Table Of Content92 IEEETRANSACTIONSONPLASMASCIENCE,VOL.38,NO.2,FEBRUARY2010
Dynamics of the Current Distribution in a Discharge
of the PF-3 Plasma Focus Facility
ViacheslavI.Krauz,KonstantinN.Mitrofanov,ViktorV.Myalton,EugeneV.Grabovski,VasilyS.Koidan,
ValentinP.Vinogradov,YuliaV.Vinogradova,andGiviG.Zukakishvili
Abstract—Inthispaper,resultsarepresentedfromstudiesofthe
dynamics of the plasma-current sheath and current distribution
in the PF-3 facility, one of the largest plasma focus machines
in the world. The experiments were done at input energy of
W =290 kJ and discharge current of I ∼2 MA, with the
chamber being stationary filled with the working gas. The cur-
rentsheathparametersweremeasuredwithabsolutelycalibrated
magnetic probes installed at different distances from the system
axisandatdifferentheightsabovetheanodeplane.Thepossibility
is demonstrated of the formation of closed current loops due to
thedevelopmentofshuntingbreakdownsintheinsulatorregion.
Themaximumresidualplasmadensityatwhichtheelectrodegap
remainsmagneticallyself-insulatedisestimated.
Index Terms—Plasma focus (PF), plasma measurements, Fig.1. SchematicviewofPFmachine—Filippovtype:(1)anode,(2)cathode,
plasmapinch,plasmasheaths. (3) insulator, (4) vacuum chamber, (C) energy storage (capacitive bank),
(S)sparkgapswitch,(L)externalinductance,(I)stageofbreakdownalong
I. INTRODUCTION the insulator and PCS formation, (II) stage of PCS radial acceleration, and
(III)stageofradialcompressionanddensePFformation.
THE dependence of the radiative and plasma parameters
of the pinch on the discharge current is one of the key
issues in studying pinch systems. The spatial distribution of currentsheath(PCS)isproduced(stageI).Producedsheathun-
the current density substantially affects mechanisms for the deraneffectofponderomotiveforcesrealizesthecomplicated
dissipation of magnetic energy and generation of radiation. motionaccompaniedbytheshock-waveproduction.
This problem isofparticular importance inplasma focus (PF) When a part of the PCS attains the anode surface, the
devices [1], [2], in which the so-called “preliminary stages,” PCS accelerated motion toward the chamber axis with veloc-
responsible for the efficiency of current transportation into a ity (104−105) m/s is starting (stage II). The current rises in
pinchingregion,playanimportantroleinthedischargedynam- that case, attaining its maximum for the time of ∼10 μs. At
ics. This paper is devoted to study the structure and dynamics the PCS cumulation at the chamber axis (stage III), a fast
ofthecurrent-carryingplasmasheathinPFwithso-called“flat” plasma compression—for ∼10−7 s—up to the densities of
set of electrodes (Filippov’s type, [1]). The simplified scheme ∼1019 cm−3 and its heating occur. At the stage of a dense
ofthefacilityofsuchtypeisshowninFig.1. pinch,thecurrentdensityofabout>107A/cm2isattainedthat
In this PF modification, anode (1) of a comparatively large resultsinadriveofstrongcurrentinstabilitiesandinanabrupt
diameter is separated from the cathode (2) with a ringlike currentdisruption.Wehaveaneffectiveplasmaswitch,andthe
insulator (3). The vacuum chamber (4) is filled with a gas energy stored in the magnetic field of a pinch is released into
(deuteriumorheavygases,dependentonthetaskstobesolved) the “loading,” i.e., an anomalous plasma heating, an intense
under pressure in the range from a few tenths of Torr up to a neutron and X-ray radiation, and the charged particle beam
fewTorr.Aftertriggeringtheswitch(S),thebreakdowninthe driveoccur.
discharge gap along the insulator (3) takes place, and plasma- The calculation of the discharge-circuit inductance with al-
lowance for the PCS dynamics is one of the most important
tasks in studying PF systems. In particular, in a Filippov-type
Manuscript received December 31, 2008; revised July 13, 2009. First
publishedJanuary15,2010;currentversionpublishedFebruary10,2010.This system, the motion of the PCS in the acceleration stage is
workwassupportedinpartbytheRFPresidentialGrantMK-298.2007.2,by practicallyunaffectedbytheelectrodegap.Asaresult,thePCS
theRFBRProjects07-02-00336and07-08-00737,andbytheRFAgencyfor
expandswithoutbound,whichleadstoanundesirableincrease
ScienceandInnovationsunderContract02.516.11.6109.
