Download Magnetic Field Line Reconnection Experiments, 1. Field Topologies

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 86, NO. A2, PAGES 649-658, FEBRUARY
1, 1981
Magnetic Field Line ReconnectionExperiments
1. Field Topologies
R.
L. STENZEL
AND W.
GEKELMAN
Departmentof Physics,Universityof California,Los Angeles,California 90024
A laboratoryexperimenton the reconnectionof magneticfield linesin plasmashasbeenperformed.A
large-volumestationaryplasmais producedand a time-varyingmagneticfield is appliedto it. In vacuum
the field exhibitsan X-type neutral point on axis. Becauseof the time variation, plasmaflowsacrossthe
separatrixand currentsalong the separatorare induced.The plasmacurrentsmodify the magneticfield
topology.Flat neutralsheetsare observedwhen flux is transferredacrossthe separatrixinto regionsof
commonflux. Forced tearing and magneticisland formation occurin the return phaseof the flux. An
axial magneticfield is appliedalong the neutralline. This first part of the report mainly dealswith the
magneticfield topologies,but subsequentreportswill presentobservationsof plasmaproperties,anomalous resistivity,particle heating, and acceleration.
the pulsedreconnection
experimentlendsitselfto digitaldata
INTRODUCTION
The reconnectionof magnetic field lines in plasmasis one
of the key problems in solar terrestrial physics. For a long
time it has been consideredas a possiblemechanismfor generation of fast particles in solar flares and magnetospheric
substorms[Dungey, 1953]. Numerous authors have proposed
theoretical models, which have been reviewed recently by
Vasyliunas[1975]. Various computer simulations have been
performed in support of the theoretical models [Ugai and
Tsuda, 1977; Hayashi and $ato, 1978]. Observations from
spacecraft[Frank et al., 1976; McPherron, 1979] generally
confirm the existenceof fast particles near regionsof neutral
points,but the data collectedfrom a singleobservationpoint
are inadequate to obtain a conclusivepicture of the largescaleprocesses.
Finally, efforts have been undertaken to model reconnection processesin controlled laboratory plasmas. Pioneering
work by Andersenand Kunkel [1969]and by A. Bratenahl and
co-workers[Bratenahland Yeates,1970;Baum and Bratenahl,
1977] stimulated a number of investigationson reconnection
processesin pinch-type plasmas [$yrovatskii et al., 1976;
Ohyabu et al., 1974]. A striking feature of these experiments
was a current interruption resulting in strongparticle acceleration. Becauseof the difficulties in diagnosinghigh-density
transientplasmasa fully detailed picture of the reconnection
processesin theseplasmashas not yet emerged.
In the presentwork a new attempt is made at understanding reconnectionprocessesin a laboratory plasma [$tenzel and
Gekelman, 1979]. Since the main advantages in modeling
spaceplasmaphenomenain the laboratoryare diagnosticaccess,repeatability,and parameter control, we have chosena
parameter regime which optimizesthese features.The opti-
acquisition.
Therepetition
rateissufficiently
high(trcp
= 2 s)
such that a large amount of detailed information is obtained
in a reasonablyshorttime interval.
In the experiment an initially stationaryuniform plasma is
producedto which a time-varyingmagneticfield is applied.
The latter has antiparallel field lines with an X-type neutral
point in the center.The time scaleduringwhich the applied
magneticfield risesis larger than the Affv6n transit time from
boundariesto the neutral point but short comparedwith the
resistive diffusion time for the correspondingdistance. The
magnetic Reynolds number is Rm •- 20. While the electrons
are stronglymagnetized,the ions remain essentiallyunmagnetized. Ideal MHD theoriesmodel the reconnectionprocessby
consideringa resistiveregioncontainingan X point or neutral
sheet surrounded by a perfectly conducting plasma. Fluid
flows into this 'diffusion'region carrying frozen influx with it;
fluid and reconnectedflux subsequentlyleave. This experiment models the dynamic reconnectionprocesseswithin and
closeto the diffusion region. The critical questionsto which
this experiment is addressedare the magnetic field topologies
and the plasma dynamicsincluding heating and acceleration,
anomalousresistivity,and fluctuations.
The self-consistent
interaction
betweenplasmaand magnetic field leadsto a complicatedspace-timedependenceof all
parameters. We have attempted to measure all important
physical
quantities
in thisexperiment.
Withoutsucha com-
plete data base, erroneousinterpretationsof the plasma dynamics are easily possible.Becausethere is such a wealth of
data, we wish to break up the subjectinto four parts.This first
paper dealswith the magneticfield topology.It will also provide a detaileddescriptionof the experimentalsetupand meamum densityis Ite = 1012cm-3, the characteristic
sizeL •, 1 m surementtechniques.In the secondpart [Gekelmanand $ten> c/%i, themagneticfieldB -• 20 G suchthatfi = nkT/(B2/ zel, this issue]we presentthe plasma propertiesin spaceand
2po)= 1. Sucha laboratoryplasmahas been developedby the time, i.e., density,temperature,and potentials.The third part
authorsby carefully scalingup hot cathodedischargedevices will deal with particle accelerationsand flows. Direct mea[Stenzel,1976].Thesepossess
mostof the deskableproperties surementsof electron and ion drifts have been performed.
of a good laboratory device:The parametersare uniform and The force balancebetweenpressureand magneticforcesis instable and can be varied over a wide regime. The plasma vestigated.In the fourth part the plasma resistivityand dispropertiesare diagnosedinternally with small probes which sipationwill be analyzed.From direct measurementsof elecprovide excellent spatial and temporal resolution without tric fieldsand currentsthe resistivityis determinedand found
causingseriousperturbationsof the system.The time scaleof to be anomalouslylarge and current dependent. The dissipatedpower can be accountedfor by excitation,ionization,
Copyright¸ 1981by the AmericanGeophysicalUnion.
electronand ion heating,and fluid acceleration.
