Microwave response of ITER vacuum windows

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Microwave response of ITER vacuum windows

Citation for published version (APA):

Oosterbeek, J. W., Maquet, P., Sirinelli, A., Udintsev, V. S., Vayakis, G., & Walsh, M. J. (2017). Microwave

response of ITER vacuum windows. Fusion Engineering and Design, 124, 442-445.

https://doi.org/10.1016/j.fusengdes.2017.01.052

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CC BY

DOI:

10.1016/j.fusengdes.2017.01.052

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Published: 01/11/2017

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ContentslistsavailableatScienceDirect

Fusion

Engineering

and

Design

j ourna l h o m e pa g e :w w w . e l s e v i e r . c o m / l o c a t e / f u s e n g d e s

Microwave

response

of

ITER

vacuum

windows

Johan

W. Oosterbeek

a

_,

_Philippe

_Maquet

b

_,

_Antoine

_Sirinelli

b

_,

_Victor

_S.

_Udintsev

b

_,

George

Vayakis

b

_,

_Mike

_J.

_Walsh

b

a_Eindhoven_University_of_Technology,_P.O._Box_513,₅₆₀₀_AZ_Eindhoven,_The_Netherlands

b_ITER_{Organization,}_Route_de_{Vinon-sur-Verdon,}_CS₉₀_046,₁₃₀₆₇_St._Paul_Lez_Durance_Cedex,_France

h

i

g

h

l

i

g

h

t

s

•MicrowaveresponseofITERvacuumwindows.

•Analyticalmicrowaveresponsedielectricslab.

•Simulatedmicrowaveresponseofdielectricslab.

•Finiteelementandﬁniteintegrationtechnique.

•Comparisonanalyticalresponsetosimulatedresponse.

•Microwaveresponseoftiltedorwedgedvacuumwindows.

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received1October2016

Receivedinrevisedform25January2017 Accepted30January2017

Availableonline24February2017 Keywords: Vacuumwindow Transmission Reﬂection Absorption Dielectricloss Losstangent Microwave ITER

a

b

s

t

r

a

c

t

DiagnosticsystemsareessentialforthedevelopmentofITERdischargesandtoreachtheITERgoals.Many ofthesediagnosticsrequirealineofsighttorelaysignalsfromtheplasmatothediagnostic,typically locatedoutsidethetorushall.Suchdiagnosticsthenrequirevacuumwindowsthatisolatethetorus vacuumand,crucially,ensurecontainmentofhazardoussubstances.Whilesuchwindowsareroutine inmanyfusionexperiments,ITERposesnewchallenges.Thevacuumwindowsaresafetyimportant componentsclass1thatmustwithstandallITERloads.Asaconsequence,inmanycasesdoubledisk windowsareusedwithmodiﬁedfrequencyresponseascomparedtosinglediskwindows.ITERisalong pulsemachinewith20MWmicrowaveheatinginstalled,givingrisetogradualheatingofwindowsdue tostrayradiation.TheparticularmicrowaveheatingschemeatITERmayalso–incaseofanerroneous polarizationsetting–resultinarefractedbeamwithmuchhigherpowerdensity.Thispaperlooksat microwaveaspectsofITERwindows.Themicrowaveresponseasafunctionoffrequencyiscalculated forproposedarrangements.Fromthisresponsetheimpactondiagnosticperformancemaybeassessed aswellasthethermalloadonthewindowitself.

1. Introduction

Vacuum windows provide lines of sight for optical and

microwaveelectro-magnetic(EM)waves.Atthewindowboundary

thewaveencountersanimpedancemismatchcausingreﬂection

whilethetransmittedfractionundergoesabsorption.Givena

par-ticularsystemanoptimizationofthewindowarrangementcanbe

madebyselectingthetypeofceramicandthicknessandspacing

betweendisks.However,windowsatITERarealsosafetyimportant

components(SIC)–astheyarebarriersforhazardoussubstances

–limitingtheseoptions.Thispaperreportsonmethodsandtools

toﬁndfractionsoftransmittedpower(T),reﬂectedpower(R)and

absorbedpower(A)asafunctionoffrequencyinthemicrowave

range. Withthesequantities theimpactof thewindow onthe

diagnosticorheatingsystemandtheloadonthewindowcanbe

evaluated.

Differentsystemrequirementscombinedwithboundary

con-ditions,suchassizesandﬁxtures,haveledtothedevelopmentof

asetofwindowsusingdifferentdielectricmaterials.Clear

aper-turesrangefrom25mmto160mminadoublediskarrangement

(withtheexceptionofCVD-diamondwindowsusedforgyrotrons

[1]).ThediskthicknessisstillunderreviewgivenSICconcerns.In

thisworkathicknessd=12mmisusedforillustrativepurposes.