V. I. Krauz, V. V. Myalton, V. S. Koidan, V. P. Vinogradov, and in the inductance of the discharge circuit. Accordingly, the
Y.V.VinogradovaarewithRRC“KurchatovInstitute,”NuclearFusionInsti- current begins to decrease long before it reaches the expected
tute,123182Moscow,Russia(e-mail:krauz@nfi.kiae.ru).
peak value [3]. Note that a similar effect, although not so
K.N.Mitrofanov,E.V.Grabovski,andG.G.ZukakishviliarewithTroitsk
InstituteforInnovationandFusionResearch,142190Troitsk,Moscow,Russia clearly pronounced, is also observed in the Mather geometry
(e-mail:[email protected]). [4].Moreover,current-densitymeasurementsperformedinthe
Colorversionsofoneormoreofthefiguresinthispaperareavailableonline
1970s[5]showedthatafractionofthedischargecurrentcould
athttp://ieeexplore.ieee.org.
DigitalObjectIdentifier10.1109/TPS.2009.2036916 flow in the vicinity of the insulator, being not involved in the
0093-3813/$26.00©2010IEEE
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KRAUZetal.:DYNAMICSOFCURRENTDISTRIBUTIONINADISCHARGEOFPF-3PLASMAFOCUSFACILITY 93
implosion process. So far, no systematic measurements of the
currentdensityinthepinchregionhavebeenconducted(except
insomeparticularexperiments;see,e.g.,[6]).Theimportance
of such measurements increases drastically with increasing
dischargeenergy.Inparticular,theshuntingofthepinchcurrent
bytheperipheralplasmacanleadtotheviolationoftheneutron
scalinginmegajoulePFfacilities.
Themaingoalsofthispaperareasfollows:
1) toinvestigatethedynamicsofthePCSinthestageofits
motiontowardtheaxis[Fig.1(II)];
2) tomeasurethecurrentflowingclosetothepinchregion.
II. EXPERIMENTALSETUPANDDIAGNOSTICS
The experiments were done on the Filippov-type PF-3
Fig.2. Magneticprobestructure.
facility [7]. The total capacity of the power supply is 9.2 mF,
maximalchargingvoltageis25kV,andmaximalstoredenergy
W is 2.8 MJ. The minimal external inductance L is 15 nH. were designed for experiments carried out in the Angara-5-1
0
There is an opportunity to install an additional matching facility [10]–[14], in which experimental conditions are close
inductance,allowingonetovaryaninitialinductance,L ,from enough to the PF-3 facility and then were adjusted to the
0
15 to 40 nH. Porcelain or glass ceramic insulators with a experimentalconditionsofthePF-3facility[15].
diameter of 0.9 m and a height of 0.25 m are used at PF-3 The most attractive result of these experiments, from our
facility.Theinsulatorsizeactuallydefinestheanodediameter. pointof view,istheunique experience of magnetic field mea-
The anode is a sectional copper disk with a total diameter of surementsnearthesystem’saxis(insidewirearrays,∼20mm
0.92 m and a thickness of 0.025 m. There is a changeable in diameter) at discharge currents in several megaamperes,
insertion in the central part of the anode. At present, a includingatechniqueofprocessingofsignalsofprobes,which
funnellikeinsertionwithadiameterof0.1mintheupperpart are destroyed in each shot. The similarity of experimental
ofthefunnelandadepthof0.07misusedintheexperiments. conditionsofourfacilities,includingalevelofelectromagnetic
The vacuum frame made of carbon steel with a diameter of noise,wasalsooneofthereasonsofourchoiceofsuchprobe
2.6mandaheightof0.45mservesascathode. design. It has allowed the applying of probes on the PF-3
The calculated value of a short-circuiting current at a max- facilitywithoutconsiderableproblems.
