboundarybetweenthe outer
magnetosphere
andtheLLBL/tail, becausein theionosphere
the governingprocesses
are not ideal MHD. Here we recall
that the field-alignedcurrentconditionis derivedfrom ideal
MHD for low-/3 slowly-movingplasmas. The currentsdo
notflowacrossthemagneticfieldlinesor streamlines
except
in the equatorialregion,wherethe/3 or velocityis not low
andthecurrentsaregenerated,
andin theionosphere,
where
ideal MHD needsto be replacedby non-idealMHD. The
Lorentz force (more accuratelythe electricfield drift in the
simulation) associatedwith these currentsdrives the ionosphericconvection,
andconsequently
mapsto anddrivesthe
convectionin the outermagnetosphere.For more detailed
thesameasthereference
runbutdoubles
theIMF strength.
Similarly,
ther• = 10cm-3 runonlydoubles
thesolarwind
density.
The difference in the standoff distance between the 10
nT run and the reference run is smaller than a fraction of
a grid size. At the sametime the magnetopause
becomes
lessflared.Suchdependence
is consistent
with observations
[Shue et al., 1998]. The bow shock moves outward sub-
stantially
andbecomes
moreopen,indicating
a thickermagnetosheathfor strongerIMF. As we know, the thicknessof
themagnetosheath
is inversely
proportional
to theupstream
magnetosonic
Machnumber.The higherIMF strength
leads
to a higherAlfv6n velocity,andconsequently,
to a lower
magnetosonic
Mach number.The decreased
magnetosonic
Mach numberresultsin a thickermagnetosheath.
The increased
IMF strength
alsoresultsin a shortermagnetotail.
Thiseffectwill bediscussed
laterin thepaper.
Whenthesolarwinddensityishigher,thehigherdynamic
SONGET AL.' SOLARWIND-MAGNETOSPHEREINTERACTION FOR NORTHWARD IMF
28,369
Table1. Locations
of theBowShock,Magnetopause
andLastClosedFieldLine
Upstream
BowShock,
RE
Z
Tail,
X
15.0(15.5)*
14.8
-56
14.1
13.5
-32
13.7
-76.2
Magnetopause,
RE
Condition
X
Y
Z
X
Reference
14.3
26.3
23
10.7(11.1)*
10 nT
15.3
29.0
25
10.5
15.0
10 cm'3
12.2
22.5
21.9
9.4
* Valuesin parentheses
arefromempiricalmodel[Shueet al., 1998].
Y
pressure
pushesthe magnetopause
inwardby •12%. An eling time for the field lines to communicateto the equatoempiricalscalinglaw of 1/6.6 [Shueet al., 1998]translates rial region of the flux tube aboutthe fact that the magnetic
at the cusp.It will takeeven
a factor of 2 increasein the dynamicpressureinto an 11% field line hasbeendisconnected
longerbefore the plasmaon theseflux tubescan be assimpendence
of the subsolar
magnetopause
on the solarwind ilated to the solar wind. We shouldpoint out that the last
•.o
densitybetweenthe simulation
andthe empiricalmodelis closedfield line on the nightsidein Plate 3a corresponds
below the resolutionof the simulation,indicatingthat the pointa in Plate3b, whichis earthwardof the shadedarea.If
topologicalboundaryas the
modeldescribes
verywell thestand-offdistanceof themag- one definesthe magnetospheric
netopause
as well as its dependence
on the solarwinddy- last closedfield line, he/shemay find a ditch on the nightto the magnetic
namicpressure.
Thedawn-dusk
terminator
distance
remains sidetopologicalsurface.This corresponds
from the magnetothe same as the reference run, while the subsolarmagne- flux tubethat hasjust beendisconnected
topauseis pushedinward,indicatingthatthe magnetopausesphericfield. The size of the ditch is determinedby the rebecomes
moreflaring.Thistendencyis alsoconsistent
with connectionrate amongotherfactors.In the equatorialplane,
may appearto havea pair of wings.
the empiricalmodels[e.g.,Shueet al., 1998]. The higher the magnetosphere
Near the cusps,thereis a gapbetweenthe daysidecurrent
solarwind densityincreases
the magnetosonic
Mach number via the Alfv6n velocity, resultingin a thinner magne- and nightsidecurrent. In a steadystate,the daysidecurrent
tosheath.This dependence
is consistent
with the simulation is fartherfrom the Earththanthe nightsidecurrent.Someof
results.The magnetotail
appearsto be longerfor the high- thesefeaturescan be betterseenin the bottom-rightpanelof
densityrun. Thisdependence
will be discussed
in morede- Plate 5. Therefore,for satellitesflying throughthe cuspretail in section 4.4.
gions,multiplecurrentsmaybe observedin a singlepassfor
stronglynorthwardIMF. The two currentsarein theopposite
4.2. Magnetopause/Topological
Boundary
direction,but the nightsidebranchhasa strongerintensityin
Plate4 showstheY component
of theelectriccurrentsin a largerregion.We believethatpart of the nightsidecurrent
increase in the stand-off distance. This difference in the de-
thenoon-midnight
meridianplane.On thedayside,mostof
the currentsare generatedat the bow shock. The Lorentz
force due to these currents decelerates the solar wind flow.
is closed via the bow shock current.
