The Control of Helicity Correlated Beam Asymmetries for...

TheControlofHelicityCorrelatedBeamAsymmetriesforParity-Viola9on

Experiments

KentPaschkeUniversityofVirginia

KentPaschkeAPS’16,SaltLakeCity

Parity-Viola9ngElectronScaHering

2

Forelectronssca,eringoffnucleiornucleons:Zcouplingsprovideaccesstodifferentlinearcombina9onof

underlyingquarksubstructure

ForverylowQ2,ore-/e-sca,ering:comparisontoStandardModelcouplingsprovidesaccessto

possibleeffectsfrom“new”physics

HAPPEX,G0,A4,PREX,SoLID

E122,E158,Qweak,MOLLER,P2SoLID

⇥�10�5 � 10�4

⇥Q2

APV =⌅L � ⌅R

⌅L + ⌅R⇥ MZ

M�⇥ GF Q2

4 ⇤ �

�ge

AgTV + ⇥ge

V gTA

⇥

� = |M� + MZ |2


PrecisionofPVeSExperiments

3

-810 -710 -610 -510 -410 -310-1010

-910

-810

-710

-610

-510

-410

100%

10%

1%

0.1%G0

G0

E122

Mainz-Be

MIT-12C

SAMPLE H-I

A4A4

A4

H-IIH-He

E158

H-III

PVDIS-6

PREX-I

PREX-II

CREX

Qweak

SOLID

MOLLER

MESA-P2

MESA-12C

Generation IGeneration IIGeneration IIIGeneration IV

PVA

)PV

(Aδ


BeamAsymmetries=FalseAsymmetries

4

QWeak: 7o, ~100 micron beam spot.

Posi9onDifference

SpotSize

�R =d

d✓

✓d�

d✓

◆

✓0

�x

D

dR

R� (0.5 ppm)

�⇥x

⇥x

IntensityAsymmetry�R =

✓d�

d✓

◆

✓0

�I


FutureRequirementsforHCBA

5

Experiment Beam Energy (GeV)

Beam Current (μA)

Charge Asymmetry

(ppb)

Position Difference

(nm)

Angle Difference

(nrad)

Size Asymmetry

(ppm)

HAPPEX-I 3.3 40 200 12 3 -HAPPEX-2 3.0 55 400 2 1 -

PREX-I 1.1 70 85 4 1 <100Qweak 1.1 180 ~20 3 0.1 <100PREX-II 1.0 70 <500 <2 <0.6 <100

MOLLER 11.0 85 <10 <1 <0.1 <10

achieved

future

HCBAhavenot(yet)provedtobethelimi9ngsystema9cerrorforanymeasurement.Butthedegreeofdifficulty(MOLLER,P2)

goesupinthefuture.


ThePolarizede-SourcePhotoemission

HVExtrac9onandInjec9on

…fromstrainedGaAscathodeproduceshighly-polarizede-beam.

PockelsCell:Allowsrapidhelicityflip

whichiskeytothemeasurements

HCbeamasymmetriesaregeneratedbydifferencesinprepara9onofcircularlypolarizedlaserlight.

Prepara9onofCircularly-polarizedLight

DevelopedandfirstusedforSLACE122

6


� =⇥

2� = �⇥

2

HelicityFlip

7

Toavoidslow-dri9s(calibra<ons,targetdensity,etc),usearapidhelicityfliptomeasuretheasymmetryat5Hz-1kHz

HAPPEX-II±λ/4retarda<onproduces±circular

polariza<on


� =⇥

2� = �⇥

2

HelicityFlip

7

Toavoidslow-dri9s(calibra<ons,targetdensity,etc),usearapidhelicityfliptomeasuretheasymmetryat5Hz-1kHz

HAPPEX-II±λ/4retarda<onproduces±circular

polariza<on

Asy

mmet

ry (pp

m)

Slug

SlowReversal:Inser<ngHalf-waveplateflipsini<allinearpolariza<on,andthefinalcircularpolariza<on


ConsequencesofImperfectCircularPolariza9on

8

Perfect±λ/4retarda<onleadstoperfectD.o.C.P.

