Kilotesla Magnetic Field due to a Capacitor-Coil Target Driven by High Power Laser.

0.97 MB·English

by  Fujioka, Shinsuke

Kilotesla Magnetic Field due to a
Capacitor-Coil Target Driven by High
SUBJECTAREAS: Power Laser
APPLIEDPHYSICS
ELECTRICALANDELECTRONIC
ENGINEERING ShinsukeFujioka1,ZheZhang1,KazuhiroIshihara1,KeisukeShigemori1,YouichiroHironaka1,
HIGH-ENERGYASTROPHYSICS TomoyukiJohzaki2,AtsushiSunahara3,NaojiYamamoto4,HidekiNakashima4,TsuguhiroWatanabe5,
HiroyukiShiraga1,HiroakiNishimura1&HiroshiAzechi1
FLUIDDYNAMICS
1InstituteofLaserEngineering,OsakaUniversity,2-6Yamada-oka,Suita,Osaka565-0871,Japan,2GraduateSchoolof
Received
Engineering,HiroshimaUniversity,1-4-1Kagamiyama,Higashi-Hiroshima,Hiroshima739-8527,Japan,3InstituteforLaser
21August2012
Technology,2-6Yamada-oka,Suita,Osaka565-0871,Japan,4DepartmentofAdvancedEnergyEngineeringScience,Kyushu
Accepted University,6-1Kasuga-Koen,Kasuga,Fukuoka816-8580,Japan,5NationalInstituteofFusionScience,Toki,Gifu509-5292,
27December2012 Japan.
Published
30January2013 Laboratorygenerationofstrongmagneticfieldsopensnewfrontiersinplasmaandbeamphysics,astro-and
solar-physics,materialsscience,andatomicandmolecularphysics.Althoughkiloteslamagneticfieldshave
alreadybeenproducedbymagneticfluxcompressionusinganimplodingmetaltubeorplasmashell,
accessibilityatmultiplepointsandbettercontrolledshapesofthefieldaredesirable.Herewehavegenerated
Correspondenceand kiloteslamagneticfieldsusingacapacitor-coiltarget,inwhichtwonickeldisksareconnectedbya
requestsformaterials U-turncoil.Amagneticfluxdensityof1.5 kTwasmeasuredusingtheFaradayeffect650mmawayfromthe
shouldbeaddressedto coil,whenthecapacitorwasdrivenbytwobeamsfromtheGEKKO-XIIlaser(at1 kJ(total),1.3 ns,0.53or
1mm,and531016 W/cm2).
S.F.(sfujioka@ile.
osaka-u.ac.jp)
Laboratorygenerationofstrong,shapedmagneticfieldsoffersanewexperimentaltestbedtostudyplasmaand
beamphysics1,astro-2andsolar-physics3,4,materialsscience5,andatomicandmolecularphysics6.Infast-
ignitionlaserfusionresearch,collimationofarelativisticelectronbeambyanaxialmagneticfieldisakey
schemetoincreasethecouplingefficiencybetweenthelaserandthecore7.Magneticfieldreconnection3,4and
collisionlessshockgeneration1inaplasmasubjecttoastrongmagneticfieldarealsocurrentresearchobjectives.
Magneticfieldisgeneratedspontaneouslyinalaser-producedplasma8,andseveralkiloteslafield9,10hasbeen
measuredinarelativisticallyintenselaser-plasmainteractionexperimentinsmallspatialandtemporalscales.
Kiloteslafieldshavebeenproducedbymagneticfluxcompressionusingimplodingmetaltubes11andplasma
shells12–15.Upto4 kThasbeengeneratedbycompressinga6-TseedmagneticfieldattheOMEGAlaserfacility.
Thismagneticfieldwasusedinacentral-ignitioninertialfusionexperiment13.Thetemperatureofthehotspot
increasesbyembeddingthemagneticfieldseedinthefusionfuelbecausethestrongfieldinhibitselectronheat
conductiontothesurroundingcoldfuel.
Although the spontaneous magnetic field generation and the flux compression scheme are useful, others
techniquesarenecessarybecausemultipointaccessibilityandcontrolledshapeofthefieldarerequiredforseveral
applications. We have demonstrated that kT magnetic flux densities can be produced using a capacitor-coil
target16.