4.3. Formation of Low-Latitude Boundary Layer
The mechanisms
leadingto the formationof LLBL have
alwaysbeenan importantsubjectfor globalmagnetosphere
models.The two majorissuesare(1) howparticlesenterthe
LLBL, and (2) what forcesdrive the flow. Previouslyproposedentrymechanisms
includediffusion,reconnection
and
impulsivepenetration.Sinceherewe discuss
only steady
impulsivepenetration
will notbe considered.
shownthatfor northwardIMF thetopologicalchangeoccurs statesolutions,
We investigate
thepossibilityof diffusiveentryby tracing
at the inner edgeof the sheathtransitionlayer [Songet al.,
theplasmaflux in theLLBL. In anMHD treatment,thedif1993].
On the nightside,themagnetopause
currentandthe topo- fusionbroadensthe regionof densitygradient.This causes
logicalboundaryof the magnetosphere
becomecompletely real masstransferif the topologicalboundaryis locatedat
different. In the noon-midnightmeridian plane most of the edgeof the high-densityregion. In contrast,the difcan be different. The populathe current is associatedwith magneticfield kinks located fusionin particletreatments
around20 to 30 R• aboveand below the equator,a region tionson the two sidesof the boundaryare different.Each of
diffusesaccording
to thedensitygradient
few satelliteshave visited yet. If one usesthis currentto thesepopulations
define the boundaryof the magnetosphere,the "magneto- of theirownpopulation.Thereforethediffusioncanbe bidisphere"would appearto be open. Betweenthe last closed rectional.After particlesare diffusedacrossthe boundary,
anddrift motionwill spreadtheseparticles
field lines and the magnetopause
currentthe magneticfield theirgyromotion
andparticlecharacteristics
are similarto (and observation- in the regionawayfrom the diffusionregion. This results
ally difficult to distinguishfrom) thosein the closedmag- in a real particleflux transfenFrom our MHD simulation
neticfield line regionin the magnetotail.This is quitenatu- results,we tracethe magneticfield linesanddeterminethe
ral, sincethesefield lineshavejust recentlylost their topo- topologicalboundaryin the equatorialplane. Plasmaentry
to streamlines
crossingthemagnetopause
topological connectionwith Earth. It will take an Alfv6n trav- corresponds
Most of themagnetopause
currentappearsin theregionupstreamof the firstclosedmagnetospheric
field line. The observations
of the sheathtransitionlayer,or plasmadepletion
layer,areconsistent
with thisregionof current.The topologicalboundaryitself containslittle currentandmarksthe
inneredgeof the magnetopause
current.Observations
have
28,370
SONG ET AL.: SOLAR WIND-MAGNETOSPHERE INTERACTION FOR NORTHWARD 1MF
logicalboundary.Sincediffusionoccursin theentiremagne- is to understand
the dependenceof the tail lengthon varitopause,one wouldexpectthat thereare streamlines
across ousupstreamparameters
and hencethe physicalprocesses
the magnetopause
over a very largeregion. In contrast,re- involved. As seenin Plate 3b, in a closedmagnetosphere
connectionentry occurin a limited locationnearlocal noon. model, the length of the magnetotailis determinedby the
Near the daysidemagnetopause,
our grid sizeis 1 -RE,and processes
thatdriveandimpedethe LLBL flow.
it is doubledin the nightside. A coarsergrid will result in
We first examinethe effectsof the viscousinteraction.In
a greaternumericaldiffusion.As shownin Plate6a, in the ournumericalmodel,thereis no physicalviscosity.The visequatorialplane,in a largeregionthe streamlines
areparal- cosityarisesowingto the numericaldiscretization.The nulel to the magnetopause
topologicalboundary,andhenceno mericalviscosityis proportionalto the size of a simulation
significantdiffusionis present.
cell. A lowerspatialresolutionin the simulationresultsin a
The plasmaentry in our simulationsis facilitatedby re- highernumericalviscosity.As shownin Plate 5, we have
connectionthat takes place at high latitudes. The recon- made severalruns with different spatial resolutionswhile
nectionprocesscutsthe magnetosheath
flux tubesand con- keepingotherparametersthe same[Gombosiet al., 1998].
nectsthem with the magnetospheric
flux tubes.Thesenewly The resolutionis inverselyproportionalto the number of
formed flux tubesbring the solar wind plasma as a whole cellsin eachrun aslabeledaboveeachpanel. The color codinto themagnetosphere
with the sameprocesses
asdescribed ing representstheintensityof the currents.As theresolution
by Songand Russell[1992] and Songet al. [1994]. Most of increases,one can seebetterresolvedcurrents.For the lowthe particleentry is concentrated
in the subsolarregion. In est resolutionrun, the tail is 58 -Rs long. As the resolution
contrast,the entry for the diffusionshouldoccurrelatively increases,the tail shortensto 55 -RE. (Here we shouldpoint
uniformally in a large spatialregion.
