Beam Current Monitors - USPASuspas.fnal.gov/materials/09UNM/BeamCurrentMonitors.pdf · toroid...
Transcript of Beam Current Monitors - USPASuspas.fnal.gov/materials/09UNM/BeamCurrentMonitors.pdf · toroid...
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BeamCurrentMonitors
AcceleratorBeamDiagnos4csW.Blokland(ORNL)
USPASandUniversityofNewMexicoAlbuquerqueNM,June23‐26,2009
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BeamCurrentMonitors
• WhyuseBeamCurrentMonitors?• Howtocoupletothebeam
– Transformer
– Resis4veWallCurrentmonitor– FaradayCups
• Limita4ons:Noise,bandwidth
• Lab
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Par4cleAccelerators
One measure of performance: Power • The amount of particles delivered at a certain
energy.
SNSPowerontarget
SNSEnergydeliveredtotarget
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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
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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
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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
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From[2]Webber.
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BeamPipeBreak
Nofieldoutsideofbeampipe.Either:
• installdetectorinsidebeampipeor
– Insidebeampipemeansinstalla4oninvacuum• useaceramicbreak
– Ceramicbreakforcesimagecurrenttofindanotherpathanditwilldoso!
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Zgap
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GapImpedance• Youbeeerdefineyourgapimpedance.Somethingwillalwaysbepresent,suchasa
pathtogroundand
capacitance.
• Zgapiscombina4onofthegap
capacitanceandallexternal
parallelelements
• Gapvoltage
canbegenerateduptobeamvoltage
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Zgap
CourtesyofJimCrisp&MikeReid@FNAL
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Currenttransformer
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€
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
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€
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
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Currenttransformer
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€
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)
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Currenttransformer
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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
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Currenttransformer
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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]
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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]
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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 )
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Add(long)cabletocurrenttransformer:addcableresistance,capacitanceandinductance:
CurrentTransformer
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€
τ droop = L /(Rf /A +RL ) = L /RL
Ac4veTransformer:useatrans‐impedancecircuittolowertheloadimpedance. €
τ rise = LsCs τ droop = L /(R +RL )
[1]
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Howtodesignacurrenttransformer:• Highsensi4vity‐>lownumberofturns,lowNs
• Highdroop4me‐>highL‐>highµ,highNs
• Fastrise4me‐>lowstraycapacitance
DesignofCurrentTransformer
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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
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DesignofCurrentTransformer
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Ac4vetransformer
Passivetransformer
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HowtomeasuretheDCcurrent?Thecurrenttransformerdiscussedseesonlychangesintheflux.TheDCCurrentTransformer(DCCT):lookatthemagne4csatura4onofthetorus.
DCCurrentTransformer
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• Modula4onoftheprimarywindingsforcesthetorusintosatura4ontwicepercycle.• Secondarywindingssensemodula4onsignalandcanceleachother.• ButwiththeIbeam,thesatura4onisshiuedandIsenseisnotzero• Adjustcompensa4oncurrentun4lIsenseiszeroonceagain.
DCTransformerOpera4on,see[1]
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DCCurrentTransformer
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• Modula4onoftheprimarywindingsforcesthetorusintosatura4ontwicepercycle.• Secondarywindingssensemodula4onsignalandcanceleachother.• ButwiththeIbeam,thesatura4onisshiuedandIsenseisnotzero• Adjustcompensa4oncurrentun4lIsenseiszeroonceagain.
Examplebandwidth:DCto20kHz,resolu4on2µA
[1]
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CurrentMonitorLimita4ons
Limita4ontotransformers:• Thepermeabilityofacorecanbesaturated:specsofmaxBfieldormaxcurrent4meproductI*t,
• Thermalnoise:
• WeissdomainsleadtoBarkhausennoiseiftermina4ngwithhighimpedance(limitforDC‐type)
• Avoidexternalmagne4cfields
• Torusmaterialhasdependencyofµrontemperatureoronmechanicalstress(micro‐phonicpickup)
• Avoidsecondaryelectronsfrombeingmeasured
€
Vn ≈ 4kbTfhighR -> µA range lower limit
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BCMTes4ngFixture
USPAS09atUNM AcceleratorandBeamDiagnos4cs
ImagebyM.Kesselman
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SNSCurrentTransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs
ImagebyM.Kesselman.
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LHCFastCurrentTransformer
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U.RaichCASFrasca42008BeamDiagnos4cs
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DesignbyBNLforSNS
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COMPONENTSINSIDEHEBTBCMASSEMBLY
USPAS09atUNM AcceleratorandBeamDiagnos4cs
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WallCurrentMonitor• Putaresistoroverthegapandmeasureitsvoltage.
USPAS09atUNM AcceleratorandBeamDiagnos4cs 29
R€
Vgap = Rgap ⋅ Ibeam
NoDCinimagecurrent
Vout
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WallCurrentMonitor
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U.Raich
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WallCurrentMonitor
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Schema4csofawallcurrentmonitoranditsequivalentcircuit[1]
Nowforthedetails:• Ceramicgaptoavoidworkinginvacuum• Distributedresistors(30to100)forbeamposi4onindependency• Ferriteringsforlowfrequencyresponse• Shieldforgroundcurrentsandnoiseprotec4on
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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]
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FaradayCups
TheFaradayCupdestruc4velyinterceptsthebeam• DCcoupled!(WithjustaresistorthesignalisVout=Ibeam*R)• Lowcurrentmeasurementspossiblee.g.,10pA• Problemwithsecondaryelectrons:
- Uselongcuporvoltagesuppressionormagne4cfield• Ifnotproperlyterminated‐>veryhighvoltage(beampoten4al)• Mustprocessbeampower(SNSfullpower1.4MW)
USPAS09atUNM AcceleratorandBeamDiagnos4cs
[1]
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FaradayCups
USPAS09atUNM AcceleratorandBeamDiagnos4cs
LowpowerFaradayCup[1] Highpower(1MW)FaradayCup[1]
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NoiseIssues
USPAS09atUNM AcceleratorandBeamDiagnos4cs
Noisecanbeaproblem!• TherearemanypowerfulnoisesourcesinAccelerators:
- Switchingpowersupplies- Accelera4ngRF- SourceRF
Caseinpoint:- SNSDTLBCM‐>singleendedandinsideacavity(duetospacelimita4ons)
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36
NoiseIssues
USPAS09atUNM AcceleratorandBeamDiagnos4cs
NoiseofDTLcurrenttransformer(insidecavity,singleended)
NoisefromRF
Noisefromswitchingpowersupplies
Beam
Grounded
[8]
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NoiseIssues
USPAS09atUNM AcceleratorandBeamDiagnos4cs
Beam
SCLBeamCurrentMonitor(singleended)
[8]
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38
NoiseIssues
USPAS09atUNM AcceleratorandBeamDiagnos4cs
Beeer:CCLBCMoutsideofcavitybuts4llsingleended.
CCLBeamCurrentMonitor(singleended)
Beam
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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
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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”