ThisiscalledtheΔphase

Acommonretarda<onoffsetcreatestoomuchphase-shi9inonestate,

tooliWleintheother

(theotherdegreeoffreedom,theasymmetricphaseshik,cancelsintheasymmetry)



8




tooliWleintheother


(Historically called “PITA” effect)

SignificantDoLPwithsmallchangeinDoCP

(DoLP)2=1-(DoCP)2

Δphaseleadstoresiduallinearpolariza<on,withtheoppositesignintheL/Rstates

Inthephotocathode,thereisapreferredaxis:QuantumEfficiencyishigherforlightthatis

polarizedalongthataxis

QEanisotropycouplestoresidual“Δ”linearpolariza<ontoproduce

anintensityasymmetryAQ.



8




tooliWleintheother


(Historically called “PITA” effect)

SignificantDoLPwithsmallchangeinDoCP

(DoLP)2=1-(DoCP)2

Δphaseleadstoresiduallinearpolariza<on,withtheoppositesignintheL/Rstates

Inthephotocathode,thereisapreferredaxis:QuantumEfficiencyishigherforlightthatis

polarizedalongthataxis

QEanisotropycouplestoresidual“Δ”linearpolariza<ontoproduce

anintensityasymmetryAQ.

Intensity

Asymmetry(p

pm)

PockelscellvoltageΔoffset(V)

PerfectDoCP

ScanningthePockelsCellvoltage=scanningtheretarda<onphase=scanningresidualDoLP


ConsequencesofPhaseGradients

9

Aspa<algradientinthephaseshi9resultsinarela<velinearpolariza<ongradientacrossthebeamspot.

Gradientinchargeasymmetrycreatesahelicity-dependent

beamprofilecentroid.

Spa<alnon-uniformityinΔphaseshi9alsocreateshighermoments(i.e.spotsizeorshape

asymmetries)

No charge asymmetry

Large Δ

Δ=0

Large -Δ

Big charge asymmetry

Big negative charge asymmetry


6.3 Formalism 123

Pockels Cell Horizontal Translation (mm)-4 -2 0 2 4

Asy

mm

etry

(ppm

)

-12000

-10000

-8000

-6000

-4000

-2000

0


m)

µPo

sitio

n D

iffer

ence

(-0.5

0

0.5

1

1.5


m)

µSp

ot S

ize

Diff

eren

ce (

-0.3

-0.2

-0.1

0

0.1

0.2

Figure 6.3.7: The data acquired by scanning the PC across the face of the beamis presented above, to illustrate the relationship between di↵erent moments of theHC e↵ects. This data was acquired with the LAPD detector oriented vertically, andthe analyzer present in the laser’s path in Figure 6.2.1. The top plot represents thezero-moment e↵ect: helicity-correlated beam asymmetry (HCBA), Aq. The secondplot represents the first-moment e↵ect along x: helicity-correlated (HC) position dif-ference, Dx. The third plot represents the second-moment e↵ect along the same axis:HC beam spot-size and shape di↵erences, Drms. Dx tracks with the first-derivativeof Aq and Drms with the first-derivative of Dx (or equivalently, second-derivative ofAq). Dx (Drms) is zero at the extrema of the Aq (Dx) curve, and the extrema inDx (Drms) correspond to the maximum slopes in the Aq (Dx) curve.

6.3.4 HCBA dependence on PC angular misalignment

The formalism presented so far assumes that the laser light is incident on the PC

parallel to the symmetry axis (optic axis) of PC. However, the laser light is usually

incident at an angle to the PC symmetry axis resulting in phase gradients. In fact,

PockelsCellHorizontalTransla9on(mm)

SpotSize

(micron)Posi9on

Differen

ce(m

icron)ChargeAsym

metry(p

pm)

Phasegradientsandtheireffects

10

Intensityasymmetryispropor9onaltothephaseΔ.

Posi<ondifferenceisroughlypropor9onaltothederiva9veoftheintensityasymmetry.

Spotsizedifferenceisroughlypropor9onaltothederiva9veof

theposi9ondifference.

Op9cs-tabledatalookingatasymmetrieswhiletransla9ngPockelscell(seesmalleffectswithrapid-flipasymmetryDAQ,100%analyzer)

Datafrom:RupeshSilwal,Ph.D.Thesis,2012


Arotatableλ/2waveplatedownstreamoftheP.C.allowsarbitraryorienta<onofresidual

linearpolariza<on

maximumanalyzingpower

minimumanalyzingpower

IntensityAsymmetryusingRHWP

11

A+Bsin(2θ)+Csin(4θ)

sin(2θ)term:imperfec<onsinRHWP

sin(4θ)term:analyzingpower*DoLP

Electron

beamintensity

asym

metry(p

pm)

Rota<ngwaveplateangle


Cathodeproper9esalsomaHerElectron

beamposi<on

diffe

rence(m

icron)


AQandposi<ondifferencesbothfollow“sin(2θ)+sin(4θ)”fit.