Paper number 80A0846.
0148-0227/81/080A-0846501.00
649
650
STENZEL AND GEKELMAN: B FIELD RECONNECTION TOPOLOGIES
J-
5m
Double Wall AI.
11GHz/•W
InterferometerVacuum
Chamber
Oxide
Coated
•
'alve
[
'
Gate
2m
Axial
Cathode
EndFlange
I(t)
Vacuum
Pumps
•
, / PLASMA
Probes
J Optical
,l
.
,,••
Diagnøstic•.//L -I!x
t0 Coil Solenoidal
Magnet
Electrodesfor
reconnection
experimt.
Moveable
endsupportfor
vacuumstation.endflange
and cathode
_
.
Fig. 1. Schematicview of the plasmadeviceand somediagnostics.
In thisfirstpart we shallshowthe serf-consistent
formation
of a neutralmagneticsheetwhenmagneticflux is transferred
acrossthe separatrix.The thicknessof the neutral sheetapproaches
theinertiallimit;thewidthexceeds
thethickness
by
an orderof magnitude.No tearingof the currentsheetis ob-
served
withinapproximately
fiveAlfv•ntransittimes.Theinducedplasmacurrentdoesnot exhibitdisruptions.
Thusit is
possible
to followthefieldtopologies
throughout
theperiodof
externalmagneticfield rise and decay.The observedtransi-
width 74 cm, length 175 cm, spacing32 cm, and thickness1
cm. The plates are parallel to the plasma column, but the
cathodeemissionis arrangedso as to produceplasma only in
the volume between the plates. The plate current returns
throughthe metallicchamberwalls(5-cm-thickaluminum)to
the current sources.The skin depth of the pulsed current is
muchsmaller(-2 ram) than the thicknessof the metallicconductors.
Thetimedependence
of theplatecurrent
or transverse
tion from neutral sheetsto X and O pointswill be presented. magneticfield is shownin Figure 2b. The waveformcorreImportantquantitiessuchas the currentdistribution,vector spondsto the currentdependencein a dampedLC (inducpotential,and inducedelectricfieldswill be derivedfrom the tance-capacitance)circuit. The power supply consistsof two
10kV, 80/•F capacitorbankswhichare discharged
via ignimagnetic field measurements.
trons,dampingresistors,
and air coretransformers
into the esEXPERIMENTAL
SETUP
sentiallyinductiveplatesystem.The supplydeliversup to 50
The experimentsare performedin a large linear discharge
plasmashownschematically
in Figure1. Usinga 1-m-diameter, indirectly heated, oxide-coatedcathodewith adjacent
(a)
zt
o -2I
mesh anode, adc dischargeis generatedin argon at a gas
pressure
Po = 2 x 10-4 torr. The plasmacolumnis radially
confinedby a constantuniformaxial magneticfield Byo= 20
G. Typicalplasmaparameters
are densityn. = 10'2 cm-3,
temperature
k T, = 10k Ti = 5 eV. While thecathodeis heated
continuously
(Ph= 50 kW heaterpower),the discharge
is pul-
15
mO
o3•m
•
sedrepetitively(5 ms on, 1 s off) soas to avoidthermal runa-
wayof thecathodedueto thelargedischarge
power(Pd•= 50
I• 75•cm
-•
V X 1500 A -- 75 kW). The spacechargelimited electron
emissionof the cathodeis highly uniform; hencethe plasma
parameters
are essentially
constant(An/n < 10%)for --80 cm
acrossBo-- Byo•y and •- 200 cm alongBo.The temporalreproducibilityfrom pulseto pulseis excellent(An/n < 5%).
The pulselengthis sufficientto reachsteadystateplasmaconditions at which time the reconnectionexperimentsare initi-
(b)
Is
(8,6kA/div)
ated.
Transverseto the axial bias magneticfield Byoa pulsed
magneticfield Bl(x, z, t) is established
whosegeometryis
sketchedin Figure 2a (the magnetotailcoordinatesystemhas
beenadoptedhere).In vacuumthe field topologyexhibitsan
X-type neutralpoint on axis(x -- z -- 0). The dashedseparatrix divides the outer common flux from the two inner cells
with privateflux encirclingeachconductor.The field is producedby passingtwo identicalcurrents(0 < I, < 25 kA) axially throughtwo parallelaluminumplatesof dimensions
in
( 100V/div)
t,(40Fsec/div)
Fig. 2. (a) Cross-sectionalview of the device showingthe transverse magnetic field geometrywithout plasma. The applied current
21, flows in a coaxial systemwhere the center conductorconsistsof
two parallel plates.(b) Time dependenceof currentI, and voltage I•,
appliedto eachplate.
STENZEL AND GEKELMAN: B FIELD RECONNECTION TOPOLOGIES
651
kA, 500V to the water-cooled
platesat a pulserepetitiontime
of 2s.
Figure 3 showsan electricalblock diagramwhich summarizesthe essentialcomponents
of the experiment.When the
spacebetweenthe plateshasbeenfilled with a uniformdischargeplasma,the plate currentis pulsedon. During the first
periodof currentrise,an inductiveelectricfield-SA/St is generated along the plasmacolumn.This field drivesa plasma
currentIp whichis dominantlycarriedby electronsdrifting
from the cathodeto a groundedend plate terminating the
plasmacolumn.The currentclosesvia the chamberwallsto
the cathode,which emitsas many electronsas are collectedat
Diff. Amp.
A.-D.
Integrator
Mini-
Large
Converter Computer
Computer
Bx(x,z,t) , Bz(x,z,t)
Loops
calibrated
with
at
- 300 points ( Ar-2 cm )
- 500 times
Hall probe
-
(Zl t- I #sec)
I0 shots/point
Fig. 4. Block diagram for the magneticfield measurements
using
magneticloopsand a digital data acquisitionsystem.
to ensurestableoperation.The stablelifetime of the cathode
the endplatesoasto maintainspacechargeneutrality.Thus coatingexceeds106pulsesor •5 weeksof continuousoperathe plasmacurrentis an inducedor secondary
currentin re- tion. It is coated and reactivated within 1 week.
sponse
to theprimarycurrentin theplatesystem.