out that the length of the tail for the runs using the same
In an MHD treatment,the forcesactingon a flow can, in upstreamparametersas the referencerun may be slightly
piinciple, be the viscousforce, pressuregradientforce and differentbecauseit is obtainedfrom differentsetting.HowLorentz force. In the LLBL, the Lorentzforce associated ever,eachof therunsis comparedwith otherrunsunderthe
with the currentscreatedby the magneticfield distortionis samesetting.)The tail lengthremainsessentiallyunchanged
sunwardpointedand hencecannotbe a driving force. We as the resolutionbecomeshigherandhigher. Thereforeone
will evaluatethe importanceof the viscousforce in section may concludethat the tail in our high-resolutionrunsis not
4.4 when we discussthe lengthof the tail. It will showthat drivensignificantlyby the viscousforce.
the viscousforce hasvery limited effectson the flow.
As discussed in the last section and shown in Plates 5 and
As shownin Plate 1a, the pressurenearthe subsolarmag- 6b, the driving force for the LLBL/tail is the pressuregranetopauseis •27 timeshigherthan that nearthe last closed dientforce from the daysideto the nightsideand the drag
magneticfield line in the midnight. The pressureoutside force is the Lorentz force associated with the cross-tail curthe last closedmagneticfield line in the midnight is even rent. Most of the cross-tailcurrentis closedwith the nightlower, which providesan additional suckingforce. This side "magnetopause"
current,and a small portioneventulower-pressureregion is associatedwith the changein the ally is divertedto becomethefield-alignedcurrents,mapsto
direction of the magneticcurvatureforce. With the large theionosphere,
anddissipates
there[Sonnerup,1980a].The
pressuregradient,the magnetosheathplasmaenteredin lo- lengthof the tail is determinedby the balancebetweenthe
cal noon experiencesan expansionwhile being draggedat driving anddragforces[Songet al., 1999].
their feet in the ionosphereas describedby Songand Russell
As pointedout by Songand Russell[1992], the driving
[1992], Yanget al. [1994], and Song et al. [ 1994]. Further
pressure
is proportional
to v/1 + • + 1, where/3is themagevidencefor the pressuredriven can be found in Plate 6b.
netosheath
plasmabetanearthe magnetopause
topological
The streamlinesin the distanttail regionare nearlyperpen- boundary
at localnoon.In thedistanttail, themagneticfield
dicular to the contoursof the pressure.Namely, the flow is
is highlystretched
andtheLorentzforcetheremayonlybe
moving antiparallelto the pressuregradient. Therefore we
a weak functionof distance.The magnetosheath
"plasma
concludethat the LLBL is primarily drivenby the pressure parameter"
v/1 +/3 + 1 nearthesubsolar
magnetopause
begradientforce. In a highly simplified model, Song et al., comesthe key parameterdeterminingthe lengthof the tail.
[ 1994] neglectedthe gradientsnormalto theboundarylayer. Figure l a showsthe dependence
of the tail lengthon the
Our simulationhas shownthat gradientsdo existnormalto magnetosheath
plasmaparameter.Thereis a generallinear
the boundaryand can be large in the flanks and nightside; relationshipbetweenthe two. In theseruns, the solarwind
seePlate 6a for example. Therefore, the observationsof the velocityandtemperature,
andthe ionospheric
conductivity
densitygradientand velocity shear [Phan et al., 1997] may are the commonparameters.In addition to the solar wind
not be necessarilycausedby viscousor diffusiveprocesses. densityandthe IMF strength,the spatialresolutionandthe
4.4. Length of the Tail
grid distributionare not the samebecausethe resultsare col-
lectedfrom runsfor differentpurposes.The differencesin
Becausethe length of the tail is one of few characteristic the grid distributionandin spatialresolutionwill causescatparametersthat specifythe size of the magnetosphere,
it has teringin the comparison.
The linearrelationship
indicates
attracted continuous interest. To us, the most critical issue that the pressure
gradientforces(not the pressureitself) in
SONG ET AL.' SOLAR WIND-MAGNETOSPHERE
INTERACTION
FOR NORTHWARD IMF
28,371
Noon-Midnight
cross-section
X
Magnetopause
(a)
•.t•,•9oetosp
here--LLBL/
,"
AB
C
c
b
a
Magnetopause
Equatorial
plane
(b)
AB
C
c
b
a
Polar
Ionosphere
(c)
11111111[111lll
'
I
I.._
"'
i
11111
iii
i
ii
i
Topological
boundaries
:
c
B
•
=
---
b
c
=-....