imal charging voltage of 25 kV and at a minimal external Eachprobeconsistsoftwoidenticalsingle-turncoilswound
inductance of 15 nH is 20 MA; the short-circuit current rise in opposite directions and encased in a common shell made
time is 18 μs. As it was aforementioned, the real current in of thin (thinner than the skin depth) NbTi foil (Fig. 2). Such
the discharge is determined by the PCS dynamics and by its a configuration makes it possible to simultaneously record
configuration [3], [8]. A series of studies on the production of two signals of opposite polarity, thereby allowing one to un-
high-power soft X-ray radiation fluxes has been done at this ambiguously distinguish the “magnetic” component against
facility in the 1980s–1990s [9]. The optimization of radiation the electromagnetic-noise background. As the magnetic probe
parameters and the dense PF formation have resulted in the consistsoftwoloops,calculationofmutualinductanceofsuch
following facility operating parameters: discharge energy, W, magnetic probes was done. The error caused by this effect
is 0.2–1.0 MJ and current on the plasma load, I , is up to is less than 1%. Due to PCS spatial and temporal dynamics,
p
4MAforheavyworkinggases(neon,argon).Mostexperiments dB/dtincreasesatPCSapproachingtotheaxis.Therefore,we
described as follows were conducted at the input energy of varythediameterofthecoilsfrom300μmattheprobeposition
W =290 kJ and the discharge current of up to 2 MA. The close to the axis to 900 μm for the probes located on the dis-
workinggaswasneonorargonatthepressureof1.0–1.5Torr. chargeperiphery(thecoilsineachprobehavepracticallyiden-
The magnetic probes are chosen as the basic technique for ticaldiameter).Itallowsthevaryingoftheprobes’sensitivity.
current-distribution dynamics studies. The main advantage of Thecoil’sself-inductanceisabout0.3nHfor300μmandabout
magnetic probes is that, with their help, the magnetic field 1.6 nH for 900 μm. Each coil is loaded on the cable with
is measured in small volume (in essence, in volume of a impedanceR=50Ω,soτ =L/R(cid:3)1ns.
probe), whereas the laser methods give an average field value Themainobstacleswhichhindermeasurementsbymagnetic
along a line of observation. At the same time, this method of probes are as follows: evaporation of screen of a probe under
measurements is a contact one, so the effect of the probe on influence of SXR and flow of particles, probes destruction,
theplasmaparametersandaccuracyofmeasurementsisavery penetration of electron beams into probes, probes screening
importantproblem.Themagnetic-probetechniqueisoneofthe bysurroundingplasma,perturbationofthesurroundingplasma
basicinstudiesofZ-pinchsystemsfromtheverybeginningof by probes, and others. All these problems have been analyzed
theirdevelopment.Practically,ineachlaboratory,theirvarious carefully in performing experiments on Angara-5-1 facility
modifications were used. In this paper, the PCS parameters [10]–[14],[16],[17].Tominimizetheprobeinfluenceonboth
weremeasuredwithabsolutelycalibratedmagneticprobesthat theplasmaandprobedestruction,thesensitivepartoftheprobe
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94 IEEETRANSACTIONSONPLASMASCIENCE,VOL.38,NO.2,FEBRUARY2010
Fig. 3. Arrangement of probes 1, 2, 3, and 4, measuring the azimuthal
magneticfieldinthePF-3chamberandlocatedatradiiof460,360,160,and
20mm,respectively.
hasaplateshapewithtransversalcrosssectionof0.7–0.8mm.
Theinfluenceoftheplasmaflowwithfrozenmagneticfieldfor
different shape of the probe has been considered in [16] and Fig.4. Resultsofmeasurementsoftheazimuthalmagneticfieldinadischarge
inargon.