The plasma
The plasma properties are diagnosed with Langmuir
currentIp flowsin the directionopposite
to theplatecurrent probes.The I-V characteristic
is sweptwithin approximately5
I•, sothat thepenetrationof magneticfluxthroughtheplasma /•s,convertedwith a fastanalog-to-digital
converter(20 MHz)
is sloweddown. This resultsin a changeof the magneticfield
and evaluated on-line with a minicomputer (MIK 11/2B).
Density, electrontemperature,and plasmapotential are found
vacuum field becomesa thin neutral sheet in a plasma. It is
from a singleplane probe. Using two identicalprobesback to
thepurposeof the experimentto investigate
the self-consistent back, the current density or relative drift velocity is found
fieldtopologies
and the plasmadynamicsin thisreconnection from the differencein the electron saturationcurrents.Using
process.
two probesspacedby a distanceAx, the differencein plasma
In the secondphase,when the applied plate current de- potentialyieldsthe electrostatic-field
E -- -Vq•,, = -A•,/Ax.
creasesin time, the electricfield is reversed.No current flows
The densityobtainedfrom probemeasurements
agreesfavorto the end plate.However,circulatingcurrentsare observed, ably with valuesobtainedindependentlyfrom a 10-GHz miand the field topologyis fundamentallydifferentfrom that in crowaveinterferometerand from dispersionmeasurementsof
vacuum,exhibitingan O-typeneutralpoint ratherthan an X whistler waves. The Langmuir probe tracesare swept prior to
point.Whenthepolarityof the appliedwaveformis reversed, and at differenttimesduring the magneticfield pulseso as to
the currentflow in the secondphaseis as describedearlier for follow the temporal variationsof the plasma parameters.
the firstphase.In the absence
of the inducedelectricfieldthe
The ion temperatureis obtainedfrom retardinggrid ion veplasmacurrentalongthe columnis negligible.
The discharge locity analyzers.Ion drifts are found analogousto electron
currentflowsbetweencathodeand griddedanoderather than drifts from the difference in saturation currents to two anato the end plate [Stenzel,1978].
lyzersor negativelybiasedplane Langmuirprobes.Sincethe
topology;for example,the curl-freeneutralX point of the
ion drift is a vector, three orthogonalpairs of differential ion
collectorsare mounted at the end of a probe so as to obtain
MEASUREMENT TECHNIQUES
The laboratoryexperiment
isdesigned
to optimizethediag- ilireciton
andmagnitude
of thelocalfluiddrifts.
nosticaccess
to the plasma.The parameterregimeallowsusto
The magnetic field is measuredwith magnetic loops and
insertprobesintotheplasmawithoutsignificant
perturbations Hall probes.The latter are usedonly in the absenceof plasma
of theplasmaor damageto theprobes.The largescalelengths in order to calibrate the loop probes.In the presenceof the
yieldgoodspatialresolution.
The longtimescaleprovides
for hot cathodethe probesassumetemperaturesas high as400øC
goodtemporalresolution.
The vacuumchamberis equipped at which only the loop probescan operate.These consistof
with approximately
50 portssothat the plasmais accessible 0. l-mm-diameter anodized aluminum wire toroidally wound
from all directions.
All the basicparametersof the experimentare carefully
as 50 turn coils with 5-ram major, l-ram minor poloidal
monitored and maintained stable.Dischargevoltage and cur-
rent, gaspressure,dc, and pulsedmagneticfieldsare measureddigitallyto within0.1%accuracy.
Beforetakingdatathe
cathodeis fully activatedand operatedfor severaldaysso •ts
lendAnode
z
t,I/
II/
Metal Plates
i
I
I
Vdis
,,
,,
tv,I
•Is
i
i
i
i
IBzl
iVsec/cm)
(G)
4x•o
-6
80.
lezl
MeshAnode Cathode
,lI
/
i
NO PLASMA
i
i-R///••,,//,/•
.•
Merci,
40
. • 20
- 60
- 40
- 20
0
20
I
40
I\ •R.
60
X (cm)
Fig. 3. Electricalbl•k diagramshow•g app•ed voltageand cur-
Fig. 5. Peakmagneticfield Bz(x),flux per axial length•(x)' and
•4y(x)alongthex axisin theabsence
of plasma.
For
rent(F, I,) • thepdma• circaits
and•du•d electric
field(-J) and vectorpotential
thewidthof theconductor
platesandthechamberinner
se•nda• cu•ent (I½)w•ch flows•rou½ thepl•ma •tween cath- comparison
ode and end anode and doses •rou½
•e chamber wall.
radius R are also indicated. I Smax----17 kA, y -- 87 cm.
652
STENZELAND GEKELMAN:
B FIELD RECONNECTION
TOPOLOGIES
VA CU UM
PL A $MA
z
(cm)
•
-10•
,
,
-30
0
x
,
,
30 -30
x
(c)
,
,
0
(cm)
30
(cm)
(f)
(o)
lo
(G)
10
-30
0
0
3O -30
0
x (cm)
x
30
(cm)
Fig.6. Comparison
oœ
themagnetic
fieldtopologies
invacuum
(Figures
6a-6c)
andinplasma
(Figures
6d-6f)att = 40
/•s.(a)and(d)Unitvector
fields
indicating
thelocaldirection
oœ
B•_.
Solidlineindicates
separatrix.
(b)and(e)Contours
oœ
constant
magnitude
JBxJ.
