Beam Current Monitors - USPASuspas.fnal.gov/materials/09UNM/BeamCurrentMonitors.pdf · toroid...

BeamCurrentMonitors

AcceleratorBeamDiagnos4csW.Blokland(ORNL)

USPASandUniversityofNewMexicoAlbuquerqueNM,June23‐26,2009

USPAS09atUNM 1AcceleratorandBeamDiagnos4cs

BeamCurrentMonitors

•  WhyuseBeamCurrentMonitors?•  Howtocoupletothebeam

– Transformer

– Resis4veWallCurrentmonitor– FaradayCups

•  Limita4ons:Noise,bandwidth

•  Lab

USPAS09atUNM 2AcceleratorandBeamDiagnos4cs

Par4cleAccelerators

One measure of performance: Power •  The amount of particles delivered at a certain

energy.

SNSPowerontarget

SNSEnergydeliveredtotarget

USPAS09atUNM 3AcceleratorandBeamDiagnos4cs

Par4cleAccelerators

•  How well do you accelerate beam? –  What percent of the particles make it to the end

•  Effectiveness of acceleration process. E.g. stripping losses 3-5% of beam

–  What percent of time are you operational? •  Damage to accelerator

–  What is the quality of your beam? •  Emittance (collider) •  Density profile (target) •  Position stability •  Radio-activation

USPAS09atUNM 4AcceleratorandBeamDiagnos4cs

ChargedBeam

•  What is the beam current?

€

Ibeam =qeNt

=qeNl⋅ βc

InanacceleratorthecurrentisformedbyNpar4clesofchargestateqperunitof4metorunitoflengthlandvelocityβ=v/c.

Thebeamisnearlyanidealcurrentsourcewithaveryhighsourceimpedance

•  We can measure the beam through the electric and magnetic fields created by the beam.

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BeamCurrentStructure

SNSBeamStructure

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BeamImagecurrents

•  Fastmovingpar4cles(movingE‐field)createanHfield.TheHfieldmovestheE‐fieldinducedimagecharges.

•  Athighveloci4esthewallcurrentspectrumisanimage(oppositesign)ofthebeamspectrum:atataspeedof0.5c,approxRMSlengthis90psor1.8GHz

Movingcharge Fastmovingcharge

USPAS09atUNM 7AcceleratorandBeamDiagnos4cs

[5][5]

BeamImagecurrentsIfthewallcurrentmirrorsthebeamcurrentthenthemagne4cfieldoutsidethebeampipeiscancelled:

Isitcompletelycancelled?•  Skindepth:thelengthinwhichthefieldsarereducedbya

factorofe(‐8.7dB).At10Mhz,atypical0.794mmstainlesspipeaeenuates53dB.

€

Ampere's Law : H • dl = I∫ and with Ibeam = - Iimage then H • dl = Ibeam + Iimage∫ = 0→ H = 0

€

δ =10 ⋅103

2πρf

with ρ the resistivity and f the frequency

USPAS09atUNM 8AcceleratorandBeamDiagnos4cs

From[2]Webber.

BeamPipeBreak

Nofieldoutsideofbeampipe.Either:

•  installdetectorinsidebeampipeor

–  Insidebeampipemeansinstalla4oninvacuum•  useaceramicbreak

–  Ceramicbreakforcesimagecurrenttofindanotherpathanditwilldoso!

USPAS09atUNM AcceleratorandBeamDiagnos4cs 9

Zgap

GapImpedance•  Youbeeerdefineyourgapimpedance.Somethingwillalwaysbepresent,suchasa

pathtogroundand

capacitance.

•  Zgapiscombina4onofthegap

capacitanceandallexternal

parallelelements

• Gapvoltage

canbegenerateduptobeamvoltage

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Zgap

CourtesyofJimCrisp&MikeReid@FNAL

Currenttransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs 11

€

Line current field : B = µ ⋅

Ibeam

2πr a ϕ

Ibeam vout

Β

R

Torus to guide the magnetic field

Measurethebeamcurrentthroughthemagne4cfieldofthebeam.