Plasma streamline
Directionof plasmaflow:
inward:(•),
outward:(•)
'
A
Direction
of current:
inward:
•), outward.'(•)
Plate 3. Global geometryof the magnetosphere
and ionosphericmapping[Songet al., 1999]. In all
panels,thick solidlinesrepresentthe separatrixsurfacesandthin solidlineswith arrowheadsindicatethe
directionof theflow,andtheshadedareasindicatetheregionsambientto newlyreconnected/disconnected
magneticfield linesthe topologicalstatusof whichis ambiguous.(a) The noon-midnight
meridianplane
of themagnetosphere
viewedfrom dusk.Circleswith crosses(dots)indicatetheplasmaflowsawayfrom
(toward)thereaderonthemorningside,butis divertedbeforereachingthenoon-midnight
meridianplane.
The magnetopause/cusp
is the surfaceconsisting
of curvesA-X-Earth on the daysideandEarth-aon the
nightside.The boundarybetweenthe outermagnetosphere
andLLBL/tail consistsof curvesB-Earth on
the daysideand Earth-bon the nightside,and the plasmapause
consistsof curves(7-Earth and Earth-c.
(b) The equatorialplaneof themagnetosphere
viewedfrom north.PointF indicateswheretheboundary
layerstreamline
turnsfromawayfrom sun-Earthline to towardthe sun-Earthline,andmapsto theendsof
the cusparc in Plate3c. (c) The northernionosphereviewedfrom top. The circleswith dotsandcrosses
indicatethedirectionsof the field-alignedcurrents,insteadof the plasmaflows.
28,372
SONG ET AL.' SOLAR WIND-MAGNETOSPHERE INTERACTION FOR NORTHWARD IMF
..l"•"
2
mmmmm
,,
40
1
mm
0.5
mm
0.1
m
mm
,,mm
-0.05
-0.1
im
-2
mmm
-3
N
mmm
mm,
ß
2O
ß
•: m
.:;;:
';•
{
ß: 'l-..:-,-,'
i•{),;:
20
mm I
i:i•L:
I
0
I
,
,
'
_I !
' I I I I
-20
i I
-40
-80
-60
x
Plate 4. The currentsin thenoon-midnight
meridianplane.The colorcodingshowstheY component
of
the currentdensity.
6O
Bz= 5 nT,83blocks,
1,026,048
cell , 55 RETail
Bz= 5 nT,43blocks,
128,256cell, 58 RETai
6O
40
40
20
20
-20
-20
-40
-40
-6o
20o
Bz=SnT, 63
64
il
6O
-,4o
-•o o•1oc
Bz 5nT, 103
.lno
k
T il
60
40
40
uf
20
20
½
-20
-•
•0
-40
20
0
-•
•0
-•
-80
-1•
-120
-140
•
0
-•
•0
-60
-80
-1•
-1•
-1•
Plate
5. Thelength
ofthetailwith
different
spatial
resolutions
[Gombosi
etal.,1998].
Theresolution
isproportional
tothecubic
root
ofthenumber
ofcells
which
isindicated
above
each
frame.
The
color
coding
indicates
themagnitude
oftheelectric
currents.
The
last
closed
magnetic
field
lineisindicated
by
thepurplelinein eachframe.
SONG ET AL.: SOLAR WIND-MAGNETOSPHERE
INTERACTION
FOR NORTHWARD
IMF
28,373
a)
•
....
•,-'•
'
7.3
. , • •. • I •J
6.4
(' ; ' • t I . .I t [..I l..L..•' ' l_S
5'2
ß
-75 -
Ill[
I ,
• • ' I
......[ ; •
;
6.1
>-50
'
u
7.2
8.4
-25
,
I
!
4
3.2
2.4
1.8
o
-10
o
-5
,
-75
-1•
i
,
-125
•
i
-1•
,
i
t
i
i
-175
x
..15
b)
Plate 6. (a) Zoom-in of the flankLLBL regionin the equatorial plane. The thin pink linesare projectionof the last
closedmagneticfield lines onto the equatorialplane. The
thickpink line indicatesthelocusof thelastclosedmagnetic
field lines. The colorcodingshowsthe velocitynormalized
by the solarwind soundspeedand the white lines with arrowheadsare plasmastreamlines.(b) Zoom-in of the distant
tail equatorialregion.The colorcodingshowsthe logarithm
of thethermalpressureandtheblacklinesarepressurecontours. The white lines with arrowheads are streamlines.
Plate 7. Velocity distributionin the equatorialplane. The
color coding showsthe velocity normalizedby the solar
wind soundspeed,which is 50 km/s, and the white lines
with arrowheadsareplasmastreamlines.The regionof highspeedflow above the solar wind with Mach number 8 is
highlightedin purple.