Inside
thecentral
contour
B•_= 0,increasing
at0.5G/contour
inFigure
6b,2 G/contour
in Figure6e.(c)and(f) Three-dimensional
display
oœ
thefieldstrength
foranX pointandneutral
sheet
topology,
respectively.
Argon3 x l0-4 Torr,y = 87 cm,Is==, = 17kA.
radius.As shownin Figure4, two orthogonalelectrostatically
shieldedloops are arrangedat the end of the probe shaft
which can be rotated by 90ø around its axis so as to determine
(a)
Z
F"-"",."'-"-..................
••
...............
• • / //t
, , • • • 11
•lso the thirdcomponent
of the magnetic
fieldvector.The
probecan be scannedalongthe horizontalpositionx at different vertical positionsz so as to determinepoint by point the
field distributionin a transverse
planey = const.By inserting
the probe into different radial ports the three-dimensional
field distribution B(r, 0 can be composedfrom data of the
various transverseplanes.
The magneticloop signalsare time integratedand recorded
at a given positionversustime. With fast analog-to-digital
convertersthe time dependenceis quantizedin up to 1024increments,and the dataare storeddigitallywith 8-bit accuracy.
Since the reconnectionprocessinvolvesshot-to-shotfluctuations, an ensembleaverageover typically 10 pulsesis performed. These average time dependencesof the three field
componentsare recordedat about 300 pointsin the transverse
plane. On a large computer(CDC 7600) the data matrix is
evaluated to yield, for example,'spatial vector plots of the
magneticfield at differenttimes.Other usefuloperationssuch
as spatial differentiation and integration to obtain currents
and vectorpotentialsare alsoperformed.The ion flow velocity is analyzedin the sameway as the magneticfield. Both
data sets can be combined in order to calculate Hall fields v x
B. These in turn are combined with electric field and current
-25
0
25
x (cm)
(b)
-10
-.25
(c)
-lO
-25
0
x
25
(crn)
Fig. ?. Comparisonof transverse
(Figure ?a) and longitudinal
(Figures?band?c)time-varying
magneticfieldcomponents
at t = 40
datato yieldtheplasmaresistivity.
Thusa detailedpictureof /•s,y = 87cm,Ismax
==17kA.(a)J•ñmax
----15.3G atx = 26cm,z =
plasma
andfieldproperties
in space
andtimeisobtained.
It -18cm.(b)Bym•
= 2.2Gatx = -14cm,z = -11cm.(c)Contours
of constant
ByaredottedforBy> O,solidforBy< O,andvaryby 0.25
forms
thebasis
forunderstanding
thecomplicated
plasma
dy- G/contour.
Note
that
there
isalso
adcmagnetic
field
component
Byo
namicsin a reconnectionprocess.
= 20 G.
STENZEL AND GEKELMAN: B FIELD RECONNECTION TOPOLOGIES
(a•
y =37 cm
(b)
y = 87 cm
653
Figure 5 showsthe x dependence
of the field strengthB,(x),
the commonflux per axial length•(x) -- $o• B, dx', and the
vectorpotential,4y-- $R• B• dx', whereR is the radiusof the
vacuum chamber. In the presentfiat plate geometrymost of
the flux (-•72%) is outside the volume between the plates.
Hence the induced electric field E•o -- -OA/Ot shows rela-
-10
(c)
y = 137 cm
-25
0
25
x
Fig. 8. Tra•vcrsc magneticfieldsB•(x, z) at three different axial
positionsy show•g the spatial developmentof the neutral sheetat a
givent•c t = 55 •s. (a), (b), (c) U•t vectorfieldsB•/B•. (•, (e),
Contoursof •nstant ]B•I •th •B• = 1.25 G/•ntour and B•
•cr closed'•ntour. I sm•
tively small variations in the region of interest.
The two-dimensionalfield distributionBx(x,z) is shownin
Figures6a-6c in vacuumand, for comparison,with plasmain
Figures6d-6f. The top graphsshowthe local directionof the
magnetic field, displayed as unit vector fields. The middle
graphspresentthe magnitude IB•l as contoursof constant
field strength.And at the bottomthe field strengthis shownin
a three-dimensionalview. In the absenceof plasma the field
exhibits an X-type neutral point in the transversefield componentsnear the geometriccenterof the parallel plate system.
Close to the null point the field is similar to that of a quad-
rupole,B(r,40- polr/(vra
2)[sin24•r + COS
24•,], wherea isthe
EXPERIMENTAL
RESULTS
characteristic distance from the currents, /, to the neutral
In orderto describethe magneticfield topologyB(r,t) one
point.The separatrix(4•-- +,r/4, +3,r/4) intersects
at right an-
linearly
hasto displaythreevectorcomponents
asa functionof three gles,satisfying57x B -- 0. The field strengthincreases
spatialcoordinates
andtime,possiblyfor differentplasmapa- with distancer from the neutralpoint, i.e., the magnitudecon-
rameters.We shall have to separatethis probleminto several toursare circles,r -- const.With increasingdistance,r the apsteps.First,the spatialdependence
will be discussed
starting proximationbreaksdown, and the field is governedby the exout with onecomponentversusonecoordinate,thentwo com- act current distribution on the plates. We find essentially
ponents
in a plane.Second,
thetimedependence
of the domi- antiparallelfield lines near the plates,vertical fieldsB• in the
nant components
will be described.Finally, the time depen- symmetryplane z -- 0, and a gradientin IBI mainly in the x
dence of current density and flux calculated from the direction. As the plate current increasesin time, the vacuum
field geometryis essentiallyunchangedexceptfor small shifts
magneticfieldswill be shown.
in the location of the X point due to current imbalancein the
Spatial Field Properties
two plates. The field strengthvaries in time proportional to
In orderto comparethe magneticfield topologiesin plasma the applied current.
and vacuumwe start out with the vacuum field properties.
In the presenceof plasma the field topology and field
, I••PLATE CURRENT
Is
/'
0•
•. •
....