Results
Figure1showsphotographsofacapacitor-coiltargetinsideandfrontviews.Twonickeldisksareconnectedbya
U-turncoil.Kilojoule,nanosecondlaserpulsesarefocusedontothefirstdiskthroughaholeintheseconddisk.A
plasmaisgeneratedatthefirstdisk,andsuprathermalhotelectronswithtemperaturesexceeding10 keVare
emitted fromtheplasmacorona17.Thehotelectronsstreamdowntheelectrondensitygradient aheadofthe
expandingplasmaplumeandimpacttheseconddisk.Theseconddiskacquiresanegativecharge,andalarge
electricalpotentialdevelopsbetweenthedisks.ThatpotentialdifferencedrivesacurrentintheU-turncoil.A
strong magnetic field pulse is generated in the coil. A previous study of this scheme18 indicated that 100-T
magneticfieldscouldbecreated.Inthoseexperiments,apick-upcoilprobewasusedtodetectthefluxdensity
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Figure1|Photographsofacapacitor-coiltargetfrom(a)itssideand(b)itsfront. ThetwonickeldisksareconnectedbyanickelU-turncoil.
atthecoil.However,suchprobesaresusceptibletotheelectromag- Figure3showsaschematicofthemagneticfluxdensitymeasure-
neticnoisegeneratedbythelaser-plasmainteractions. mentwithFaradayeffect19.Thehorizontallypolarizedsecondhar-
TheFaradayeffectisamagneto-opticalphenomena,producinga monic of a Q-switched Nd:YAG laser (at a wavelength l of
rotationoftheplaneofpolarizationthatislinearlyproportionalto 0.532 mm) was used as the probe light. The probe light pulse is
thecomponentofthemagneticfieldinthedirectionofpropagation. coincident with the GEKKO laser. Fused silica was used as the
TheangleofrotationhisproportionaltothelengthLoftheoptical Faraday medium with a Verdet constant of 298 6 12 deg/T m at
pathinthemedium,theVerdetconstantVofthemedium,andthe 0.532 mm.The fused silica has a cylindrical shape whose diameter
magneticfluxdensityHaccordingtoh5LVH. and length are 600 mm and 100 or 500 mm, respectively. The rear
The average value of the flux density within a Faraday medium surfaceislocated600 mmawayfromthecoil,thereforethecenterof
(B@measureinTable1)issimplycalculatedas theFaradaymediumis650or850 mmawayfromthecoilforthe100
or500 mmthickmedium,respectively.
h
H ~ , ð1Þ Thetransmittedprobelightisimagedbylens1ontotheiris.The
measure VL central part of the image, having a diameter of 100 mm on the
Thethickness(100or500 mm)oftheFaradaymediumiscomparable Faradaymedium,isselectedbytheiris.Theimageistransferredto
tothedistancebetweenthecoilandthecylinder.Nonuniformityof thevisible streak camera bylens 2. Heat absorption and bandpass
themagneticfieldinthemediumisnotnegligible.Peaknormalized filtersbetweentheirisandlens2excludethelaserharmonicsandthe
profile of themagnetic flux density along the path of probe, H^ðxÞ thermalemissionfromtheplasma.Itwasexperimentallyconfirmed
that the our imaging system detects only the probe light. The
showninFig.2,wascalculatedwiththeinitialshapeoftheU-turn
Wollastonprismdividestherotatedlightintohorizontalandvertical
coil,wherexisacoordinatealongthepathofprobe.
components.
Magneticfluxdensityatthearbitraryposition,H(x),iscalculated
Theequatoroftheimageisselectedbyaslitonthestreakcamera
as
cathodeinFig.3andthestreakimageisrecordedonaCCDcamera.
HðxÞ~HmeasureðxRH^ðxÞ , ð2Þ T(Ihe1rIot)a5tiocnosahn/(gcloeshh1issidnehte)rbmetiwneedenftrhoemhotrhiezoinnttaelnIsitayndravteiortiIcHa/l
H^ðxÞdx H V H
I components.Thetemporalresolutionis150 ps.