28,374
SONGET AL.' SOLARWIND-MAGNETOSPHERE
INTERACTION
FORNORTHWARD
IMF
gradientforce associated
with cuspreconnectionentry processes.If therewere a significantviscousforce, one would
expectthe curveto becomeflat at largervaluesof the tail
length. As shownin Figure la, up to 150 R•, the effectof
2.8
(a)
c, 2.5 nT
2.6
(10/cc,
5nT)
•/ (5/cc,
3nT)
2.4
(5/cc,
5nT)
•/
(•5/•,10
nT)
2.2
the viscousforce is not very strong.
Gombosiet al. [1998] reportedthat the tail lengthis approximatelyproportional
to thereciprocalof the strengthof
the IMF. Figure lb showsthe resultsof the tail lengthas
functionsof the solarwind plasmaparameterfrom simulations. It is clear that when the solar wind densityremains
the same,the tail lengthdependslinearlyon the solarwind
plasmaparameter.When the solarwind densitychanges,
becauseof the processes
at the bow shockand in the magnetosheath,the plasmaparameternear the magnetopause
changesat a slightly different rate from the trend by varying the magneticfield strength.
We now examine the effects of the solar wind Mach num-
2.0
I
I
I
I
[
I
I
I
t
50
0
[
I
I
I
I
100
I
I
I
I
I
200
150
Tail Length (Re)
ber. Since the tail length is proportionalto the magnetosheathplasma beta near the subsolarmagnetopause,it
is proportionalto the plasmabeta downstreamof the bow
shock. To understandwhat determinesthe plasma beta
downstream of the bow shock, we first take a look at the
(b)
3.5
,2.5 nT)
(10/cc,
5nT)
/%
/ (5/cc,
3nT)
3.0
cc, 4nT)
2.5
(5/cc,
5nT)
/o
2.0
,
0
,
,
(5/cc, 10 nT)
•
[
50
•
,
,
I
I
,
t
I
'
100
Tail Length (Re)
I
150
,
,
•
,
200
changein the lengthof a magneticfield line, which equals
the ratio of the magneticfield strengthand plasmadensity.
When the IMF is tangentto the subsolarbow shock,there
is little stretchingor shorteningin the magneticfield lines
acrossthe bow shock. The lengthof a magneticfield line
remains similar acrossthe bow shock. The plasma beta
downstreamof the bow shockwill then be proportionalto
the ratio of the plasmaheatingfactor,which determinesthe
downstreamtemperature,to the magneticfield compression
factor. In the range of normal solar wind Mach number,
the heating factor increaseswith the Mach number much
fasterthan the magneticfield compression
factor does. For
a higher sonicMach number,the magnetosheath/3will be
higherleadingto a longertail. This is confirmedby a pair of
runswith a sonicspeedof 40 km/s andsonicMach numbers
10 and 8, respectively.The tail is 58 RE long for the Mach
10 run and 51 R• for the Mach 8 run. Unfortunately,the
plasmaparametersnearthe subsolarmagnetopause
for these
two cases were not documented.
Figure 1. (a) Dependenceof the tail length on the magThe effect of the sonic speedor solar wind temperature
netosheathplasma parameterv/1 +/3 + 1. (b) Dependenceof the tail lengthon the solarwind plasmaparameter aloneis more complicated.A high sonicspeedwill reduce
v/1 +/3 + 1. The 4 nT casein Figure1b wasarchivedgraphi- the solar wind Mach number and hence the heating at the
cally butnotdigitally.The magnetosheath
plasmaparameter bow shock. However, dependingon whetherthe reduction
for this case is not available.
of theheatingcanmakeup the higherupstreamtemperature,
the resultingtemperatureaownstreamof the bow shockmay
be eitherhigheror lower or same.Thereforethe tail may be
different
runsremainsimilar.A higherinitialpressure
sim- eitherlongeror shorter
or samedepending
onthevalueof
ply stretchesthe tail longer. This is consistentwith our un- the Mach number.