_...r.......i._V_••••.•LP__LA__SMA
CURR•NT
Ip
•
300
t (psec)
VI
(d)
I
-30
0
x
30 -30
(cm)
x
(cm)
Fig. 9. Characteristic
fieldtopologies
Bx(x, z) at differentphasesI-III of the currentwaveformssketchedin Figure9a
(I•, Ip not to scale).Unit vectorfields(Figures9b-9d) andcorresponding
contours
of constantIBll (Figures9e-9g)show
thetemporaltransitionfroma horizontalneutralsheetin phaseI (Figures9b and9e)via an X-typeneutralpointin phase
II (Figures9c and 9f) to a verticalneutralsheetat III (Figures9d and 9g). Herey -- 87 cm, ISmax----23 kA, 1.7G/contour.
654
STENZEL AND GEKELMAN:
B FIELD RECONNECTION
TOPOLOGIES
pared with either the static axial componentor the average
transverse
field. The signof By(t)changesspatially,but dominantly,By•oand Byopoint in the samedirection.The observation of By<0indicatesthe presenceof transversecurrentsJl,
which will be shown later (Figure 12b).
While Figures 6 and 7 show the three vector components
(Bx, By,Bz) in two dimensions(x, z), we now completethe
-30
0
30
x (cm)
Fig. 10. Magnetic field topologiesB.•/B.• during phase IV indicated in Figure 9a when the vertical neutral sheettearsinto one or
more magnetic islands (Figures 10a and 10b) which evolve into a
singlegrowing O-type neutral point (Figure 10c). Here y -- 87 cm,
spatial picture by showingthe dependenceon the remaining
axial coordinatey. Figure 8 displaysthe dominant transverse
fieldsBx (x, z) in three x-z planesat a distancey -- 37, 87, and
137 cm from the cathode.The plate electrodesextend from y
-- 13 cm to y -- 188 cm. The first plane is locatedat a distance
Ay -- 24 cm from the end of the plateswhich is lessthan the
vertical plate separation (H -- 32 cm). Presumablydue to
fringing field effectsand the proximity to the cathode, a neutral sheethas not yet developed,and the field geometryresembles that of a flattened X point. However, at y -- 87 cm, and
especiallyat y -- 137cm, well-developedneutral sheetsare observed.To first order, the axial variationsin the central region
of the platesare negligiblecomparedwith the transversegradients. However, there is some tendency for the neutral sheet
to fiatten and to lengthen in x direction with increasingdistance from the cathode. This may be related to the fact that
Ismax = 23 kA.
for largey valuesonly field lineswith Bx = 0 (noteByo-- 20
G) lead to the cathode,while othersspiralaroundthe plates
strength are drastically changed due to the induced plasma
through vacuum. Thus strongfield-aligned currentscan only
currents.Even thoughthe plasmacurrentsIp are small com- flow in the neutral sheet region. In fact, experiments with
paredwith the plate currentIs -• 10Ip,the field modifications larger axial bias fields show less pronouncedneutral sheets
are strong, since the vacuum fields are relatively small be- also in the middle plane.
tween the plates. Figures 6d-6f show the observedfields inside the plasma at a time when the plate current rises.As pre- TemporalField Properties
dicted by the classicalpicture of merging [Dungey,1953],the
The current through the metal plates,I•, and hencethe apantiparallel horizontal field lines fiatten near the neutral re- plied magneticfield, vary in time (seeFigure 2b). The plasma
gion. The separatrixnow intersectsalong a line rather than a currentsI• drivenby the inducedelectricfield -OA/Ot change
point, indicating a topologicalchangefrom a first- to second- in responseto the applied currentsI• oc -•A/•t oc -•Is/•t.
order contactpoint. The arrow plots are unit vectors;they do Hence the total magnetic field, which can be viewed as a sunot indicate magnitude. Along the sheet the magnitude of the perpositionof the fields of two current systems,changesin
transversefield Bl= 0 (which is consistentwith a neutral sheet configurationand strengthwith time. The difficultyin predictwithin the limit of measurementreduction,1 x 10-• G). The ing the resultantfield lies in the complicatedbehavior of the
contour plot (Figure 6e) showsthat the field vanishesover a plasma as a conductor,i.e., its fluid character,anisotropies,
and nonlinearities. We have therefore investigated the field
broad central region of width to height ratio Ax/Az -• 35 cm/3
cm > 10. The width of the neutral sheet Az defined as half
topologyas a function of time. The transversefields B•.(x, z)
are of primary interest. In Figures 9-11 some characteristic
width at half maximumof the currentdensityprofile,Jy-- (1/
Po)(V x B)• canbe asnarrowasAz = 1.5cm, corresponding field patternsare shown which are selectedfrom the typically
to a few collisionless
skin depths,c/%,e-• 0.6 cm, which is 29 time stepsgenerateddigitally in each data run.
considered to be the narrowest width of a current channel.
Traditionally, most of the attention has been focusedon the
The probe diameter is I cm; the instrumentalwidth causedby
initial phaseduring which the currentIs riseslinearly in time.
If the rise time could be made long in terms of the Alfv6n
this setsthe spatial scale.The neutral sheet,which is also visible as a troughin Figure 6f, remainsstableagainsttearingfor transit time, a steadystate flow acrossthe separatrixwould, in
•80 /•s or four Alfv6n transit times from plates to neutral principle, be achieved,but in practicethere is a limit for the
sheet.The formation of a neutral sheetoccursself-consistently peak current (here •50,000 A) and hence for the rise time
as a result of the induced plasma currents.No other external (here approximatelyfive Alfv6n transit times). In other experfields or currentsare imposedto synthesizea sheetconfigura- iments [Baum and Bratenahl, 1977] the relevant time span can
tion [Syrovatskiiet al., 1976].
alsobe limited by the availableplasmato flow acrossthe sepIn Figure 6 we have presentedtwo componentsof the mag- aratrix. Thus in our experimentwe are observingdynamic reneticfield,i.e., the4projection
of the total field B -- (Bx,B• Bz) connectioneventsrather than steadystate conditions.