LargeDoLP=largeposi<ondifference

->Gradientincathodeanalyzingpower

Electron

beamposi<on

diffe

rence(m

icron)

WithLargeΔvoltageoffset


4θtermmeasures:analyzingpower*(gradientinDoLP)

+(gradientinanalyzingpower)*DoLP

12


Laserspotcentroiddifference,a9erlinearpolarizer(maximum“analyzingpower”)

Ver<calposi<on

differen

ce(μ

m)

YawAngle(mrad)

IHWPOUT

IHWPINSimultaneouszeroposi9ondifferencesforpitchandyawangles(sameforboth

waveplatestates)canbefound,represen9ngbestaveragealignment

alongop9caxis.

•Off-axisbeammixesindexofrefrac<onbetweenop<candextraordinaryaxes

•DivergentbeamcouplesΔ-phaseshi9toangle

•Anglecouplestoposi<onResult:aposi<on-sensi<veΔ-phase

Spatial distribution of Δ phase associated with Pockels cell

Pockels Cell

Untilted.

non-zerosize

differences

Pockels Cell Tilted.

non-zeroposition

differences.

BeamDivergenceandCellAlignment

13

BeamDivergenceandCellAlignment

6.4 Controlling Helicity-Correlated (HC) E↵ects 130

Pockels Cell Rotation (mrad)-8 -6 -4 -2 0 2 4 6 8

Asy

mm

etry

(ppm

)

-80000

-60000

-40000

-20000

0

20000

40000

60000


m)

µPo

sitio

n D

iffer

ence

(

-2

-1

0

1

2


m)

µSp

ot S

ize

Diff

eren

ce (

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

-0

Figure 6.3.10: The Pockels Cell (PC) misalignment in angle relative to the beampropagation direction results in large HC e↵ects, as is evident in these plots. Thesee↵ects are contained in HCBA of Eq. 6.3.25. The plots presented above refer to dataacquired with the PC rotated in the range of ± 8 mrad in the xz-plane about itscenter. These data were acquired with the LAPD detector oriented at 45� to thehorizontal, and with the analyzer present in the laser’s path in a setup similar to thatof Figure 6.2.1. The top plot presents the HCBA as a function of the PC rotationangle. The middle and bottom plots present the HC position di↵erence, and HC spot-size and shape di↵erences measured along one of the PC birefringence axis (which isat 45� from the horizontal) as a function of the PC rotation angle.

respectively. Considering broadly, there are two ways to suppress Aq:

• Use a photocathode with no analyzing power ( ✏T = 0): When HAPPEX-III

and PREX ran, ✏T = 0 was only achievable with a photocathode that yielded

electrons with a substantially reduced beam polarization of ⇠ 35%. The very

SpotSize

(micron)Posi9on

Differen

ce(m

icron)ChargeAsym

metry(p

pm)

PockelsCellTiltAngleScan(mrad)

Spatial distribution of Δ phase associated with Pockels cell

Pockels Cell

Untilted.

non-zerosize

differences

Pockels Cell Tilted.

non-zeroposition

differences.

Higherorder:evenwhenaligned,thiseffectwillleadto“quadrupole”breathingmode

ofbeamspot.

14


SpecializedTechniquesforSourceLaserOp9cs

Strainedvacuumwindowisbirefringent.DoLP=0doesn’tmeanthespa<alvaria<onofLPiszero

15

•Measurephasegradients(1stand2ndmoments)•Enhancedby100%polarizer.•Requireintegra9ngDAQ,segmentedphotodiodes•Characteriza9onofop9cs.Carefulalignment.• Ingeneral,moreproblemsthanknobs

Testsonlasertable

Testsonelectronbeam•Vacuumwindow,cathodeprovidetheirownfeatures•Precisionisharder,3%analyzingpower

NextChallenges:•RapidFlip•BeamHalo•Laserinterference

TakeadvantageofwaystosuppressHCBAinthebeam


Feedback

16

AdjustPC“delta”phasetokeepDoLPminimized

Simplealgorithmdrivesconvergenceofthemean

as1/N

IntensityFeedback

Posi<onFeedback•Laserposi9onfeedbackcouplestotoomanyotherproblems•Magnetsinlow-energyinjector•Unlikeintensityasymmetryfeedback,thistreatssymptomsbutnotcause

Adiaba9cDampingAreaofbeamdistribu<oninthephasespace

(emiWence)isinverselypropor<onaltomomentum.