derstanding
that the tail lengthis determinedby the balance
betweenthe driving and drag forces. Here we shouldpoint
out that becausethe Iield-alignedcurrentsare derivedfrom 5. Discussion
only a smallportionof thetail currents,theionospheric
drag
5.1. Definition of the Magnetopause
may have only very limited effectson determinationof the
Thedefinitionof themagnetopause
wasoncethoughtsimlengthof thetail. The conclusionwe drawfrom thisanalysis
is that our numerical model is consistent with the theoretical
ple and straightforward.However,it is not trivial for northmodelin whichtheLLBL is primarilydrivenby thepressure ward IMF. Usingthe conventional
definitionof the magne-
SONG ET AL.: SOLAR WIND-MAGNETOSPHERE
INTERACTION
FOR NORTHWARD IMF
28,375
topause,the regioncontainingmostof the current,the mag- ward. The magneticfield line thenmovesinto or out of the
netopauseidentifiedusingthe magnetometer[Russelland pagebeforeit reachespoint B. It is worthmentioningthat
Elphic, 1978], which is mostsensitiveto the currents,is the the stagnationpoint is point B and not point A in Plates3a
plasmadepletionlayeridentifiedusingtheparticlemeasure- and3b, althoughthe flow velocitydropssignificantlyacross
ments [Paschmannet al., 1978], which are most sensitive the magnetopause
topologicalboundary. Becausepoint A
to particlecharacteristics
but notthe currents.After investi- is not a stagnationpoint, the mathematicalsingularitydisgatingthis inconsistency,
Songet al. [1993] suggestedthat cussedby Sonnerup[1980b] does not exist at the magnethe magnetopause
shouldbe definedas a physicalconcept topause.Becausethe topologicalchangeoccursat point A,
insteadof a singlesignaturemeasuredby a particularinstru- the magneticfield is magnetospheric
at point B. The flux
ment. A particularsignaturemeasuredby a certaininstru- tube splitsat local noon and the plasmaflows azimuthally
ment shouldbe usedto determinethe relativelocationof the to the morningor eveningside. This is consistentwith the
satellitewithin the overall structure.The physicalmeaning idea of the stagnationline proposedby Sonnerup[1980b] to
of the signaturemay changewith the IMF conditions.Our solvethe dilemma.Thereforethe long-standing
problemof
simulations
showclearlythedifferencebetweenthetopolog- stagnation
pointversusstagnationline is solved.
ical boundaryand the magnetopause
currentin the subsolar
region.
Inthecusp
regions,
their
relationship
becomes
even5.2.Cusp
Reconnection
morecomplicated.
Reconnection
onthenightside
of thecusps
fornorthward
To defineof the magnetopause
in the distanttail is more IMF wasfirstproposedby Dungey[1961]. Songand Rusdifficult as the topologicalboundarybecomesirrelevantto sell [ 1992] summarizedindirectevidencefor sucha process.
the current. One may suggestto definethe magnetopauseGosling et al., [1991], Feldman et al. [1995] and Kessel
according
to the topologicalboundary.However,according et al. [1996] providedmoredirectevidence.In particular,
to the standardpictures,the magnetotailneutralsheetcur- Feldmanet al. [1995] showedevidencefor conjugatererent is closedwith the magnetopause
currentin the distant connectionin the two hemispheres.Similar evidencewas
tail. The topologicalboundarycannotprovidethe current also shownin laboratorysimulationsof the magnetosphere
closure.When onedrawsa O-typetail currentsystem,he/she [Dubininand Potamu,1981]. Cusp reconnectionhas been
includestopologicallymagnetosheath
regionin the magne- shownin all computersimulationmodelsfor northwardIMF
totail.
as we summarized
in the introduction
section.
It is an observationalchallengeto identify the last closed
Therehasbeendebateoverwhetherthe reconnection
promagneticfield line in the distanttail near the equatorial cessat the two cuspstakesplace si.multaneouslyon the same
plane.Immediatelydownstream
of the lastclosedmagnetic flux tube. Our simulation domain and IMF conditions are
field line, both the magneticfield and plasma are indistin- symmetricwith respectto the XY and X Z planes.No apguishablefrom the magnetospheric
ones. It movesslower preciabledifferenceis foundbetweenthe two hemispheres
than the solar wind, as shownin Plate 7, and almost empty in our simulations. Therefore, in principle, the reconnecwith the solarwind population.The magneticfield wouldbe tion processat the two cuspstakesplace simultaneously
on
dominatedby the Z component.The X componentwill re- the samemagneticfield line. Here we cautionagainstsimverseits polarityfurtherdownsteam.For the referencerun, ple useof the magneticfield line tracingprogramto identify
it will go up to 200 RE downstreamfrom the Earth before whetherthe reconnectionprocessis symmetric.Becausethe
the flow becomessimilar to the solar wind speed,as shown magneticfield near the reconnectionsite is very weak, the
in Plate7. The plasmadensityandpressurewill remainsig- uncertaintyin the magneticfield line tracingis large. If one
nificantlysmallerthanthe solarwind valueseventafter 250 usesa symmetricsimulationsetupandconcludesthatthe reRE. For the 10 nT run, the flow velocity reachesthe sheath connection
processis not symmetric,a physicalexplanation
speedat •50 RE and reachesthe solarwind speedat •75 is needed.
RE. After 50 RE, the densityandpressurestartsincreasing,
Whenthe IMF hasan X component
or the geomagnetic
but it is not able to reach the solarwind densitywithin 250 dipoleis tilted in the X direction,the north-south
symmeRE. Nevertheless,observationsof absenceof the magneto- try will break.It is possiblethatthereconnection
processat
tail 200 RE downstreamfrom theEarthhavebeenreporteda the two cuspsis not simultaneously
on the sameflux tube.
few times[Fairfield,1993;Fairfieldet al., 1996], supporting Eachhemisphere
may developan openmagneticfield line
closedmagnetosphere
models.
region.If thereconnection
ratesaresameat thetwo cusps,
the
trailing
reconnection
event
has no direct effect on the
Althoughthe magnetopause
topologicalboundarysepaionospheric
convection
pattern
and
topologicalboundaries
ratesthe solar wind from the magnetosphere
domain, it is
in
the
hemisphere
corresponding
to
the
leadingreconnection
not a tangentialdiscontinuityin local noon and midnight
event.