Figure 9b showsthe observedfield topologyduring phaseI,
into the x-z plane. The third component,B• consistsof the
uniformconstantbiasmagneticfield Byo-• 20 G, and a time- the riseof the externalcurrent,sketchednot to scalein Figure
varyingfield By<o
createdby plasmacurrentsflowingin the x- 9a. It is characterizedby the long thin neutral sheetdescribed
z plane. Figure 7 showsat a given time (t -- 40/•s) and axial earlier. It develops within one to two Alfv6n transit times
position(y-- 87 cm, y = 0 at cathode)both transverse(Figure (•20/•s) and remainsrelatively unchangeduntil the external
7a) and axial (Figures7b and 7c) field components.It is ap- current reachesits maximum. Near the current peak, denoted
parent that the time-varying axial componentis small corn- as phase II, the neutral sheetbecomesshorter and thicker un-
STENZEL AND GEKELMAN: B FIELD RECONNECTION TOPOLOGIES
(o)
(b)
I1 Ill////*."."."."
Z
........
"-.•.\\%,
(g)
(e)
(h)
), i-J
1\\\%%\%%%%1I%1•'•//////////J
I\\\x%%%•,
(c)
-25
(d)
.......
(f)
x
0
(era)
655
25
-25
(i)
x
0
(cm)
25 -25
x
0
25
Fig. 11. Temporalchangeof the field topologyfrom a magneticisland(phaseV in Figure9a) into a neutralsheet
(phaseVI). The displayincludes
linearlyscaledvectorfieldsB_•(x,z) (Figures1ld-11f), unit vectorfieldsB•_/B•_(Figures
1la-1 lc) whichenhancethe fieldstructure
nearthenulls,andcontourmapsB_c-- const(Figures1lg-11i). The O point
(Figures11a,lid, and 1lg) flattensinto an elongated
island(Figureslib, lie, and 11h)whicheventuallyapproaches
a
sheetwith two adjacentflat X points(Figures1lc, 1If, and 11i). Here y -- 137cm, ISmax----17 kA, 1.25G/contour.
are pushed vertically out of the observationregion, presumably into the surfaceof the metal plates.The 'forced' tearing
processis readily understoodif one considersthe temporaldecreaseof the plate current and the increaseof the plasma curWhen the latter decreasesthe electric field reversessign and rent (seeFigure 9a). Tearing occurswhen the O-type fields of
growsagain.Plasmacurrentsare now inducedto flow in the the plasma currents dominate over the X-type fields of the
sameaxial directionas the plate currents.Whereasin the first plate currents.In fact, when the plate current goes through
phasethe plasmacurrentsinhibitedthe flux transferfrom pri- zero denoted as phase V, the magnetic field exhibits only
vate to common flux cells, they now slow down the reverse closed field lines linked with the plasma currents. This O
flux transfer.This processleadsto the formationof a neutral point topologyis essentiallydepictedin Figures 1la, 1ld, and
sheetelongatedin the z direction,shownin Figure9d and de- 11g.
After the zero crossing,the plate current increasesagain but
notedas phaseIII. This verticalneutralsheetis considerably
broader than the earlier horizontal sheet.It also existsonly for now in reverse direction. This results in an increase of the hora relativelyshortperiodof time and thenis forcedto tear into izontal and a decreaseof the vertical field components,forming an elliptical island elongatedin x direction (Figures I lb,
O and X points.
The tearingprocessoccurringin phaseIV is demonstrated 1le, and 1lh). Two X points move in toward the elongatedO
in Figure 10. Initially one (Figure 10b) or two (Figure 10a) point (Figures 11c, 1If, and 11i). The long fiat island finally
magneticislandsare formed which rapidly coalesceinto a collapsesinto a neutral sheet. Its length extendsover nearly
single
growing
island
(Figure•0c).Theassociated
X points the entire plane of measurement(Ax = 50 cm). The topology
is the same as in Figure 9b, but the field directions are re-
til it assumes
the shapeof a nearly curl-freeX type neutral
point (seeFigure9c). Phenomenologically,
this transitionis
explainedby the vanishingof the inductiveelectricfield,
henceplasmacurrentsnear the peak of the plate current.
versed.
If the external current would continue to oscillate, the field
topologieswould repeatedly go through the cycle described
above.However,the actualcircuithasa stronglydampedcurrent waveform, so that subsequentcyclesare not comparable
with initial ones.Furthermore, the two plate currentsare difficult to keep balanced in time, which causesvertical asymmetries in the field pattern noticeable in Figure 11.
Currents, Flux
Fig. 12. CalculatedcurrentdensityJ = V x B//• (a) Axial currentdistribution
displayed
ascontours
Jy= constin increments
of 0.2
A/cm2/contour.
Characteristic
values:
minimumJy(17cm,
-1 cm)=
2
2
-1.68 A/cm, maximum
Jz(25cm,5 cm)-- 0.195A/cm, spatialav-
erage(Jy) = -0.58 A/cmz, positiony = 137cm, time t = 55 •. (b)
Perpendicular
currentdensityJ_L(x,z) at t = 40/•s,y = 87 cm. Charac-
From the measurementof the local time-varying magnetic
fieldsone can obtain by spatialdifferentiaticmthe p!_as_m__a_
rent densityJ -- V x B//,o and, by integration,the flux
B ßda and vectorpotential(V x A -- B) whosetime derivative
yields the induced electric field (E = -/}A//}t). These quantities are important in describingreconnectionprocessesand
will be discussedhere, sincethey are basedon magnetic field
measurements.For example, we will show quantitatively the
excessflux building up as a result of the slower merging rate
thanin vacuum.Additionally,moredetaileddata
teristicvalues:maximumJ_L(--12
cm, 9 cm) = 0.27 A/cm2, average in plasmas
on currents and electric fields will be presentedlater in con(J_L)----0.09 A/cm•, Ismax----17 kA.