[17] in two approximations—analytically for a subsonic flow
andnumericallyforasupersonicflow.Thesecalculationshave insert in the anode center, this protected the probe from a
shown minimal measurement errors ∼7% for the plate shape prematurebreakdownfromtheanode.Althoughthisprobewas
oftheprobescreen.Thetimeofelectromagneticfielddiffusion destroyed in every shot, it provided important information on
throughsuchashieldis∼1.5ns. thecurrentdynamicsintheaxialregionduringseveralhundred
Probes were calibrated by a technique stated in [11] and nanosecondsafterthearrivalofthePCS.Inordertoquicklyre-
[16]bytheirplacementinahomogeneousmagneticfieldwith placethedestroyedprobewithoutimpairingvacuumconditions
known amplitude and known frequency. The circuit based on inthedischargechamber,avacuumgatewasdesigned.
Helmholtz coils was used. The calibration error was ±5%.
Sensitivity of the probes used in our experiments was 14–
20 V·ns/kG. The total error of the measurements in view of III. EXPRIMENTALRESULTS
allthelistedabovefactors,includingcalibration,wasapproxi- Fig. 4 shows the results of current measurements in a PF
mately15%–20%. discharge in argon. The distance between the probes and the
Thecurrentwasdetermined bynumericalintegrationofthe anode plane are 26 mm for probes 1, 2, and 3 and 20 mm
probe signal under the assumption that the current-carrying forprobe4.TheprobesignalsappearsuccessivelyasthePCS
plasmawasaxisymmetric.Lastassumptionmayhaveessential propagates toward the axis. Since the PCS is noncylindrical,
influenceontheaccuracyofthecurrentreconstruction,partic- its anode part moves faster. Due to the inclined shape of the
ularlyinacaseoftheprobeplacedclosetotheaxis.Accuracy sheathandhighPCSvelocityatthefinalstageofcompression,
oftheprobeinstallationconcerningthesystemaxiswassuper- the signal from probe 3 appears immediately before pinching,
vised before each shot. In addition, for mistake minimization, althoughthedistancefromtheaxisisfairlylarge(160mm).By
the probe position relative to the pinch was checked with the thisinstant,thetotalcurrenthasalreadyappreciablydecreased
helpofapinholecameraandaframecamera[15]. in comparison with its amplitude value because of the rapid
The total discharge current was measured by the Rogowski increaseinthedischarge-circuitinductance.
coilandbythenumericalintegrationofthesignalsofthecali- An important point is that, within measurement errors, the
bratedmagneticprobesplacedoutsidethedischargechamber. signalsfromprobes1,2,and3coincidewiththetotalcurrentat
In our experiments, we used two modifications of probes, the corresponding instants, i.e., the current is efficiently trans-
whosearrangementisshowninFig.3.Initsphysicalessence, ported toward the axis: as the PCS passes near the probes, the
these modifications are identical and differ only in probe de- currentmeasured byeach probe isequal tothetotaldischarge
sign (for example, in coil diameter). Probes on the discharge current. Fig. 5 shows the waveform of the time derivative of
periphery(farfromthesystemaxis)areinlesshardconditions the current measured by the probe located at the radius of
(currentandPCSvelocityisless,theshockwaveisweaker,and 20 mm. It can be seen that the useful signal (before probe
skin-layerthicknessismore)thatallowstousemoresimpleand destruction) lasts for about 1 μs. Points “A,” at which the
mechanicallyreliabledesign.ToinvestigatethePCSdynamics symmetryofthesignalsisviolated,markthedestructionofthe
atlargedistancesfromthesystemaxis,weusedthesemultishot probecoilsduetohigh-voltagebreakdown.
probesintroducedthroughvacuumsealsandinstalledatradiiof Therefore,theabsolutevalueofthecurrentatradiilessthan
160,360,and460mm,thelastprobebeingsituatedagainstthe 20mmwasreconstructedonlyuptotheinstantcorresponding
anode edge (the anode diameter was 920 mm). The design of to the breakdown of one of the coil. The current amplitude
ports also allowed us to vary the distance between the probe in this region is 0.75 MA, which amounts to ∼30% of the
andtheanodeplane. maximum current. It should be noted that both the amplitude
The current near the axis was measured with a single-shot of this signal and the character of its subsequent decay agree
probe installed at a radius of 20 mm and at a height of 10– well with the signal from the probe located at the radius of
20 mm above the anode plane. In combination with a conical 160mm(seeFig.6).