xxF {x VFigure 4 is a streak image of a magnetic field measurement. A
R F 500 mm-thickcylinderwasusedastheFaradaymediuminthisshot
Herex andx arethepositionsofthefrontandrearsurfacesofthe (35869).Inthereferenceimage,forwhichacapacitor-coiltargetwas
F R
Faradaymedium.InTable1,magneticfluxdensitiesat850 mmaway notdrivenbytheGEKKO-XIIlaser,onlythehorizontalcomponent
fromthecoilarelistedforthecomparison. waspresent.Whenthecapacitor-coiltargetwasdrivenbytwobeams
Table1|Summaryofmagneticfluxdensityat850mmfromthecoil
ShotID lL EL IL ILl2L B@measure B@850mm Method
mm J W/cm2 W/cm2mm2 T T
35866 1.053 1000 4.331016 4.831016 11006130 9906120 FR:500mm
35870 1.053 990 2.131016 2.331016 15006330 8806190 FR:100mm
35869 1.053 740 1.631016 1.731016 480660 430660 FR:500mm
35868 0.526 190 4.131015 1.131015 180650 160650 FR:500mm
35477 0.526 540 8.231014 2.231014 N/A 3368 Pickupcoil
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Figure2|Peaknormalizedprofileofthemagneticfluxdensityalongthepathofprobe,whichwascalculatedwiththeinitialshapeoftheU-turncoil
usedinthisexperiment. ThesurfaceoftheFaradaymediumwaslocatedat600mmawayfromthecoil.100mmor500mm-thickfusedsilicacylinderwas
usedastheFaradaymedium.
ofthelaser,averticalcomponentappearsandthehorizontalcom- Maximum rotation angle of 162 6 7 deg. was obtained with a
ponentdisappears1.5 nsafterthelaserirradiation.Thisdelayinthe 500 mm-thick fused silica cylinder in the highest intensity shot
magneticfieldindicatesthattheseconddiskneeds1.5 nstoacquire (35866).Thethickness ofacylinderwaschangedfrom500 mmto
hotelectronstodrivecurrentinthecoil.Theintensityratiowas0.26 100 mm to confirm that the rotation is occurred in the cylinder.
60.07, corresponding to 71 66 degrees of rotation. The average Rotation angle of 45 6 8 deg. was obtained with a 100 mm-thick
densityofmagneticfluxintheFaradaymediumiscalculatedtobe cylinder (35870). Positions of the cylinder center (650 mm or
480660 TfromtherotationangleandaVerdetconstant.Itwas 850 mm)weredifferent,twolaserbeamswerenotoverlappedcor-
foundthattheprobelightwasblockedsoonafterthemagneticfield rectlyintheshot(35870),andtheintensitywasahalfofthehighest
generation. intensity. With the consideration of the above differences, the
Figure3|MagneticfluxdensitymeasurementusingtheFaradayeffect. Acylindermadeoffusedsilica,whosediameterandlengtharerespectively
600mmand500or100mm,islocatedawayfromthecoil.Horizontallypolarizedsecond-harmoniclightfromaNd:YAGlaserisusedastheprobe.The
transmittedprobelightisimagedbylens1ontotheiris.Thecentralpartoftheimage,havingadiameterof100mmontheFaradaymedium,isselectedby
theiris.Theimageistransferredtothevisiblestreakcamerabylens2.Heatabsorptionandbandpassfiltersbetweentheirisandlens2excludethelaser
harmonicsandthethermalemissionfromtheplasma.TheWollastonprismdividestherotatedlightintohorizontalandverticalcomponents.
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Figure4|Streakimagesofthehorizontalandverticalcomponentsoftheprobebeamin(a)thereferenceand(b)themagneticfieldgeneration(35869)
shots.
dependenceoftherotationangleonthecylinderthicknesssupports cylinder to obtain a scaling law of the flux density against laser
thattherotationisoccurreddominantlyinthecylinder. intensity and wavelength. Table 1 and Fig. 6 summarize the max-
Thetransmittanceofthefusedsilicarecoveredwithintheduration imummagneticfieldobtained.Averagevaluesofmagneticfluxden-
oftheprobelightpulseinoneshot(35870).Thetemporalevolution sitywithintheFaradaymedium(B@measure)andthefluxdensityat
of the magnetic flux density was calculated from the intensity 850 mmawayfromthecoil(B@850 mm)werelistedinTable1.The
ratio. Dynamics of a plasma between the two nickel disks was maximumvalueofthemagneticfluxdensitymeasuredinthisexperi-
simultaneouslyobservedfromthesideusinganx-rayimagingsys- mentwas15006330 T,650 mmawayfromthecoil.Thedottedline
temcoupledtoanx-raystreakcamera. inFig.6showsalinerlineasB(I )52.7310214I .Peakdensityof
L L
Figure5(a)plotstheevolutionofthemagneticfluxdensitymea- themagneticfluxseemstobeinproportionaltolaserintensitynot
suredwiththeFaradayeffect.Thehatchedregionindicatesthedura- productofintensityandthesquareoflaserwavelength.