656
STENZEL AND GEKELMAN:
12001
'
400
o
0
'
'
'
B FIELD RECONNECTION
I
TOPOLOGIES
show reasonableagreementin waveform and absolutevalues,
confirming that the plasma current is axially continuous.
However, when the applied current decays,the induced electric field and plasmacurrent reversesign.Sincethe end anode
doesnot emit electrons,its current is negligibly small. The axial plasmacurrent observedin the middle of the deviceis assumed to be closedvia transverseion currents flowing to the
metal plates.Becauseof the relativelylarge surfacearea of the
platesthe ion losscurrent can accountfor the positiveaxial
electron current. The experiment has also been run with reverse polarity of the applied current. Consequently,the induced plasma currents are smaller in the first quarter cycle
and larger in the secondwhen the electron current closesvia
the end anode.
-400
Fig. 13. Axial plasmacurrent-Ip versustime determinedfrom
magneticfield measurementsand from the externallymeasuredend
anode current (bold line). Here Isms,,= 17 kA.
nection with the subjectsof anomalousresistivityand dissipation.
The axial currentdensityprofileJy(x, z), corresponding
to
the neutral sheettopology(Figure 8c) is shownin Figure 12.
The current flowsmainly in a sheetof haft width at haft maximum Az -• 3.5 cm correspondingto sevencollisionlessskin
depths(c/6o•e-• 0.5 cm). This valuerepresents
an upperlimit,
sincethe observedwidth is broadenedby the spatialresponse
of the magneticprobe(Az -• 1 cm) and by averagingover fluctuations from pulseto pulse.Current channelsas narrow as Az
-• 1.5cm have beenobservedand reportedearlier.[Stenzeland
Gekelrnan,1979].It is interestingto note that the current density generally exhibits two maxima near the ends of the neutral sheetrather than a singlepeak in the middle. The narrow
current channel as well as the magnitude of the peak current
density(Jy-• -1.7 A/cm2)implythatthecurrentis carriedby
electrons.The correspondingrelative electron drift velocity
for a MaxwellJan distribution with Te -- 5 eV is calculated to
be v,•/v•-- 0.08. Outside of the current channel there are regionsof reversecurrents,but when averagedover the plane of
The magneticflux through a surfacearea $ is given by •b-ffs B da, where da is a surfaceelement with normal parallel
to B. Since the time-varying magnetic field is dominantly
transverseand independentof y, it is sufficientto considerthe
flux per axial length•b'-- •/y -- f (-B,, dz + Bz dz). Conventionally, the flux in our field geometrycan be classifiedinto
two groups:(1) private flux associatedwith field lines encircling each conductor plate, and (2) common flux encircling
both plates.Sinceall field lines are confinedto within the cylindrical chamber wall of radius R, the common flux can be
foundfrom•bc'-- foa B• dx, the privateflux from•,' -- foa/•
Bx dz, where H is plate spacing,and the total flux is •b/-- •b/4-
•b•,'.
The vectorpotentialA definedby B -- V x A hasan axial
componentgivenby Ay -- f (-B,, dz + B• dx) with O/Oy-- O.
The line integration startsappropriately at the chamber wall
where the magnetic field rapidly goesto zero due to the surface return currents.Thus the vector potential on the separa-
tor is identicalwith the commonflux,Ay (0,0) ----•c'. The time
derivative of the vector potential yields the induced electric
field Ey = -OAy/Ot.
The induced electric field along the separatorEy(0,0) is
measuredwith a loop probe consistingof two parallel wires
alongthe x axis and a shortwire in y direction(Ay -• 4 cm) at
x -- 0. The open loop voltagemeasuredjust outsidethe cham-
ber wall yieldsEy = Vo/Ay.By time integrationthe vectorpotential or flux is found. Typical measurementresultsboth ie
measurement,
the currentdensityis nonzero(<Jy > -- -0.58
vacuum(subscriptv) and with plasma(subscriptp) are shown
A/cm2), implying that a net currentis inducedas schemati- in Figure 14.The inducedelectricfield (Figure 14a) is smaller
cally shown in Figure 3. This current is also measuredinde- when the plasma current risesand larger when it decaysin
pendently at the end anode. A comparisonbetween the two
comparisonwith the fieldsin vacuum.The differenceis due to
separatecurrent measurementswill be presentedin Figure 13.
Figure 12b showsdirection and magnitude of the transverse
the flux changeassociatedwith the plasma current. The com-
currentdensityJ•_--(J,,, Jz) -• (-•By/•z, •By/•x)/p.owith By
from Figure 7 and •/•y -• 0 accordingto Figure 8. The transversecurrentsare partly Hall currents(Jl I Bl) and partly
the projection of field-aligned currentsin the x-z plane. On
the averagethe transversecurrent densityis small; yet locally
it may not be negligible comparedwith the axial current density.
Since the magnetic field strength and topology change in
time, the current and its distribution also vary temporally.
Here we will only showthe time variation of the total plasma
current which is calculatedby integratingthe current density
(x7x B)y/poover the crosssectionbetweenthe metal plates.
o,t
\' .
ø1/ \\
I/
_\\
001
I//
0•
0
t (•sec)
•
0
t (•sec)
100
For comparison,Figure 13 also showsthe measuredcurrent
Fig. 14. (a) •ial-indu•d
electric field Mong the neutral l•e
flowing betweenthe end anode and ground.During the rise of
vacuum
(•)
and
in
plasma
(•)
versus
t•e. Thepl•ma cu•ent
the applied current in the metal plates the induced plasma to •e end anode is also indicated.(b) Co•on flux •r axial length
current is negative,i.e., flows toward the cathode oppositeto • vacu• and in plasma versust•e. Here I sm• • 8.5 •, y • 87
the electrondrift. The two independentcurrent measurements C•.
