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


Par4cleAccelerators

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

energy.

SNSPowerontarget

SNSEnergydeliveredtotarget


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


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.


BeamCurrentStructure

SNSBeamStructure

USPAS09atUNM AcceleratorandBeamDiagnos4cs 6

BeamImagecurrents

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

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

Movingcharge Fastmovingcharge


[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


From[2]Webber.

BeamPipeBreak

Nofieldoutsideofbeampipe.Either:

•  installdetectorinsidebeampipeor

–  Insidebeampipemeansinstalla4oninvacuum•  useaceramicbreak

–  Ceramicbreakforcesimagecurrenttofindanotherpathanditwilldoso!


Zgap

GapImpedance•  Youbeeerdefineyourgapimpedance.Somethingwillalwaysbepresent,suchasa

pathtogroundand

capacitance.

•  Zgapiscombina4onofthegap

capacitanceandallexternal

parallelelements

• Gapvoltage

canbegenerateduptobeamvoltage


Zgap

CourtesyofJimCrisp&MikeReid@FNAL

Currenttransformer


€

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


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


€

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


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


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


€

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


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

Rise‐4meanddroop‐4me


€

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


€

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


Ac4vetransformer

Passivetransformer

HowtomeasuretheDCcurrent?Thecurrenttransformerdiscussedseesonlychangesintheflux.TheDCCurrentTransformer(DCCT):lookatthemagne4csatura4onofthetorus.

DCCurrentTransformer


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

DCTransformerOpera4on,see[1]

DCCurrentTransformer


• 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


ImagebyM.Kesselman

26

SNSCurrentTransformer


ImagebyM.Kesselman.

LHCFastCurrentTransformer


U.RaichCASFrasca42008BeamDiagnos4cs

DesignbyBNLforSNS

28

COMPONENTSINSIDEHEBTBCMASSEMBLY


WallCurrentMonitor•  Putaresistoroverthegapandmeasureitsvoltage.


R€

Vgap = Rgap ⋅ Ibeam

NoDCinimagecurrent

Vout

WallCurrentMonitor


U.Raich

WallCurrentMonitor


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:


[4]

[4]

33

FaradayCups

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

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


[1]

34

FaradayCups


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

35

NoiseIssues


Noisecanbeaproblem!• TherearemanypowerfulnoisesourcesinAccelerators:

- Switchingpowersupplies- Accelera4ngRF- SourceRF

Caseinpoint:- SNSDTLBCM‐>singleendedandinsideacavity(duetospacelimita4ons)

36

NoiseIssues


NoiseofDTLcurrenttransformer(insidecavity,singleended)

NoisefromRF

Noisefromswitchingpowersupplies

Beam

Grounded

[8]

37

NoiseIssues


Beam

SCLBeamCurrentMonitor(singleended)

[8]

38

NoiseIssues


Beeer:CCLBCMoutsideofcavitybuts4llsingleended.

CCLBeamCurrentMonitor(singleended)

Beam

39

NoiseIssues:CommonMode


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,[email protected][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”

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