Controlling%20Helicity-Correlated%20Asymmetries%20in%20a%20Polarized%20Electron%20Beam

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Controlling Helicity-Correlated Asymmetries in a
Polarized Electron Beam
Kent Paschke University of Massachusetts, Amherst
Some slides adapted from G. Cates, PAVI 04
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World Data near Q2 0.1 GeV2
3 /- 2.3 of proton magnetic moment 0.2 /-
0.5 of proton electric FF 20 /- 15 of
isoscaler magnetic FF
Caution the combined fit is approximate.
Correlated errors and assumptions not taken into
account
HAPPEX-only fit suggests something even
smaller GMs 0.12 /- 0.24 GEs -0.002 /-
0.017
Preliminary
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Precision goals for PVeS experiments
JLAB Generation 1 2 3 4

• HAPPEX dA 1 ppm
• A4 dA 300 ppb
• G0 dA 300 ppb
• HAPPEX-II He dA 250 ppb
• HAPPEX-II H dA 100 ppb
• SLAC E158 dA 15 ppb
• PREx dA 15 ppb
• QWeak dA 5 ppb
• Moller at 12GeV (e2e)

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Helicity-Correlated Beam Asymmetries

• Helicity-correlated intensity (charge)
  asymmetries
• Helicity-correlated position differences
• This is what has been considered for 2nd
  generation (precision goals at the 10-7 level)
• See G.D. Cates, PAVI 04 presentation.
• Helicity-correlated beam spot size asymmetries,
  x/x correlations in general, higher-order
  helicity-correlated effects
• If detector is sufficiently symmetric,
  higher-order effects will be dominant!
• One needs to be careful to focus on the largest
  problems and develop systems for measuring,
  removing, and/or estimating corrections for
  higher order helicity-correlated beam parameters.
  (Not in this talk.)

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The Polarized e- Source
Optical Pumping
of strained GaAs cathode produces
highly-polarized e- beam.
HV Extraction and Injection
Preparation of Circularly-polarized light
Pockels Cell Rapid Helicity Flip

HC beam asymmetries correspond to differences in
preparation of circularly polarized laser light.
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Feedback is effective as far as that goes
position
charge
Charge and position feedback successful for G0
forward-angle
Figures from K.Nakahara
Helicity-correlated cut laser power to zero
charge asymmetry
Helicity-correlated deflection by a
piezoelectric-controlled mirror
This works, but these are heavy hammers for a
subtle problem. Does nothing to fix higher-order
problems, may even create them. Preferred
strategy configure system with care to minimize
effects. If you do it right, all problems get
small together! If you do your best there, you
can use feedback to go the last mile (or
nanometer).
At least, so you hope.
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Fine Control of Beam Asymmetries in Laser Optics
Recent work Lisa Kaufman, Ryan Snyder, Kent
Paschke, T.B. Humensky, G.D. Cates
Cates et al., NIM A vol. 278, p. 293 (1989) T.B.
Humensky et. al., NIM A 521, 261 (2004) G.D.
Cates, Proceedings from PAVI 04
Close Collaboration with the JLab Electron Gun
Group in analyzing causes and developing solutions
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Various Causes of Helicity-correlated Beam Changes

• Steering effects Pockels cell
• Imperfect circularly polarized light
• Intrinsic birefringence of the Pockels cell
• Other birefringent beamline elements (vacuum
  window)
• Phase gradient in beam before Pockels Cell
• Laser divergence in the Pockels cell
• Quantum Efficiency Anisotropy Gradient
• Beam element/helicity electronics pickup
• Quantum Efficiency Variation (QE holes)
• Cross-talk between different beams cathode
  effects or cross-talk in electron-beam transport

(partial list)
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Piezoelectric Steering

• Signature of steering
• scales with lever arm
• not related to beam polarization
• does cancel on slow reversal

