Controlling Helicity-Correlated
Asymmetries in a Polarized
Electron Beam
Kent Paschke
University of Massachusetts, Amherst
Some slides adapted from
G. Cates, PAVI ‘04
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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
Preliminary
PAVI ’06 Milos May 20, 2006
GEs = -0.002 +/- 0.017
Kent Paschke – University of Massachusetts
Precision goals for PVeS experiments
JLAB
Generation
1
2
• HAPPEX:
dA ~ 1 ppm
•
•
•
•
dA ~ 300 ppb
dA ~ 300 ppb
dA ~ 250 ppb
dA ~ 100 ppb
A4:
G0:
HAPPEX-II He:
HAPPEX-II H:
3
• SLAC E158:
• PREx:
• QWeak :
4
• Moller at 12GeV (e2e)
PAVI ’06 Milos May 20, 2006
208Pb
dA ~ 15 ppb
dA ~ 15 ppb
dA ~ 5 ppb
Kent Paschke – University of Massachusetts
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 helicitycorrelated 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 helicitycorrelated beam parameters. (Not in this talk.)
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
The Polarized e- Source
Optical Pumping:
… of strained GaAs cathode
produces highly-polarized e- beam.
Preparation of
Circularly-polarized light
HV Extraction and Injection
Pockels Cell:
Rapid Helicity Flip
HC beam asymmetries
correspond to differences in
preparation of circularly
polarized laser light*.
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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.
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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)
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
Signature of steering:
• scales with lever arm
Red, IHWP Out
Blue, IHWP IN
Y position diff. (um)
The piezoelectric Pockels
Cell acts as “active” lens
X position diff. (um)
Piezoelectric Steering
Translation (inches)
• not related to beam polarization
• does cancel on slow reversal
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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.
Now L/R states have opposite sign
linear components.
A common retardation offset over-rotates
one state, under-rotates the other
Right helicity
This couples to “asymmetric
transport” in the optics
system to produce an
intensity asymmetry.
Left helicity
Significant DoLP with small change in DoCP
( DoLP)2  1  ( DoCP) 2
This is the D phase
PAVI ’06 Milos May 20, 2006
In the photocathode, there is a preferred axis:
Quantum Efficiency is higher for light that is
Kent
Paschkealong
– University
of Massachusetts
polarized
that axis
Measuring analyzing power
Intensity Asymmetry (ppm)
Perfect
DoCP
Scanning the Pockels Cell voltage
= scanning the retardation phase
= scanning residual DoLP
A simplified picture:
asymmetry=0 corresponds to
minimized DoLP at analyzer
Pockels cell voltage D offset (V)
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
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
Intensity Asymmetry using RHWP
maximum
analyzing
power
Electron beam intensity
asymmetry (ppm)
minimum
analyzing
power
Rotating waveplate angle
PAVI ’06 Milos May 20, 2006
4q term measures
analyzing power*DoLP
(from Pockels cell)
Kent Paschke – University of Massachusetts
What happens if there are phase gradients
across the laser beam?
A gradient in the phase results in a DoLP gradient across the beamspot.
Large D
Medium D
Small D
Big charge
asymmetry
Medium charge
asymmetry
Gradient in charge
asymmetry creates a beam
profiles with helicitydependent centroid.
Small charge
asymmetry
Same effect (Charge asymmetry
gradient -> position difference)
can be created by constant linear
polarization but gradient in
Cathode Analyzing Power
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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.
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
Electron beam position
difference (micron)
Position Differences using RHWP
Position differences also
follow “2q/4q” fit.
4q term measures:
analyzing power*(gradient in DoLP)
Electron beam position
difference (micron)
Rotating waveplate angle
+
(gradient in analyzing power)*DoLP
With Large D voltage offset
Large DoLP -> large position difference
-> Gradient in cathode analyzing power
Rotating waveplate angle
To minimize all effects, keep DoLP small and stay at small effective analyzing power
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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
Vertical position difference (mm)
Laser spot centroid difference, after linear
polarizer (maximum “analyzing power”)
IHWP IN
IHWP OUT
Yaw Angle (mrad)
PAVI ’06 Milos May 20, 2006
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.
Kent Paschke – University of Massachusetts
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. <300 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.
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
Beam Position Differences, Helium 2005
HC beam asymmetries
correspond to differences in
preparation of circularly
polarized laser light*.