Forexample:from100keVinjec9onenergyto

3GeVattarget:

Ifbeamop<csdeviatefromdesign,significantcorrela<onscandevelop

1C-Line

before matching

matched


Adiaba9cDamping

18

JLabexperimentshaveseensuppressionfactorsat5-30x


Adiaba9cDamping

18

JLabexperimentshaveseensuppressionfactorsat5-30x

Noteveryexperimenttookthesebenefits(PREX-I,Qweak)

QweakInjector~150nmattarget

SlowHelicityReversals

Effec9venessreliesonflippinghelicitywithoutchangingsystema9ceffect...youneedtherightflipforthespecific

possiblesystema9ceffect

“slow” helicity reversals are an important component of a comprehensive strategy to

control HCBANot all HCBA are measured: spot size/shape, phase

space correlations, halo…

OneExample:IHWPFlipssignofcircularpolariza9on,butalsoofthecathodeanalyzingpowerwithrespecttothePockels

cellvoltagesomostlaserop9csasymmetriesdon’tcancel

SLACE158

InjectorSpinManipula<on

g-2Precession

•Solenoids+2Wienrota9ons•Ideallykeepsenvelopethesame•Robustopera9onessen9al

forhighbeamenergies(11GeV),smallfrac9onalchangeinenergyprovidesπrota9on


SuccessfulControlofPosi9onDifferences

20

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2%#"3*4%&(35#$%1%%&-36"#%789$&%

6"#83-*$'%%

."'85"3%:%;3#%

-3<)$%:%=>;?%3&-6%

!"#$%&$'()*'%+&"#%,-..$/001%

2%#"3*4%&(35#$%1%%&-36"#%789$&%

6"#83-*$'%%

."'85"3%:%;3#%

-3<)$%:%=>;?%3&-6%

Performance during HAPPEX-II proton run

Position differences < 2 nm

Angle differences < 2.5 μRad

• Achieve position differences in 100 KeV injector of ≈50 nm using HAPPEX-II protocols.

• Rely on adiabatic damping reduction of ~100 (half the theoretical maximum).• Should lead to 0.5 nm goal. Be prepared to use feedback (might be

necessary simply because of measurement resolution and random jitter).

Plans for 12 GeV Moller:

Widths dominated by jitter(not measurement resolution).

HAPPEX-II(2005)RunAveraged:

Energy:-0.25ppbXTarget:1nm

XAngle:0.3nradYTarget:2nm

YAngle:<0.3nrad

FastHelicityFlip-RTPWhy are we trying to use RTP?

KD*P Cell

Piezoelectric Ringing � At 2kHz helicity switching,

100μs deadtime

is 20% loss of data

RTP Cell

Observe

� Virtually no ringing (<0.2%)

� Faster transition 12μs

� At 2kHz switching, deadtime reduced by ~10x

MOLLERwillrequire2kHzfliprateKD*PPockelscellcan’tkeepup

Qweakmanaged~70μs=7%dead9me

Why are we trying to use RTP?

KD*P Cell

Piezoelectric Ringing � At 2kHz helicity switching,

100μs deadtime

is 20% loss of data

RTP Cell

Observe

� Virtually no ringing (<0.2%)

� Faster transition 12μs

� At 2kHz switching, deadtime reduced by ~10x

RTPisnotpiezo-electric

transversedesign,newchallengeslongitudinaldesign• EachcrystalisO(1000)waveplate• reflec9on,analyzingpower• uniformity• compensa9ngdesigneliminates“breathingmode”


RTP-newtechnology,newchallenges

22

Commercialcellwasnotsuitable

Mount Redesigned

TestmountofRTPcrystals

• LargephaseshikinS2,notcorrectablewithHVoralignment

• Largergradients(10xoverKD*P)

UsedunmountedRTPcellsforstudies• rela9vealignmentiscrucial• Gradientsreduced(s9lllargerthanKD*P)• Significantanalyzingpowerateachsurface• etalon-unstablepowerandasymmetryDespitechallenges,s<llthe

mostpromisingavenue

Otherop9ons:KerrCell• Largegeometry,notsymmetric• Selffocusing• Ioncontamina9on-volumecharge

HaloAsymmetryQweak:AsymmetryinsmallanglescaWered-beam

monitorsindicatedasymmetryhalo

• canbe>10ppm(requires104suppression)• Correlatedtomaindetector• showntobescaHeredfrombeamline• sensi9vetobeamop9cs,RFphase


AsymmetricHalo

24

AsymmetryvariesacrosseachRFbunch

UpstreamofChopper

DownstreamofChopper

Intensity

Intensity Asymmetry

Asymmetry


SourcesofHalo

25

àHelicity correlated movement of centroid is 1µm.