AsdiskmaterialITERforeseesfusedsilica,crystallinequartz,

sap-phire,zincselenide,siliconnitride,andCVDdiamond.Forexamples

inthispaperpropertiesoffusedsilicaareused,typeInfrasil301TM

bythecompanyHeraeuswith

r=3.81,and tanı=2.9×10−4 at

90GHz.

http://dx.doi.org/10.1016/j.fusengdes.2017.01.052

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Fig.1.Frequencyresponseofafusedsilicadiskwithd=12mm(radius: TEM-modepropagationconsidered).

2. Reviewofmicrowavewindowresponse

Thetheoryofreﬂectionandtransmissionofmultipledielectric

slabsiswellunderstood[2].Applicationtovacuumwindowsin

waveguidesismorespeciﬁc,althoughgoodliteratureisavailable

heretoo,e.g.[3–5].Inthissectionareviewisgivenonhowto

ana-lyticallyobtainamultilayerdiskresponseincludinglossesinsidea

waveguide.Thisisfollowedbycomparisontoresultsfroma

sim-ulationcodewiththeaimtoalsoassessmorecomplexstructures

suchasdoubledisktiltedwindows.

2.1. Responseofasingledielectricslab

AnEM-waveperpendicularlyincidentonadielectricslabof

infi-nitethicknesswillbepartlyreflecteddenotedbythefieldreflection

coefﬁcientbontheboundary.Incaseofnon-magneticmaterials

b=1−n1+n [2],withntherefractiveindexn=

√

rand

rthe

rela-tivepermittivity.Ratnormalincidenceisinsuchcase2

b andis

minimizedfornapproachingunity.Apracticaldiskhasthickness

dgivingrisetomultiplereﬂectionswithinthediskleadingtoan

interferencepatternofTandRasfunctionoffrequency.The

mul-tiplereﬂectionsinthissimplegeometrycanbesummedandthey

convergetogivethetotalreﬂectedfractionofelectricﬁeldtotand

thetotaltransmittedfractionofelectricﬁeldttot[2]asfollows:

tot= b

1−e−jϕ

1−b2e−jϕ , ttot= (1−b2)e−j(1/2)ϕ 1−b2e−jϕ . (1)

ϕistheelectricallengthofoneroundtripinsidethedielectric:

ϕ=2ˇd withˇ thephase constant of the propagationconstant

ˇ=2/andthewavelengthinside thedielectric,i.e.the

vac-uumwavelengthdividedby√

randdthethicknessofthedisk.

Lossescanbetakenintoaccountbyredeﬁning

rasthecomplex

permittivity

r=

r(1−jtanı),inwhichthetermtanıistheloss

tangentand

ristherealpartoftherelativepermittivity.Withthis

deﬁnitiontherealpartofˇrepresentstheattenuationconstant

andtheimaginarypartrepresentsthephaseconstant.Bytaking

thecomplexconjugatesoftotandttot,RandTareobtainedand

A=1−T−R.Fig.1showsaplotofT,R,AonadBscale(10·log10

ofthequantities).Amodestfrequencyisusedtoallowsimulation

later.

Transmissionisoptimizedincasetheinitialreﬂectedwavefront

isin counter phase withthewavefrontsreﬂected bythe

inter-nalreﬂections.Thisis calledresonantand occurswhen tot=0

Fig.2.AbsorbedfractionsofpowerinthediskofFig.1.

resultingind=m·1

2withmaninteger.Thetransmission

can-notbeat0dB(100%)duetotheabsorbedfractionofpower.These

lossesareinthiscaseat−20dB(1%).Intermsofsignallossforthe

systemthisislow,butathighpower,suchascausedbygyrotrons,

thedielectricheatingmaybehigh.Toassessthelossesquicklyone

couldalsolookatthesingle-passlossoranapproximationincase

ofmultiplereﬂections.Thesingle-passlossfollowsfromthe

atten-uationconstant˛inthepropagationconstant=˛+jˇ,recalling

thatthevariationwithdistanceoftheelectricﬁeldiswrittenas

E(z)=E0e−z,withzthedistanceinthedirectionofpropagation.