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The simplest consequences of imperfectly
circularly polarized light
Polarization Induced Transport Asymmetry (PITA
effect) creating intensity (charge) asymmetry AQ
Perfect l/4 retardation leads to perfect D.o.C.P.
A common retardation offset over-rotates one
state, under-rotates the other
Right helicity
Left helicity
In the photocathode, there is a preferred axis
Quantum Efficiency is higher for light that is
polarized along that axis
This is the D phase
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Measuring analyzing power
Scanning the Pockels Cell voltage scanning the
retardation phase scanning residual DoLP
Voltage change of 58 Volts, added to both the
and - voltages, would zero the asymmetry.
A rotatable l/2 waveplate downstream of the P.C.
allows arbitrary orientation of DoLP
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Intensity Asymmetry using RHWP
Electron beam intensity asymmetry (ppm)
Rotating waveplate angle
4q term measures analyzing powerDoLP (from
Pockels cell)
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What happens if there are phase gradients across
the laser beam?
A gradient in the phase results in a DoLP
gradient across the beamspot.
Gradient in charge asymmetry creates a beam
profiles with helicity-dependent centroid.
Same effect (Charge asymmetry gradient -gt
position difference) can be created by constant
linear polarization but gradient in Cathode
Analyzing Power
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Evaluating phase gradients and their effects
Optics-table data looking at asymmetries while
translating Pockels cell
Intensity asymmetry is proportional to the phase
D.
Position difference is roughly proportional to
the derivative of the intensity asymmetry.
Spot size difference is roughly proportional to
the derivative of the position difference.
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Position Differences using RHWP
Position differences also follow 2q/4q fit.
Electron beam position difference (micron)
4q term measures analyzing power(gradient in
DoLP) (gradient in analyzing power)DoLP
Rotating waveplate angle
To minimize all effects, keep DoLP small and stay
at small effective analyzing power
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Beam Divergence and Fine Alignment of Cell

• New!
• Off-axis beam mixes index of refraction between
  optic and extraordinary axes
• Divergent beam couples D-phase to divergence
  angle
• Beam divergence couples angle to position,
  resulting in a position-sensitive D-phase

Laser spot centroid difference, after linear
polarizer (maximum analyzing power)
Simultaneous zero position differences for pitch
and yaw angles (same for both waveplate states)
can be found, representing best average alignment
along optic axis.
Higher order when alignment is complete, this
effect will lead to quadrapole breathing mode
of beam spot.
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Strategy for success

• Well chosen Pockels cells and careful alignment
  minimize effects.
• Adjust RHWP to get small analyzing power.
• Not large, but not zero. You want to be able to
  tune DoCP on cathode to counteract vacuum window
  effect
• Adjust voltage to maximize DoCP on cathode
• Use feedback on PC voltage to reduce charge
  asymmetry.
• Pockels cell voltage feedback maximizes circular
  polarization, which is good for both zeroth AND
  higher orders

This technique is robust. lt300 nm position
differences in injector for HAPPEX-H setup, and
for G0 back-angle setup (same algorithm for
optics alignment, different personnel)!
If you still care about the remaining position
differences use position feedback, keeping in
mind you may just be pushing your problem to the
next highest order.
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Beam Position Differences, Helium 2005
unless you decide to add helicity information to
the electron beam after it is generated from the
cathode
HC beam asymmetries correspond to differences in
preparation of circularly polarized laser light.
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Injector Position Differences for 2005 HAPPEX-H
After configuration position differences in
injector had maximum around 200 nanometers
200 nm
-200 nm
Additional suppression from slow reversal and
adiabatic damping
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Adiabatic Damping
Area of beam distribution in the phase space
(emittence) is inversely proportional to momentum.
From 100 keV injection energy to 3 GeV at target,
one expects helicity-correlated position
differences to get smaller
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Taking Advantage of Phase Space Reduction