tionoftheprobepulseblackout.Figure5(b)showsanx-raystreak A pick-up coil probe was also used to detect the magnetic flux
imageoftheplasma.Thezerooftimeisthebeginningofthelaser densityinthelowestlaserintensityshot(35477).Thediameterofthe
irradiation.Themagneticfielddevelopsat1.5 nsinFig.5(a),anda pick-upcoilwas5 mmandthecoilwaslocatedat100 mmfromthe
plasmaisgeneratedattheseconddiskatthissametimeasshownin capacitor-coiltarget.Thepick-upsignaliseasilyaffectedbyelectro-
Fig.5(b).Consequently,hotelectronswithanexpansionspeedof5.1 magnetro noise generated by laser-plasma interactions. In our
3107 cm/s arrive atthesecond diskand produced aplasma.The experimental conditions, we obtained a meaningful signal only at
magnetic field once disappears at 3.0 ns in Fig. 5(a), but plasma thelowestintensityandagreenlaserirradiation.
emissionattheseconddiskincreasesatthattime.Aplasmaplume Magneticfieldspontaneouslygeneratedbylaser-plasmainterac-
withanexpansionspeedof2.53107 cm/smayarriveat3.0 nsafter tionsoverlapsasbackgroundonasignal.Aplanarnickeldiskwith-
the laser irradiation. The resulting potential difference drives the outacoilwasirradiatedbythelaserandthespontaneousfieldwas
currentintheplume. measuredwiththepick-upcoil.Thefielddensitygeneratedwiththe
Wemeasuredthemagneticfluxdensitiesbyvaryingtheintensity U-turn coil was ten times higher than the spontaneous one, and
andwavelengthofthedrivelaserandthethicknessofthefusedsilica directionofthespontaneousfieldisdifferentfromthatofthefield
Figure5|(a)Temporalevolutionoftheintensityratiobetweenhorizontalandverticalcomponentsandthemagneticfluxdensityusing100-mm-thick
fusedsilicacylinder.Thehatchmarksinthegraphrepresentthedurationofthattheprobelightwasblocked.(b)Anx-raystreakimageoftheplasma
generatedinthetargetcapacitor.
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Figure6|Variationofthemagneticfluxdensityat850mmfromthecoilasafunctionofthelaserintensity. Theredcirclesandgreensquaresrepresent
thefluxdensitygeneratedbya1.064-mmlaseranda0.526-mmlaser,respectively.TheclosedorclosedmarksrepresentresultsobtainedwiththeFaraday
rotationorthepick-upcoilmeasurements.ThedottedlineshowsalinerlineasB(I )52.7310214I .
L L
generatedbytheU-turncoil,therefore, weneglectedthespontan- Discussion
eousfieldintheFaradayrotationmeasurement. ThefirstimportantdiscussionissueisavalidityoftheFaradayrota-
Figure 7 shows temporal change of the magnetic flux density tionmeasurementforlargeBanddB/dtachievedinthisexperiment.
measuredwiththepick-upcoil.Thefielddecayswithacharacteristic Inourexperiment,BanddB/dtreach1.5 kTand3 kT/ns,respect-
timeof28 nsthatisnotsofarfromthedecaytimeofaclosedcircuit ively. Faraday rotation angles for a GaP crystal at a wavelength of
withcharacteristicL/R517 ns,whereR,5.431022VandL,9.2 632.8 nmweremeasuredasafunctionofafieldstrengthupto400 T
310210 Hwereused,respectively.Thedeepdiparound3 nsisfound measured by a pick-up coil20. The rotation angle shows a linear
intheevolutionofthefield.Thisphenomenonisfoundalsointhe increase withthefield strengthand thecoefficient of10100 deg/T
Faraday rotation measurement as shown in Fig. 5, but the mech- m that is very close to the value measured at weak field strength
anismisnotclear.Peakfluxdensitywas3368 T,thisisalsoshown (10050 deg/Tm).
inFig.6andTable1. TheFaradayrotation inafusedsilicafiberwasrecentlyusedin
magneticcompressionexperimentwithalaser-acceleratedfoilanda
cavity15.Thetimehistoryofthemagneticfieldduringthecompres-
sionwassuccessfullymeasured,measuredamplificationagreeswith
theratiobetweeninitialandfinaldimensionsofthefieldembedded
area.BanddB/dTreached800 Tand1 kT/nsintheirexperiment,
thereforethisresultrevealsthattheFaradayrotationmeasurement
canbeusedforatleastB,800 TanddB/dt,1 kT/ns.