*unless you decide to add helicity
information to the electron beam after
it is generated from the cathode
• Problem clearly identified
as beam steering from
electronic cross-talk
X Angle BPM AT 3 GeV!
micron
• Tests verify no helicitycorrelated electronics noise
in Hall DAQ at sub ppb level
• Large position differences
mostly cancel in average over
both detectors, cancels well
with slow reversal
ppm
Raw ALL Asymetry
Helicity signal to
driver reversed
Helicity signal to
driver removed
Problem: Helicity signal deflecting the beam through electronics “pickup”
Kent Paschke – University of Massachusetts
PAVI ’06 Milos May 20, 2006
Large beam deflections even when Pockels cell is off
Injector Position Differences for
2005 HAPPEX-H
After configuration:
Electron beam vertical
position difference (micron)
position differences in injector had maximum around 200 nanometers
200 nm
-200 nm
Location in Injector
Additional suppression from slow reversal and adiabatic damping
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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 helicitycorrelated position
differences to get smaller
3 GeV
 95
335 keV
Design
transport
The critical parameter in position difference
isn’t sqrt(emittence)
The projection along each axis is sensitive to
coupling.
Bad match
to design
transport
X’
If the coupling develops, it is difficult to remove…
To take advantage of adiabatic damping, keep machine
close to design to minimize undesired correlations.
PAVI ’06 Milos May 20, 2006
X
Kent Paschke – University of Massachusetts
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
X-BPM (mm)
Y-BPM (mm)
without
X-PZT
(Source)
1C-Line
1C-Line
with
X-BPM (mm)
Y-PZT
(Source)
PAVI ’06 Milos May 20, 2006
Factor between
5-30 observed
during HAPPEX-H
Y-BPM (mm)
1C-Line
1C-Line
Kent Paschke – University of Massachusetts
Hydrogen 2005 position differences
5*Dx’
micron
micron
Dx
Dy
Run Averaged:
Energy: -0.25 ppb
X Target: 1 nm
X Angle: 2 nm
Y Target : 1 nm • Degradation of source
Y Angle: <1 nm
setup at end of run but
good adiabatic damping
PAVI ’06 Milos May 20, 2006
micron
4*DE/E
4*ppm
micron
5*Dy’
Kent Paschke – University of Massachusetts
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.
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
Backup
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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 <xi 2>
No significant JLab bounds on Δ<I2>, Δ<E2>, Δ<X2>, Δ<X’2>, Δ<Y2>, or Δ<Y’2>.
(“Significant” means they haven’t been proven to be smaller than 1 ppm.)
(also, no significant JLab bounds on the
15 unique Δ<xixj>.)
Examples of currently invisible <xi2>:
Simple breathing .
Same <x>, <I>,
Different <x2>
PAVI ’06 Milos May 20, 2006
Xi
How big are these terms?
Do these effects cancel under halfwave plate reversal?
Interaction between scraping and
intensity feedback.
Differential intensity bounce.
Same <x>, <I>,
Same <x>, <I>,
Different <I 2>
Different <x2>
Xi
Kent Paschke – University of Massachusetts
time
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 (10:1 scale
between size in accelerator and senstivity for experiment)
• Periodic phase changes can be used to randomize or reverse the
sign of position differences
horizontal phase advanced by 60o
while vertical stays fixed
PAVI ’06 Milos May 20, 2006
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
Kent Paschke – University of Massachusetts
Figures from Beck, PAVI’04
PhaseTrombone, Results from First Test in Hall A
Data from 2004 (Bogacz and Paschke):
Phase Trombone
Setpoint (Dqx , Dqy)
Dx (mm)
0.3 mm
Dy (mm)
0.3 mm
Dqx(mrad)
Dqy (mrad)
0.01 mrad 0.02 mrad
(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
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
Polarized beam without PC
Slide from M.Poelker
60 degree
optical delay line
s-polarized
atten
Fiber-based
laser
Fast RF
phase
shifter
steering
mirror
l/2
l/4
atten
p-polarized
l/2
s and p
polarized
Fast phase shifter moves beam IN/OUT of slit;
Downside:
extract
current
Kent Paschke
– University of Massachusetts
PAVI
’06 Milos May
20, 2006 2x required beam
Position differences at the end of H-2005
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts
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?
PAVI ’06 Milos May 20, 2006
Kent Paschke – University of Massachusetts