STENZELAND GEKELMAN.'B FIELD RECONNECTIONTOPOLOGIES
mon flux shownin Figure 14b is smallerwith plasma currents
than without. The private flux showsa correspondingexcess
of flux as long as the plasmacurrent flows in the oppositedirection to the plate current (t -< 80/zs).When the plasma current reversesdirection, the commonflux is larger and the private flux smaller than in vacuum. However, since the field
topologychangesfrom X to O point, the original distinction
of the two flux groupscan no longer be made. The full time
5
z0
(cm)_5
-10
behaviorof the 'private'flux•{,) = $_n/2øBx(o.
z.,)dz is shown
-25
in Figure 15 and demonstratesthe abovedescribedbehavior.
The completespatialdependenceof the vectorpotential is
obtainedby addingto the commonflux •,:' = Ay (0,0) an in-
erementalpotentialA,4y(x,z)--J'o
x Bz{x,.z)dx'-J'o
• B•x.•,•dz'.
657
-20
-10
o
x
10
20
25
(cm)
lb)
1.5
While the first contribution was shownin Figure 14, the sec-
lt•6
ond one is givenin Figure 16.The contourmap of A,4y(Fig-
1.0
ure 16a) showsquantitatively the distribution of the vector
potential.Furthermore,sincelines of constantAy represent
magneticfield lines (dx/dz = B•/BO and the line spacingis a
measurefor the fieldstrength(B = IV x Ayl), the displayis an
alternate but equivalent description of the field properties
comparedwith, e.g., Figures 6a and 6b. Sign and magnitude
of AA•.• are bestshownin the three-dimensional
displayof
Figure 16b.The surfacehasa saddlepoint at the origin [A,4y
(0,0) = 0]. The potentialincreases
towardthe current-carrying
0.5
Ay
o
Vsec
I
'
-0.5
plates and decreasesmost rapidly in _+xdirection toward the
chamberwall whereAy = O.However,in the presenceof the
magnetic island the potential surfaceexhibits a maximum at
the O point, i.e., the center of the plasma current profile.
DISCUSSION
AND CONCLUSION
The present laboratory experiment offers a unique possibility to investigatein detail the dynamic interaction of magnetic fields with plasmas.In this first part we have concentrated on the magnetic field measurements.A major result
was the observationof a neutral sheetwhich developedselfconsistentlyupon compressingflux through an X-type neutral
point. The evolutionof this field topologyhas long been postulated to occur in solar flares and the magnetosphere
[Dungey,1953],althoughtherethe flux dynamicsis thoughtto
be causedby plasma flows rather than time-varying currents.
We also observedthe forced tearing of field lines when the
self-generatedfieldsby plasmacurrentsdominateover the externally applied fields. Such a formation of magnetic islands
can conceivably also occur in space when plasma flows
change in time. The field topology in this experiment is
1.5
z'•.....-.• "•' x
25
-1.5
10
(cm)
0
x
z (cm) -10 -25
Fig. 16. (a) Contoursof constantvector potential (magnetic field
lines) at y = 137 cm and t = 60/zs. Integration startsat the origin
[A,4y(0,
0) = 0];eachcontourrepresents
a change
of 7.5 x 10-s V s/
cm. (b) Three-dimensionaldisplay of the vector potential increment
A,4y(x,z). The total potentialis obtainedby addingthe commonflux
(seeFigure14b)asintegration
constant
to A,4y.Here1Smax
•--'17kA.
strictly
threedimensional,
although
in thecentral
regions
of
the long conductorplates the transversefields are an order of
magnitudelarger than the axial time-varyingfields.
From the magneticfield measurements
a numberof important quantitieshave been evaluated.The current density is
found, and the resultanttotal plasmacurrent confirmedby
end plate currentmeasurements.
The vectorpotential and induced electric field have been determined. Currents and elec-
tric and magnetic fields will later on be used to calculate en-
ergyflows(E x H), storedenergy(B2/2po),dissipation
(E. J),
resistivity(E/J), and acceleration(J x B). Thus the magnetic
field measurements
providethe mostimportantdata in the reconnectionproblem.However,it has to be complementedby
measurementsof the plasma propertiesin order to examine
the transferof magneticto particle energies.
It shouldbe pointedout again that the presentdata represent ensembleaveragesover 10 pulsesper point, i.e., several
thousandpulsesper plane.Thus only the repetitivepart of the
eventsis displayed,and fluctuationsare averagedout. Mag-
neticfieldfluctuations
aresignificant
nearneutralregions,
and
it is conceivablethat instantaneously,the neutral sheethas far
moreStructure
thandisplayed
here.Fluctuations
in the cur-0.5
rent densityare more pronouncedthan thosein the magnetic
field, sincethe latter is an integral value over the current distdbution. However,no impulsiveinterruptionsof the plasma
current have been observed, which seems to be a character-
Fig. 15. Privateflux per axial lengthin vacuumand in Plasma•Here
Ism•x -- 17 kA, y = 137 cm.
istic feature of inversepinch devices.A careful study of the
fluctuation phenomenawill be performed in the future.
658
STENZEL AND GEKELMAN: B FIELD RECONNECTION TOPOLOGIES
Acknowledgments.
We wishto thank N. Wild and T. McFadden
for assistance
in data collectionand programing.The authorsalsoap-
preciatediscussions
with F. Coroniti,C. Kennel,andP. Baum.The
research
wassupported
by theDivisionof Atmospheric
Sciences,
National ScienceFoundation,under grant ATM 77-18736.
The Editor thanks P. J. Baum for his assistancein evaluating this
paper.
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(Received March 6, 1980;
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