SolvingtheMaxwellequationsaccountingforlossesitisshown

thatforlow-lossmaterials˛≈(f

rtanı)/c[6].Thesingle-pass

absorbedfractionofpoweris1−e−2˛z,whichfor˛z1canbe

approximatedby2˛zandsingle-passAbecomes:

ASP≈

2f

rtanı

c d. (2)

Nickel[7]showedthatinthecaseofmultiplereﬂectionstheloss

maybeapproximatedby:

AApprox≈ f (1+

r)tanı c d, (3) i.e.afactor(1+

r)/2

rlargerthenthesingle-passresult.The

threedifferentresultsforthelostfractionofpowerinthediskare

plottedinFig.2.

Eq.(3)givesaminoroverestimatebutissafetouseinallcases.

2.2. Multipledisksinwaveguide

ThemodelusedinSection2.1usesTEM-modepropagationand

asingledisk.HoweveratITERmultiplediskssituatedinsidea

wave-guidewillbeused.Dependingontheratioofradiustowavelength,

TEorTMpropagationmustbeusedopposedtoTEM.Insuchacase

dividingthewindowassemblyincascadedsectionsandapplying

matrixcalculusmaybeused.Suchworkiscoveredin[3–5].Here,an

extractforcircularwave-guidesusingthedominantTE11modeis

reproducedtoallowassessmentofITERwindowsandcomparison

totheresponseobtainedusingsimulation.

TheS-matrixforadiskinwaveguideisgivenby:

S= 1 1−2 mne−2mnd

mn

1−e−2mnd

₁₋2 mn

e−mnd

1−2 mn

e−mnd _mn

1−e−2mnd

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Fig.3. Smallscaledoublediskarrangementformodelling:(a)disksareparallel, (b–c)withtilteddisks.Rotating(b)overthehorizontalaxisclockwise90◦_(as_seen

fromtheright)gives(c).Thewindowradiusis3mm,zisthedirectionofpropagation. Theoverallarrangementisenclosedinacircularwaveguide.

Inwhichthemode-dependentpropagationcoefﬁcientis:

mn=

k2

cmn−

rk20 (5)

withk0=2f/candkcmnisthequantitythatmodiﬁesthe

prop-agationdependingonmodeandwave-guide size.Foracircular

waveguide withdominant TE11 modekcmn=1.841/r withr the

radiusofthewaveguide[8].Themode-dependentreﬂection

coef-ﬁcientforTE-modesmnis:

mn=

1−

kcmn/k0

2 −

r−

kcmn/k0

2

1−

kcmn/k0

2 +

r−

kcmn/k0

2 (6)

The equations have been implemented in a MATLAB® code

whichreadsd,thediskspacingand

rofeachsectionfromaspread

sheetandcomputestheS-matrices.WhilesuchS-matricesare

con-venientforlabmeasurementstheyarenotwellsuitedformatrix

manipulationandthuseachS-matrixisconvertedtoa T-matrix

assuggestedin[5].TheT-matricesaremultipliedrighttoleftand

theoverallproductisconvertedbacktoanS-matrix.Risextracted

asS11S∗₁₁andTisextractedasS21S∗₂₁.Lossesareincludedagainby

replacingtherelativepermittivitywiththecomplexpermittivity.

Thecodetakesafewsecondstorun.AresultisshowninSection2.3.

2.3. Simulationmodel

A fundamentally differentmethod to obtainthe microwave

responseistousesimulation.ThefrequencydomainsolverofCST

MICROWAVESTUDIO(2016)wasusedwhichisbasedonﬁnite

ele-ments.Byusingsimulationmodelswithphysicalsizesofseveral

wavelengthsthistechniquecanbeusedintandemwiththe

ana-lyticalmethodsinSections2.1and2.2.Asmallscaledoubledisk

windowwasdrawnupandthefrequencyresponsewasobtained.

Fig.3(a)showsthesimulationmodel.

Fig.4showsthefrequencyresponseobtainedwithsimulation

comparedtotheanalyticalresponseofSection2.2.Themodeltakes

severalminutestorun.

3. DiscussiononITERwindows

3.1. Frequencyresponse

Toassesstheimpactofthewindowonsystemperformance,

andtopossiblytunethicknessanddiskspacing,themethodology

ofSection2.2maybeused.Forexample,thehighreﬂectionstarting

Fig.4. ResponseofthewindowinFig.3ausingthemultiplediskmodel(subscript ‘ana’)andthesimulation(subscript‘sim’).Thecurvesofanalyticalresponseandthe simulatedresponseoverlap.