This
is
because
the
electric
field
associated with the
wheresolarwind fluxesenterandtail fluxesexit the magnefirst
reconnection
event
will
map
along
the magneticfield
tosphericdomain. To understand
the steadystateprocesses
of the solarwind entry,onecanfollow the motionof mag- line to the otherhemisphere.It equalsthe electricfield asneticfield linesin Plate3a startingat the cuspbasedon the sociated with the second reconnection event. The second
Petschekreconnectionpicture [Petschek,1964]. He/she can reconnection event does not send an additional electric field
seethat the magneticfield line near point A movesEarth- to the other foot of the flux tube.
28,376
SONG ET AL.: SOLAR WIND-MAGNETOSPHERE
5.3. Cusp and Polar Cap
In a static closedmagnetospheremodel which assumes
the magnetosphereto be vacuum without convection,the
last closedmagneticfield lines convergealong the magnetopauseto a singularpoint at eachcuspandthenmap to the
ionosphereat the magneticpole in each hemisphere[e.g.,
INTERACTION
FOR NORTHWARD IMF
Newell et al. [1997] further pointed out that a short interval of southward
IMF fluctuations
canleadto a muchlonger
durationof ionosphericsignaturesthat are associatedwith
an openmagnetosphere.Ionosphericsignaturesfor quasisteadystatenorthwardIMF may bemoredifficultto identify
and are certainlyrare.
Crooker, 1979; Siscoe, 1988]. When convection is added
5.4. Effects of IonosphericBoundary Conditions
to such a model, the electric field near the poles becomes
As the firststepto modelthe magnetosphere-ionosphere
singular and hence the model cannot be completelyselfconsistent. Various ad hoc ways have been thoughtto re- interaction,we have useda highly simplifiedionospheric
move the singularpoints [e.g., Siscoe,1988; Toffolettoand model. The Petersen conductance has been assumed to be
depends
Hill, 1989]. In our model, the magnetosphereis not empty uniformandstationary.In reality,the conductance
andit is in motion.The magnetospheric
motionis coupledto on local time and latitude,and varieswith magnetospheric
is basedon our unthe ionospherevia the line-tie process[Coronitiand Kennel, precipitations.The followingdiscussion
derstanding
of
the
formulisms
employed
in our model and
1973]. For the magneticfield lines near the magnetopause,
does
not
necessarily
describe
the
processes
takingplacein
when they convectfrom the daysideto the nightside,their
reality.
The
effects
will
be
investigated
and
reported
in our
ionosphericfootprints convect with them. Therefore the
future
papers.
magnetopause
mapsto an extendedline in local time in the
As seen from equation(5), the spatial variation of the
ionosphereasshownin Plate 3c, ratherthana singularpoint,
conductance
can be considered as a source, in addition to
in eachhemisphere.The daysideand nightsidebranchesof
the
field-aligned
currents,of the divergenceof the electric
the magnetopause
map back-to-backin the ionospheresepafield,
and
hence
the
rotationof the velocityfield. If the cenratedby the topologicalboundary,which can be interpreted
ters
of
the
field-aligned
currentsareassociated
with a higher
as the ionosphericcusp. However,the physicalsolutionsat
conductance
(which
may
not
be
always
true),
the effect of
thisline of topologicalboundaryare not singularbut disconthe
conductance
gradients
tends
to
enhance
the
convection
tinuouswhen•nappingto the high-altitudemagnetosphere.
Thepolarcapreferred
to in ourdiscussion
is a high- driven
bythePetersen
currents.
If thetotalamount
ofthe
latitude
ionospheric
region
which
hasdifferent
observational
field-aligned
current,
which
maybedetermined
bythemagcharacteristics
fromthemidlatitude
ionosphere.
Ourdeft- neticfielddistortion,
inparticular
bymagnetic
fieldshears,
nitionmaybedifferent
fromthatusedin ionospheric
ob- isfixedfora given
solar
windcondition,
theeffect
ofthe
servations.
According
toourdefinition
andourmodel,
this conductance
gradients
maybeanenhanced
ionospheric
conregion
should
observe
low-energy
precipitation
particles
of vection.
Consequently,
theenhanced
ionospheric
convection
solarwindoriginbecause
it corresponds
to theLLBL/tailwillbecoupled
tothemagnetosphere.
It would
beinterestregion
inthemagnetosphere.