ValidityoftheFaradayrotationmeasurementforthelargeBand
dB/dtachievedinthisexperimentisstillanopenquestion,however,
nonlinearityoftheFaradayeffectinducedbylargeBanddB/dtseems
not to cause a significant error in the estimation of field strength,
becausethosetwovaluesobtainedinourexperimentareonlytwoor
threetimeslargerthantheexperimentallyvalidatedvalues.
Theseconddiscussionissueistotalenergyofthemagneticfield
generatedbythelaser-drivencapacitorcoil.Bycomparingthemea-
suredfielddensityandthatcalculatedwiththeinitialshapeofthe
U-turn coil, current in the coil and total energy of the field were
estimated to be 8.6 MA and 15 kJ. The field energy was obtained
byintegratingmagneticfieldenergy(B2/m )atthefieldpeaktiming
0
inthecalculationspace(23435 mm3).Thetotalenergyisincon-
ceivable,because15 kJismuchlargerthanthelaserenergy(1 kJ).
Explosion of the coil due to ohmic heating by a large current and
Figure7|Temporalevolutionofthemagneticfieldmeasuredwitha consequentimplosionofthefieldinsidethecoilisacandidatemech-
pick-upcoil.Thedottedlineisanexponentialcurvewiththedecaytimeof anism to explain the experimental result, but we have no experi-
28ns. mentalevidenceforthat.Black-outoftheprobelightfoundinthe
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0:6961663l2 0:4079426l2 0:8974794l2
Table2|Verdetconstantoffusedsilicaatvariouswavelengths n2ðlÞ~1z z z : ð4Þ
l2{ð0:0684043Þ2 l2{ð0:1162414Þ2 l2{ð9:896161Þ2
l V
ConsequentlytheVerdetconstantat532nmiscalculatedtobe287deg/Tm.
nm degT21m21 Byanothermethod,theVerdetconstantat532nmwasdeterminedtobe310deg/
Tmbyinterpolationofdata35,36listedinTable2.fittedtothepowerlaw
632 212.21335
589 274.55035 VðlÞ~4:13539|108: ð5Þ
546.1 288.47736 l2:2455
435.8 472.83736 V5298612deg/TmisusedinthethisstudyasaVerdetconstantofafusedsilicaat
334.2 859.46236 0.532mm.
302.2 1099.5336
284.8 1271.9536 Errorinestimationofmagneticfluxdensityfromfaradayrotation.Intensityratio
betweenhorizontalandverticalcomponentsoftherotatedlight(I /(I 1I )has
H H V
fluctuationof60.07ofatypicalvalue.Thisfluctuationwasconsideredinthe
Faradayrotationmeasurementmaybeexplainedbythecoilimplo- calculationoftherotationanglefromtheintensityratio.UncertainlyofVerdet
sion, because the probe light is blocked when the imploding coil constantofafusedsilicaat0.532mmlight(V5298612deg./Tm)wasconsidered
inthecalculationofthemagneticfluxdensityfromtherotationangle.Theupperand
collidesatthecenterofthecoil.Onlyasmallportionofthemagnetic
lowervaluesofthefluxdensitywerecalculatedbyusingV5286and310deg./Tm
field(100 mmindiameterand500 mminlength)wasmeasuredin fromtherotationangle,respectively.Consequenterrorwasintherangefrom612to
the experiment, spatial distribution of the magnetic field must be 631%ofthefluxdensity.
measured to conclude why the strong field is generated by the
laser-drivencapacitor-coiltarget.Thismeasurementisafuturework.
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License:ThisworkislicensedunderaCreativeCommons
Attribution-NonCommercial-NoDerivs3.0UnportedLicense.Toviewacopyofthis
license,visithttp://creativecommons.org/licenses/by-nc-nd/3.0/
Acknowledgements
Howtocitethisarticle:Fujioka,S.etal.KiloteslaMagneticFieldduetoaCapacitor-Coil
TheauthorsthankthetechnicalsupportstaffattheGEKKO-XIIfacilityforlaseroperation,
targetfabrication,andplasmadiagnostics.TheauthorsacknowledgeDr.N.Hasegawa TargetDrivenbyHighPowerLaser.Sci.Rep.3,1170;DOI:10.1038/srep01170(2013).
(JAEA)andDr.K.Kondo(TIT)forvaluablecontributionstothisexperiment.Theauthors
SCIENTIFICREPORTS |3:1170|DOI:10.1038/srep01170 7