Fig.5. Simulatedresponseofdoublediskwindowwithtiltsatanangleof5◦

(sub-script‘sim’)comparedtoanalyticalresponseofdoublediskmodelwithnotilts (subscript‘ana’).

atf≈64GHzinFig.4maybeshifted.Theassembliesalsouse

var-ioustiltsofthediskstorejectundesiredsignals.Theeffectofsuch

tiltsmaybeinvestigatedbysimulation.Aconﬁgurationwiththe

ﬁrstdisktiltedatanangleof5◦ withrespecttoyandthesecond

disktiltedatanangleof5◦ withrespecttoz(coordinatesystem

asinFig.3band c)hasbeensimulated.Theresultis plottedin

Fig.5withrespecttotheresultofthesimulationusingparallel

disks(Fig.4).Therearetwokeyobservations:(i)asmalloverall

frequencyshift,and(ii)spikesappearonthesignal.Thesmallshift

infrequencyislikelycausedbythesmallmodiﬁcationtothecavity

lengthandcaninthiscasebeprojectedtotheanalyticalmodel.

Thespikeswereinvestigated furtherby usingthetime domain

solver,whichisbasedonﬁniteintegrationtechnique.Computation

timesincreasedtoabout15minbutagainthespikeswereobtained

indicatingthatinthisprecisegeometryandexcitationthey

mathe-maticallyexist.Veriﬁcationmeasurementsarerequiredsuchasfor

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3.2. Losses

Lossesaregenerallylowwithrespecttosignal/noiseofthe

sys-tembuttheycausealoadtothewindowincaseofhighstraypower.

ForrefractedbeamsAshouldbecalculatedusingEq.(3)asincidence

anglesaremostlyunknownbutwillshifttheinterferencepattern.

Thepowerabsorbedinsidethediskiscomputedbymultiplication

oftheexpectedstraypowerdensityp[Wm−2][10–12]withthe

disksurfaceS[m2_]_and_absorption_A:_P_[W]₌_p_·_S_·_A._As_a

hypothet-icalexample,takearefractedgyrotronbeamwithincidentpower

density1.25MWm−2,diskdiameter110mm,absorbedfractionat

170GHz=3%.Thepowerinthediskisinthiscase≈350W.This

isalargevaluebutnotallwindowswillbeatriskfromrefracted

beams[11]andmitigationmeasuresmustbedeveloped.Isotropic

stayradiationlevels–incidentonallcomponents,allanglesand

polarizations–areexpectedtobeatleastafactorof 10lower,

althoughisotropicstrayradiationabsorptioncoefﬁcientsitselfmay

beuptoafactoroftwohigher.Measurementandanalysisareunder

investigation.

4. Summary

Basicoperationofaresonantdielectricdiskhasbeenreviewed

tofacilitatetuningthemicrowaveresponseofvacuumwindows

andtoassesslosses.Equationsforamultiplediskarrangementare

reviewedandacomputermodelisdescribed.Comparisonismade

againstsimulationandgoodagreementisfound,openingthe

pos-sibilitytoassessmorecomplexstructuressuchastiltedorwedged

windowsofsmallelectricallength.

Theviewsandopinionsexpressedhereindonotnecessarilyreﬂect

thoseoftheITEROrganization.

References

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[4]H.-U.Nickel,etal.,PlaneTransverseWaveguideWindows–Surveyof FormulasforReﬂection,Transmission,andAbsorption,in:ConferenceDigest, SixteenthInternationalConferenceonInfraredandMillimeterWaves,26–30 August,1991,Lausanne,Switzerland,1991.

[5]H.J.Hartfuss,T.Geist,FusionPlasmaDiagnosticswithmm-Waves, Wiley-VCH,2013.

[6]S.Y.Liao,MicrowaveDevices&Circuits,3rded.,PrenticeHallInc.,1990.

[7]H.-U.Nickel,HochfrequenztechnischeAspektezurEntwicklung

rückwirkungsarmerAusgangsfensterfürMillimeterwellengyrotronshoher Leistung,FZKarlsruhe,FZKAReportNo5513,1995.

[8]T.Moreno,MicrowaveTransmissionDesignData,ArtechHouse,Inc.,1989 (originallypublished:NewYork:McGraw-Hill,1948).

[9]A.Simonettoetal.,65–100GHzTransmissionMeasurementsonVacuum Windows,IstitutodiFisicadelPlasma,ReportFP04/01.

[10]F.Gandini,etal.,StraypowerestimatesfromECexploitationduringITER plasmaoperations,in:AIPConf.Proc1406,vol.173,2011.

[11]A.Sirinelli,etal.,EvaluationofECstrayradiationinITERanditsimplication fordiagnostics,in:Proc.ofScience,EPDS,2015.

[12]J.W.Oosterbeek,etal.,LoadsduetostraymicrowaveradiationinITER,Fusion Eng.Des.96–97(2015)553–556.