[1]

Assumethebeamislongenoughtoberegardedasalinecurrent.E.g.SNSRing:250metersfor1usec

€

H ⋅ dl =∫ NpIp + NsIs = Ip +NsIs with Np =1 ⇒

H = (Ip +NsIs) /2πr (1)

Φ = BS∫ dS= µHA = µA(Ip +NsIs) /2πr with A as area (2)

Vs = −Ns ⋅dΦdt

= Is ⋅ Rs (3)

Currenttransformer

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Vs

Ampere’sLaw:

€

Is ⋅ Rs = −Ns ⋅µA2πr

⋅d(Ip +NsIs)

dt with Ls = Ns

2µA2πr

⇒

dIsdt

+Rs

LsIs = −

1Ns

⋅dIpdt

(4)

Is(iω)Ip (iω)

= −1Ns

⋅iω

(iω + Rs /Ls)

Flux:(thintoroidapproxima4on)

Faraday’sLaw:

Combine(2)and(3):

vs

Ip

Rs

N turns

Ip

Rs Vp

toroid material permeability = µ0µr cross section = A Mean radius = r

Primary winding Np turns

Integration path dl

Is

Secondary winding Ns turns

Laplacerewrite:

Differen4alequa4on:

H

Currenttransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs 13

€

Is(iω)Ip (iω)

=1Ns

⋅iω

(iω + Rs /Ls)

When

€

Ps = Is2Rs =

Ip2

Ns2 Rs €

Is =IpNs

€

iω >> Rs /Ls

Great, we got our transfer function and now we can figure out what the behavior is of our current transformer:

Power: (transferred from beam)

Currenttransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs 14

The inductance plays an important role in the design of transformer. Note that in the calculation for inductance, the geometry of the setup plays and important role as well as the µ and windings.

Inductance of a torus with a square cross section:

€

Φ = BS∫ dS= µHdS

S∫ = µI2πr

ldrrin

rout

∫ =µI2π

l ln routrin

with L = NΦI

then

L =µN 2l2π

ln routrin

and µ = µ0µr

rin

ι

µr

rout

dS

µr can be > 10000.

€

Ls = Ns2Lp

Currenttransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs 15

Too bad there is also a capacitance: we get an LCR circuit:

€

1Z

=1R

+1iωL

+ iωC⇒

Z =iωL

1+ iωL /R − (ωL /R) ⋅ (ωRC)

[1]

LRCProper4es

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€

For low frequency : ω << R /L→ Z = iωLFor high frequency : ω >>1/RC→ Z =1/iωCFor mid frequency : R /L <<ω <<1/RC→ Z ≈ R

€

Z =iωL

1+ iωL /R − (ωL /R) ⋅ (ωRC)

log

ωR/L 1/RC

It’sabandpasswitha:− droop4metdroop− rise4metrise

Whatareproper4esofanLRCcircuit?

[5]

Bandpasseffectsonpulseshape

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• Rise4metrise:definedasthe4meittakestheamplitudetogofrom10%to90%.• Rise4meconstantτrise:andτrisecorrespondstothe4meforanincreasebye−1=37%.

Rise‐4meanddroop‐4me

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€

tdroop =ln0.9 − ln0.1

ω low

=2.197ω low

=2.1972πf low

≈1

3 f lowω low = R /L⇒tlow ≈ 2L /R or tlow ≈ 2τ low with τ low = L /R

€

trise =ln0.9 − ln0.1

ωhigh

=2.197ωhigh

=2.1972πfhigh

≈1

3 fhighωhigh =1/RC⇒

trise ≈ 2RC or trise ≈ 2τ rise with τ rise = RC

• Droop4me

€

A∝ (1− e− t /τ rise )

Add(long)cabletocurrenttransformer:addcableresistance,capacitanceandinductance:

CurrentTransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs 19

€

τ droop = L /(Rf /A +RL ) = L /RL

Ac4veTransformer:useatrans‐impedancecircuittolowertheloadimpedance. €

τ rise = LsCs τ droop = L /(R +RL )

[1]

[1]

Howtodesignacurrenttransformer:• Highsensi4vity‐>lownumberofturns,lowNs

• Highdroop4me‐>highL‐>highµ,highNs

• Fastrise4me‐>lowstraycapacitance

DesignofCurrentTransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs 20€

τ rise = LsCs

€

Vs = IsRs =IbNs

Rs

€

τ droop = Ls /Rs

€

L s =l

2πln rout

rin

⋅µ ⋅ N s

2

€

τ rise = RC withoutcable

withcable

DesignofCurrentTransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs 21

Ac4vetransformer

Passivetransformer

HowtomeasuretheDCcurrent?Thecurrenttransformerdiscussedseesonlychangesintheflux.TheDCCurrentTransformer(DCCT):lookatthemagne4csatura4onofthetorus.

DCCurrentTransformer

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• Modula4onoftheprimarywindingsforcesthetorusintosatura4ontwicepercycle.• Secondarywindingssensemodula4onsignalandcanceleachother.• ButwiththeIbeam,thesatura4onisshiuedandIsenseisnotzero• Adjustcompensa4oncurrentun4lIsenseiszeroonceagain.

DCTransformerOpera4on,see[1]

DCCurrentTransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs 23

• Modula4onoftheprimarywindingsforcesthetorusintosatura4ontwicepercycle.• Secondarywindingssensemodula4onsignalandcanceleachother.• ButwiththeIbeam,thesatura4onisshiuedandIsenseisnotzero• Adjustcompensa4oncurrentun4lIsenseiszeroonceagain.

Examplebandwidth:DCto20kHz,resolu4on2µA

[1]

24

CurrentMonitorLimita4ons

Limita4ontotransformers:• Thepermeabilityofacorecanbesaturated:specsofmaxBfieldormaxcurrent4meproductI*t,

• Thermalnoise:

• WeissdomainsleadtoBarkhausennoiseiftermina4ngwithhighimpedance(limitforDC‐type)

• Avoidexternalmagne4cfields

• Torusmaterialhasdependencyofµrontemperatureoronmechanicalstress(micro‐phonicpickup)

• Avoidsecondaryelectronsfrombeingmeasured

€

Vn ≈ 4kbTfhighR -> µA range lower limit

USPAS09atUNM AcceleratorandBeamDiagnos4cs

25

BCMTes4ngFixture

USPAS09atUNM AcceleratorandBeamDiagnos4cs

ImagebyM.Kesselman

26

SNSCurrentTransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs

ImagebyM.Kesselman.

LHCFastCurrentTransformer

USPAS09atUNM AcceleratorandBeamDiagnos4cs 27

U.RaichCASFrasca42008BeamDiagnos4cs

DesignbyBNLforSNS

28

COMPONENTSINSIDEHEBTBCMASSEMBLY

USPAS09atUNM AcceleratorandBeamDiagnos4cs

WallCurrentMonitor•  Putaresistoroverthegapandmeasureitsvoltage.

USPAS09atUNM AcceleratorandBeamDiagnos4cs 29

R€

Vgap = Rgap ⋅ Ibeam

NoDCinimagecurrent

Vout

WallCurrentMonitor

USPAS09atUNM AcceleratorandBeamDiagnos4cs 30

U.Raich

WallCurrentMonitor

USPAS09atUNM AcceleratorandBeamDiagnos4cs 31

Schema4csofawallcurrentmonitoranditsequivalentcircuit[1]

Nowforthedetails:• Ceramicgaptoavoidworkinginvacuum• Distributedresistors(30to100)forbeamposi4onindependency• Ferriteringsforlowfrequencyresponse• Shieldforgroundcurrentsandnoiseprotec4on