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KRAUZetal.:DYNAMICSOFCURRENTDISTRIBUTIONINADISCHARGEOFPF-3PLASMAFOCUSFACILITY 95
Fig.8. Pinholepicturesofthedischargeinneon,W =540kJ,P =1torr:
(a)port7(60◦),diaphragmof0.2mm,filterBeof17μm;(b)port6(90◦),
diaphragmof0.4mm,filterBeof10μm.
Fig.5. Currentderivativeobtainedwiththemagneticprobeinstalledatthe
radiusof20mmandreconstructedcurrentwaveform.
Fig.9. Signalsofp-i-ndiode,filterAl8μm:(a)solidtrace—detectorD2
(90◦)anddashedtrace—detectorD5(60◦);(b)solidtrace—detectorD2(90◦)
anddashedtrace—detectorD3(90◦).
Themaindetectorsetincludesfourp-i-ndiodes[(2)and(3)]
Fig.6. Currentmeasuredwithmagneticprobesindifferentpositionsatthe
instantclosetothePCSpinchingattheaxisandtotalcurrentderivativedI/dt. with replaceable filters, allowing one to realize the measure-
ments in the preset spectral ranges. The p-i-n diode D2 is ori-
entedonthezoneofthepinchformationandseesboththepinch
and anode surface. Detector D3 sees only part of the pinch:
its bottom border of registration is at 1 cm above the anode
plane. It allows the investigating of the longitudinal dynamics
of soft X-ray source. The pinhole camera allowing to produce
a 2-D image of the X-ray radiation zone, integral in time and
in spectrum, is located at position (4). Additional p-i-n diode
D5 is placed in position (5) at the angle of 60◦ to the system
Fig. 7. Diagram of X-ray measurements: (1) main detector unit; (2), (3), axisthroughport(7).Similarport(notshowninFig.7)located
and(5)p-i-ndiodesD2,D3,andD5,respectively;(4)pinholecamera;(6)and symmetrically concerning an axis was used for installing the
(7) diagnostic ports; (8) transitional tube; (9) anode; (10) cathode; and
second pinhole camera, i.e., second pinhole camera and diode
(11)insulator.
D5 are placed on different ports. However, in the assumption
Presumably,duetoitsnoncylindricalshape,thePCSreaches of pinch axial symmetry, we consider that the field of sight
the probe located at a height of 20 mm above the anode plane is the same and differs only by the angle of observation. If,
already after the formation of the pinch in the cavity of the in the case of using the pinhole camera installing in the main
conical anode (the signal of probe 4 reaches the maximum detector unit (1), the field of vision is cut by the anode plane,
after the peak in the total current derivative). At this instant, the second pinhole camera “sees” the zone below the anode
the current begins to be switched to the insulator region. As a planewithintheanodedeepening.Theexampleofthepinhole
result,afterpinching,thesignalsfromalltheprobesarelesser picturesobtainedinthedischargewithneonisshowninFig.8.
thanthetotalcurrent. Onecanseethatthesignificantpartofthepinchisintheconic
The confirmation to the stated earlier assumption of the deepeningatthecenteroftheanode.Moreover,thetemporary
beginning pinch formation in the anode deepening lower than analysis of signals of p-i-n diodes D2 and D5 has shown
theanodeplanewasobtainedatstudiesofsoftX-rayradiation that pinching first takes place in the deepening and only then,
[18].ThediagramofmeasurementsisshowninFig.7. due to “zipper effect,” pinch occurs above the anode surface
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96 IEEETRANSACTIONSONPLASMASCIENCE,VOL.38,NO.2,FEBRUARY2010
Fig.10. Dischargeinneon:totalcurrent(1)andcurrentsmeasuredbytheprobes(2,3and4)locatedatradiiof460,160mmand20mm,respectively,at
differentheightsabovetheanodeplane;(a)h=26mm.(b)h=86mm.