• Major work invested to controlling beam
  transport as designed (Yu-Chiu Chao)
• Transport matching design (linacs arcs) now
  routine.
• Improvements in the 5MeV injector major step
  forward
• Configuration very stable over 2 months
• Next battle 100 keV injector

Factor between 5-30 observed during HAPPEX-H
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Hydrogen 2005 position differences
5Dx
Dx
micron
micron
Dy
5Dy
micron
micron
4DE/E
Run Averaged Energy -0.25 ppb X Target 1 nm X
Angle 2 nm Y Target 1 nm Y Angle lt1 nm
4ppm

• Degradation of source setup at end of run but
  good adiabatic damping

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What is needed for the future

• The next generation experiments at JLab (QWeak
  and PREx) will increase demand to understand and
  control higher order effects.
• Significant progress has been made by thoroughly
  understanding the origins of the effects.
• Continued empirical work is critical.
• Need to focus on passive suppression, while
  exploring what might be gained through (the right
  kind of) feedback.
• Improvements in beam diagnostics and sensitivity
  measurements will be required. This may involve
  new hardware... and new thinking.

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Backup
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Non-linearity in Beam Corrections
Based on slides by Dave Mack

• Magnitude depends on product of
• Nonlinear response in apparatus,
• and
• Size modulation at frev in beam ltxi 2gt

No significant JLab bounds on ?ltI2gt, ?ltE2gt,
?ltX2gt, ?ltX2gt, ?ltY2gt, or ?ltY2gt.
(Significant means they havent been proven to
be smaller than 1 ppm.)
(also, no significant JLab bounds on the 15
unique ?ltxixjgt.)
How big are these terms? Do these effects cancel
under half-wave plate reversal?
Examples of currently invisible ltxi2gt
Simple breathing . Same ltxgt, ltIgt, Different ltx2gt
Interaction between scraping and intensity
feedback. Same ltxgt, ltIgt, Different ltx2gt
Differential intensity bounce. Same ltxgt,
ltIgt, Different ltI 2gt
Xi
Xi
time
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Phase Trombone

• Goal vary beta phase
• implemented with eight existing quads at the
  beginning of the Hall A arc
• Allows for independent beta fcn phase control in
  horizontal and vertical planes
• Uses
• Allows one to trade off position and angle
  differences (101 scale between size in
  accelerator and senstivity for experiment)
• Periodic phase changes can be used to randomize
  or reverse the
• sign of position differences

• Constraints
• Preserve beam size at the location of the
  Compton polarimeter
• Preserve large dispersion at center of arc
• Preserve ability to independently vary spot size
  at target

horizontal phase advanced by 60o while
vertical stays fixed
Figures from Beck, PAVI04
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PhaseTrombone, Results from First Test in Hall A
Data from 2004 (Bogacz and Paschke)
Phase Trombone Setpoint (??x , ??y) ?x (?m) ?0.3 ?m ?y (?m) ?0.3 ?m ??x(?rad) ?0.01 ?rad ??y (?rad) ?0.02 ?rad
(0o,0o) 2.9 2.0 -0.08 -0.19
(30o,0o) 2.7 1.2 -0.07 -0.22
(-30o,0o) 2.8 3.2 -0.07 -0.16
(30o,30o) 1.0 1.2 -0.12 -0.21

• Promising approach, but not applied in 2005
• Local phase trombone undone by over contraints
  (too few independent quads)
• Linac phase trombone promising, but brief test
  was ambiguous. Diagnositics are probably
  insufficient.
• Electronics pickup made tests uninterpretable

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Polarized beam without PC
Slide from M.Poelker
60 degree optical delay line
steering mirror
atten
l
Fiber-based laser
/2
atten
Fast RF phase shifter
Fast phase shifter moves beam IN/OUT of
slit Downside extract 2x required beam current
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Position differences at the end of H-2005
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Improved measurement of high-frequency beam
parameters
Calculated response of slow beam monitors with
fast raster
What are the implications of such non-linear
response for false asymmetries, or normalization?