KurtAulenbacher,studyreportedatPAVI‘06

Onepossiblesource:fringesoflaserspot

Largeenhancementoftheintensityasymmetryispossibleforfringes.Noteasytocontrolinthepolarizedsourceconfigura9on.


Recordofachievements,butnewchallenges

26

Significantprogresshasbeenmadebythoroughlyunderstandingtheoriginsoftheeffects,withnanometerlevelofposi<ondifferencecontrol.

•Rapidhelicityflipwithhigh-precisiontechnology•Robustlimitsonspotsizeasymmetry•Halocrea9on,monitoring

Thenextgenera<onexperiments(MOLLER,P2)willpresentnewchallenges

State-of-the-artissufficientforPREX-IIandCREXgoals


Backup

27

KentPaschkeAPS’16,SaltLakeCity28

ThepiezoelectricPockelsCellactsas“ac9ve”lens

Transla9on(inches)

Xpo

si<o

ndiff.(u

m)

Ypo

si<o

ndiff.(u

m)

Red, IHWP OutBlue, IHWP IN

Signatureofsteering:•scaleswithleverarm•notrelatedtobeampolariza9on•doescancelonslowreversal

HCBAExample:PiezoelectricSteering


BeamPosi9onDifferences,Helium2005

29

HCbeamasymmetriescorrespondtodifferencesinprepara<onofcircularly

polarizedlaserlight*.*unlessyoudecidetoaddhelicityinforma9ontotheelectronbeamakeritisgeneratedfromthe

cathode

Problem:Helicitysignaldeflec<ngthebeamthroughelectronics“pickup”Largebeamdeflec<onsevenwhenPockelscellisoff

Helicitysignaltodriverreversed

Helicitysignaltodriverremoved

•Problemclearlyiden9fiedasbeamsteeringfromelectroniccross-talk

•Testsverifynohelicity-correlatedelectronicsnoiseinHallDAQatsubppblevel

•Largeposi9ondifferencesmostlycancelinaverageoverbothdetectors,cancelswellwithslowreversal

XAngleBPM

micron

RawALLAsymetry

ppm

AT3GeV!


BeamIntensityMonitor

30

9/10/2014' MOLLER'Science'Review' 25'

Random'Beam'FluctuaBons'and'Beamline'InstrumentaBon'Use'Qweak'experience'(@'1'kHz'data'rate)'→'Assess'MOLLER'specifica4ons'(@'2'kHz'data'rate)'for'beam'fluctua4ons/monitoring'

Monitor'type' MOLLER'spec.' Qweak'observed'

Beam'charge' 10'ppm' 65'ppm'

Beam'posi4on' 3'µm' 6'µm'

Beam''property' MOLLER'spec.' Qweak'observed'Intensity' <'1000'ppm' 500'ppm'Energy' <'108'ppm' 6.5'ppm'Posi4on' <'47'µm' 48'µm'Angle' <'4.7'µrad' 1.4'µrad'

Random'beam'fluctua4ons'(“jiver”)'@2'kHz:'''If'12'GeV'machine'is'as'“quiet”'as'6'GeV'machine,'these'will'be'easily'sa4sfied!'

Beamline'monitor'precision'@2'kHz:'''•  Posi4on'nearly'sa4sfied'•  Charge'monitoring'will'require'

further'developments'

JLab:1497MHzresonantcavity

Futurerequiresimprovedprecision

shownhere:“triplet”forx,y,Imonitoring

Tomeetprecisiongoal(randomnoise)10ppmprecisionat2kHz

•IntrinsiccavityS/Nsufficient,requiresimprovedsignalprocessing

•Measuredbycomparingdifferen9almeasurementsbetweentwomonitors

•Poten9alfornoisecommontosignalprocessing-checkvs.independentsignals,derivefromhigh-precisionscaHeringmeasurements


Posi9ondifferences,EndofHAPPEX-2005

31

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