[Fig. 9(a)]. “Zipper effect” was also confirmed by analysis of account an opportunity of PCS inclined passage. The electron
signals of detectors D2 and D3 [Fig. 9(b)]. The hot dense temperature estimated from the value of the skin depth under
plasma radiating soft X-ray rises on a height of 1 cm (field of the assumption of the Spitzer conductivity is 5–10 eV. In the
sight of the detector D3) for 7 ns, which corresponds to the finalstageofcompression,theskindepthneartheaxis(within
axialvelocity1.4·106 m/s.Itisnecessarytoemphasizethatit r =20mm)maybeevenlessthan1cm.
is “phase velocity” caused by the noncylindrical shape of the Anothersituationisobservedintheexperimentswithneon.
compressedPCS(“zippereffect”),itisnotconnectedwiththe Fig. 10 shows current waveforms measured in a discharge in
axialmasstransport. neon, the other conditions being the same as in a discharge
Unfortunately, it is difficult to bring the probe closer to in argon. In this case, the efficiency of current compression
the pinch because of the large probability of high-voltage toward the axis is substantially worse. It can be seen that
breakdownontotheprobe.However,takingintoaccountgood the current measured by the probe installed at r =460 mm
similarity between the signals from the probes located at the (≈1.3MA)comprisesonly≈75%ofthetotaldischargecurrent
radii of 20 and 160 mm, the current value in the pinch region at the instant corresponding to its peak value. Similar result
canbereliablyderivedfromthecurrentmeasuredbytheprobe wasobtainedatprobesheightabovetheanodeplaneof86mm
located at 160 mm at the instant corresponding to the peak in [Fig.10(b)].Interestingly,thesignalfromtheprobeinstalledat
thederivativeofthetotalcurrent. 160 mm first reaches the value of the signal measured by the
It is also obtained that, in the process of the PCS compres- probe installed at 460 mm and, for a time, practically repeats
sion to the axis, the current derivative measured by magnetic it. However, it then grows abruptly, reaching the total current
probes increases from ≈0.9·1012 A/s (at r =460 mm) up value.
to ≈3·1012 A/s (at r =160 mm). At the final stage of the Thedifferenceinthecurrentwaveformscannotbeexplained
PCS compression (at r =20 mm), current derivative reaches onlybythePCSdynamicsinZ-direction.Thisdifferencemay
≈1.5·1013 A/s.Inourcase be attributed to the fact that the probes record currents flow-
ing through different contours that may form due to shunting
(cid:2) (cid:3)
breakdowns.
V
I˙≈I· r , (1) Theshuntingbreakdownsandcurrentleakagebehindofthe
δ
skin mainPCSarethewell-knownphenomenonandischaracteristic
not only for PF systems but also for Z-pinches as a whole. In
whereI isthetotalcurrentflowinginPCSatthemomentofits particular,anopportunityofformingclosedcurrentloopsnear
passingthroughtheprobe,Vr isaradialcomponentofthePCS theinsulatorisunderlinedin[5].Thefractionofcurrentflowing
velocity,δskinistheskindepth.Theaveragevelocityatvarious in the moving piston, as well as the mass swept-up factor,
stages of the PCS radial compression can be appreciated by is an important parameter in the rather currently popular Lee
the shift between the signals’ occurrence on the neighboring model [19]. The reasons resulting in the shunting breakdowns
probes. For example, average velocity on the section 460– are rather various and are presently widely discussed [20]. As
360mmis≈3·106cm/s.Takingintoaccountthattotalcurrent oneofthemainreasons,theinfringementofmagneticisolation
practically does not change during PCS passing through the of the interelectrode gap behind of main current sheath is
probeandusethemeasuredvalueofcurrentderivative,wecan considered [21]. We will discuss it in more detail as follows.