32

Wait,thereismore

LowtoMidbandModel

Iin/n

BroadbandModel

Iin/n

2ζ=√(RL/RL+Rs)((Rs√C/Le+(1/RL)√Le/C)

ωo=√1/(RL/RL+Rs)LeC

Evenaresistorisnotaresistor:

USPAS09atUNM AcceleratorandBeamDiagnos4cs

[4]

[4]

33

FaradayCups

TheFaradayCupdestruc4velyinterceptsthebeam• DCcoupled!(WithjustaresistorthesignalisVout=Ibeam*R)• Lowcurrentmeasurementspossiblee.g.,10pA• Problemwithsecondaryelectrons:

- Uselongcuporvoltagesuppressionormagne4cfield• Ifnotproperlyterminated‐>veryhighvoltage(beampoten4al)• Mustprocessbeampower(SNSfullpower1.4MW)

USPAS09atUNM AcceleratorandBeamDiagnos4cs

[1]

34

FaradayCups

USPAS09atUNM AcceleratorandBeamDiagnos4cs

LowpowerFaradayCup[1] Highpower(1MW)FaradayCup[1]

35

NoiseIssues

USPAS09atUNM AcceleratorandBeamDiagnos4cs

Noisecanbeaproblem!• TherearemanypowerfulnoisesourcesinAccelerators:

- Switchingpowersupplies- Accelera4ngRF- SourceRF

Caseinpoint:- SNSDTLBCM‐>singleendedandinsideacavity(duetospacelimita4ons)

36

NoiseIssues

USPAS09atUNM AcceleratorandBeamDiagnos4cs

NoiseofDTLcurrenttransformer(insidecavity,singleended)

NoisefromRF

Noisefromswitchingpowersupplies

Beam

Grounded

[8]

37

NoiseIssues

USPAS09atUNM AcceleratorandBeamDiagnos4cs

Beam

SCLBeamCurrentMonitor(singleended)

[8]

38

NoiseIssues

USPAS09atUNM AcceleratorandBeamDiagnos4cs

Beeer:CCLBCMoutsideofcavitybuts4llsingleended.

CCLBeamCurrentMonitor(singleended)

Beam

39

NoiseIssues:CommonMode

USPAS09atUNM AcceleratorandBeamDiagnos4cs

Differen4alnoiseonlongtwinaxwithfarendshieldgrounded.Leu:topandboeom,noiseoneithercenterconductorinto50ohms(each20mV/div);center,difference(2mV/div);(mostofresidualsignalduetodigitalscopesubtrac4on).Right:samesignalsfaster4mescale(each20mV/divand1uS/div).From[2]Webber.

Ifnoiseiscoupledintobothwires,wecanrejectit!‐>commonmodenoiserejec4onbytakingthedifference.

Youwilldothisasalabexperiment.

20mV

2mV

20mV

BCMLunch4meSeminar 40

References

[1]ForckP.,“LectureNotesonBeamInstrumenta4onandDiagnos4cs”,JointUniversityAcceleratorSchool,p.forck@gsi.de[2]WebberR.C.,“TutorialonBeamCurrentMonitoring”,BIW2000,pp83‐101.[3]WebberR.C.,“ChargedPar4cleBeamCurrentMonitoringTutorial”,BIW1994,pp3‐23[4]WebberR.C.,“LongitudinalEmieance:AnIntroduc4ontotheConceptandSurveyofMeasurementTechniques,IncludingDesignofaWallCurrentMonitor”BIW1993[5]Denard,J.C.“CERNAcceleratorSchoolonBeamDiagnos4cs”,28May–6June2008,Dourdan.[6]HammondP.,“Electromagne4smforEngineers”,PergamonPress.[7]WatersC.,“CurrentTransformersprovideaccurate,isolatedMeasurements”,PowerConversion&IntelligentMo4on,IssueDecember1986[8]PlumM.,“LANLCurrentMonitorPickupFinalDesignReview”,March2002.[9]EdministerJ.,“Schaum'sOutlineofElectromagne4cs”