Thefreshsolar
windfluxwill ingtosee,in ourfuture
simulations,
whether
theenhanced
havethehighest
intensity
nearthecuspwhichislocated
at magnetospheric
convection
wouldleadto a longer
magne•83 ø latitudewith somespreadaroundthe local noon,becausein the cuspregion, the solar wind can have a large
field-alignedpopulation.As the flux tubesmovetailwardin
the LLBL, they continuouslylosethe field-alignedcomponent of the particles. The pitch anglediffusiondue to the
wave-particleinteractionwill providefield-alignedparticles
butat a lowerflux. Thereforewe expectthattheprecipitation
will be significantlylower on the nightsideof thecuspsthan
in the daysidecusps.In contrast,low latitudesto the polar
cap map to the outermagnetosphere
wherethereis little solar wind population.We expectthat the ionospheric
precipitationis dominatedby particlesof magnetospheric
origin.
The flux shouldbe lower,andthe energyshouldbe higher.
In ionospheric
observations,
thepolarcapis oftenreferred
to as the regionwithoutparticleprecipitationof solarwind
totailor not,becausethisprocess,asis described,
is a positivefeedback
process.
Nevertheless,
whenincludingthegradientsin the conductances,
we expectthat the conclusions
drawn in our studyremainqualitativelyvalid.
In this study,we have not includedthe Hall currents. In
a steadystate,the electricfield is curl-free.Combiningthis
condition with the uniform conductance condition used in
the simulation, the Hall conductance will have no effect on
the magnetosphere-ionosphere
couplingdescribedby equation (5) evenif we had assumedthe Hall conductanceto have
a finite value. The effectsof the Hall currentswill appear
when allowinggradientsin the conductances.
Theseeffects
remainto be investigated.
As discussed
in section4.4, becausethe ionospheric
drag
contributes
to only a smallfractionof the total magnetotail
origin.
Thisdefinition
ofthepolarcapisbased
onthephys-drag,weexpect
thattheionospheric
conductance
willhave
icalprocesses
forsouthward
IMF.Observations
haveshownonlyminimal
effects
onthetaillength.
thatsuchdefinedpolarcapmay be absentfor northwardIMF
[Newellet al., 1997]. Instead,duringtheseperiodsthe iono- 5.5. High Speed Sheath Flow
spheric
DMSPsatellites
observed
low-energy
precipitation. Chenet al. [1993]reported
theobservations
of themagTheseobservations
areconsistent
withourmodelexpecta-netosheath
flowthatmoves
fasterthanthesolarwindspeed.
tions. We note that ionosphericobservations
have been in- In our referencesimulationrun, a fast flow does occur in
terpretedto indicatea closedmagnetosphere
for northward the equatorialplane,butit startsat •75 R• tailwardof the
IMF [Troshichevand Nishida, 1992; Newell et al., 1997]. Earth, as shownin Plate 7, and centeredaround100 R•.
SONG ET AL.: SOLAR WIND-MAGNETOSPHERE
This regioncan be as closeas 20/•E and centeredat 50
/•E for the 10 nT case. The maximummagnitudeof the
speedis lessthan5% higherthanthe solarwind speedfor
thereference
runandslightlymorethan10% for the 10 nT
case.In thenoon-midnight
meridianplane,similarfastflow
INTERACTION
FOR NORTHWARD
IMF
28,377
The simulationresultsalsoraisea few issuesas how to
interpretobservations.
Topological
boundaries
seenin simulationsareof globalnature.The localplasmaandmagnetic
field diagnostics
may not be alwaysdirectlyrelatedto the
changes
in globaltopology.Oneexampleis the lastclosed
alsoexists.Nevertheless,the outwardmotionof the subsolar magneticfield line on the nightside. It is observationally
magnetopause
withincreasing
positi,•e
Bz inferredby Chen challenging
to identifythe last closedmagneticfield line.
et al. [1993] is not shownin our simulations,as shownin The topologicalboundarybetweenthe magnetosheath
and
Table 1.
the magnetosphere
is locatedat the inner edge of the magnetopausecurrentlayer in the subsolarregion and has little
relevanceto the magnetopause
currentin the distanttail.
6. Conclusions
Likewise,the signaturesand definitionof the polar cap need
We have simulatedthe solar wind-magnetosphere-iono-to be reviewedaccordingto IMF conditions.
spheresystemfor due northwardIMF usingseveraldifferAcknowledgments. This work was supportedby NSF/ONR
ent upstreamparametersand spatial resolutions. Qualita-
tively,thereis a steady
statesolution
for thesystem.This under
Award
NSF-ATM9713492,
bytheNSF-NASA-AFOSR
in-
solution
isindependent
oftheinitial
conditions.
Thissteadyteragency
grant
NSFATM-9318181,
and
byNASA
HPCC
Grand
state
solution
can
beunderstood
physically.
Changes
intheChallenge
Cooperative
Agreement
NCCS5-146.
Janet G. Luhmann thanks Michael Goodman and Olaf Amm
upstreamconditionsand spatialresolutionsresultin quantitative differences
in the solution.
We have not seen drastic
for
their assistance
in evaluating,
this paper.
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