estimate the PCS skin depth. The PCS skin depth is found to Themainconsequenceoftheshuntingbreakdownsmaybethe
decrease from 6 ± 1 cm at r =460 mm to 3 ± 1 cm within dischargecurrentswitchingoverinanewcircuitandformation
theregionofradiusof160mm.Itisnecessarytonotethatthis independentcurrentloops.Adiagramillustratingtheprobable
estimation is estimation “from above,” as we do not take into scenario of the discharge development inthe presence of such
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KRAUZetal.:DYNAMICSOFCURRENTDISTRIBUTIONINADISCHARGEOFPF-3PLASMAFOCUSFACILITY 97
Fig.11. Diagramillustratingtheformationofclosedcurrentloops.
shuntingbreakdownsandtheformationofasequenceofseveral of the current flowing in the circuit (I). If the conditions for
closedcurrentloopsisshowninFig.11. developing the next breakdown are kept, it is possible to form
An increase in the discharge voltage due to the increase in thesecondclosedloop(II)[Fig.11(d)].Therefore,thiscanlead
the inductive component of the load impedance as the PCS totheformationofseveralclosedcurrentloopsseparatedfrom
propagates toward the axis [Fig. 11(a)], as well as the abrupt the main discharge circuit. Moreover, our probes can measure
increase in the pinch impedance at the instant of maximum currentsflowingindifferentcurrentcircuits.
compression,cancauseashuntingbreakdownofthedischarge Unfortunately, no voltage measurements were performed in
gap.Themostprobableplaceofsuchbreakdowndevelopment thisseriesofexperiments.Nonetheless,bymeasuringthetotal
istheareaneartoinsulator[Fig.11(b)].Thisbreakdownshunts dischargecurrentoritstimederivativeandsolvingthedifferen-
the power supply and disconnects the current flowing in the tialequationforthedischargecircuit(withoutallowanceforthe
main layer. As a result of current reconnection, the closed ohmiccomponentofthevoltage),wecanfindtheinductanceof
current circuit (I) is formed. New current sheath (II) departs the circuit L(t)=L +L (t), where L is the constant com-
0 p 0
from the insulator and starts to move to the axis similarly ponent of the inductance and L (t) is the variable component
p
to the movement of the first layer on the initial stage of the which varies as the PCS propagates toward the axis and thus
discharge [Fig. 11(c)]. Thus, the magnetic piston “pushes” calculatetheinductivecomponentofthevoltage.Fig.12shows
closed current loop (I) placed in front of it, which can result the calculated time dependences of the voltage for different
in compression of the captured magnetic field and in increase working gases. It is shown that the overvoltage between the
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98 IEEETRANSACTIONSONPLASMASCIENCE,VOL.38,NO.2,FEBRUARY2010
where ω is the electron gyrofrequency (in radians per sec-
ce
ond), τ is the electron–ion collision time (in seconds), n is
ei e
the electron density (in cubic centimeters), z ∼(T )0.5 is the
e
degreeofionization,andB istheazimuthalcomponentofthe
ϕ
magneticinductionofthefirstPCSintheregionoftheshunting
breakdown(ingauss).From(2),weobtain
T3/2 I
n ≥2.8×1011 e . (3)
e zlnΛR
Unfortunately, we do not know the experiments devoted to
theresidualplasmaparameters(T orn)measurements.In[23],
in considering a discharge in deuterium in the MHD model at
aninitialpressureof1torrandadischargecurrentamplitudeof
1.5MA,theelectrontemperaturewasassumedtobe3–5eVin
thestageofPCSformation.Usingthedataofourmeasurements
ofPCSskindepthintheassumptionofSpitzerconductivity,it
ispossibletoestimatetheplasmatemperature.Ondistantradii,
itmakes5–10eV.Itisnecessarytonotethatdischargecurrent
atthisinstantreachesvalueofmorethan1MA.Wecanassume
thattemperatureofresidualplasmaintheinsulatorregionwill
beequalorlessthisvalue.
From the analysis of oscillograms of the discharge in neon
(Fig. 10), we can assume that the first breakdown occurs in
the area of insulator in the initial stages of the discharge
development.Havingacceptedasanestimationaveragevalues
of the current, I ∼1 MA, and the temperature, T ∼5 eV,
we obtain the shunting condition in the insulator region (R=
46 cm) n ≥7×1015 cm−3, which, under our initial condi-
e
tions(P =1.5torr),is∼15%oftheinitialdensity.Therefore,
0
Fig.12. MeasuredtimedependenceofthetotaldischargecurrentI(t)and if we assume that the residual gas is the one left after the
calculated time dependence of the voltage Uins(t) in the insulator region; propagation of the first PCS, then less than 15% of the gas
r(t)isthecalculatedmeanradiusofthePCS(P0=1.5Torr,U0=8kV):
(a)Argon.(b)Neon. shouldpenetratethroughthisPCS.Otherwise,currentshunting
leads to the formation of the second PCS, which snowplows
electrodes is stronger for a discharge in argon. At the same the residual gas (plasma) as it propagates toward the axis,
time,forneon,smallrepeatingvoltagespikesthatcorrespondto thereby decreasing its density. If the residual plasma density
fallsbelowthethresholdvalue,nofurthercurrentshuntingand
thepinchingofthesubsequentPCSsgeneratedduetoshunting
PCSformationtakeplace.
breakdowns are observed. This effect is apparently related to
The estimations done earlier do not claim to be exhaustive.
thelower“snowplow”efficiencyinthelattercase.
Ourmainpurposewastodemonstratethat,dependingon“snow
A key feature of a PF discharge is that the development of
plough”efficiency,occurrenceofconditionsatwhichmagnetic
shuntingbreakdownsisimpededbystrongmagneticinsulation
isolation of the interelectrode gap may be broken is quite
behind the PCS. The electric strength of the electrode gap
possible.
dependsonmanyfactors,suchastheassemblingqualityofthe
electrodesystem,thedegreeofitstraining,theoptimizationof
the initial conditions, etc. An important factor in determining IV. CONCLUSION
thegapstrengthistheresidualgasdensitybehindthePCS[21]. It has been demonstrated that the probe diagnostics can be
Foran“untrainedsystem,”thisdensityisdeterminedmainlyby efficientlyappliedtoPFstudies.Usingasetofmagneticprobes
outgassingfromtheelementsoftheelectrodesystem,whilefor installedatdifferentpositionsalongthePCSpath,itispossible
a“trained”system,itdependsonthe“snowplow”efficiency. notonlytoevaluatethecurrentinthepinchingstagebutalsoto
Letusestimatefrombelowtheresidualgas(plasma)density measurethedynamicsandparametersofthePCSandcalculate
that is sufficient to switch the current from the axial region to the inductance of the discharge circuit. The opportunity of
the insulator region. If the residual plasma is not magnetized shuntingbreakdownsdevelopment,interferingthecompression
(ω τ <1) by the magnetic field of the first PCS, then it of the total discharge current to the axis, is shown. In spite
ce ei
can shunt the discharge current. The magnetization parameter of all this, we do not assert that argon is the more preferable
ω τ intheregionoftheshuntingbreakdowncanbeestimated gas. Apparently, the bad compression of the current in the
ce ei
asfollows[22]: discharge with neon testifies about the not optimum selection
oftheinitialdischargeconditions(gaspressure,initialcharging
B T3/2 voltage, etc.) in the given series of experiments. The probe
ω τ ≈1.4×1012 ϕ e <1, (2)
ce ei zn lnΛ measurementscanappearastheratherusefultoolatachoiceof
e
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KRAUZetal.:DYNAMICSOFCURRENTDISTRIBUTIONINADISCHARGEOFPF-3PLASMAFOCUSFACILITY 99
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