PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts 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 Q 2 ~0.1 GeV 2 Caution: the combined fit is approximate. Correlated errors and assumptions not taken into account Preliminary ~3% +/- 2.3% of proton magnetic moment ~0.2 +/- 0.5% of proton electric FF ~20 +/- 15% of isoscaler magnetic FF HAPPEX-only fit suggests something even smaller: G M s = / G E s = /

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts Precision goals for PVeS experiments HAPPEX:  A ~ 1 ppm A4:  A ~ 300 ppb G0:  A ~ 300 ppb HAPPEX-II He:  A ~ 250 ppb HAPPEX-II H:  A ~ 100 ppb SLAC E158:  A ~ 15 ppb PREx:  A ~ 15 ppb QWeak :  A ~ 5 ppb Moller at 12GeV (e2e) JLAB Generation Pb

PAVI ’06 Milos May 20, 2006 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 2 nd generation (precision goals at the 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.)

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts The Polarized e - Source Optical Pumping: HV Extraction and Injection … of strained GaAs cathode produces highly-polarized e - beam. Pockels Cell: Rapid Helicity Flip Preparation of Circularly-polarized light 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 charge position 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. Charge and position feedback successful for G0 forward-angle Figures from K.Nakahara

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts Fine Control of Beam Asymmetries in Laser Optics 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 Recent work: Lisa Kaufman, Ryan Snyder, Kent Paschke, T.B. Humensky, G.D. Cates

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 Piezoelectric Steering The piezoelectric Pockels Cell acts as “active” lens Translation (inches) X position diff. (um) Y position diff. (um) Red, IHWP Out Blue, IHWP IN Signature of steering: scales with lever arm 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 Right helicityLeft helicity Polarization Induced Transport Asymmetry (“PITA” effect) creating intensity (charge) asymmetry A Q Perfect ± /4 retardation leads to perfect D.o.C.P. A common retardation offset over-rotates one state, under-rotates the other This couples to “asymmetric transport” in the optics system to produce an intensity asymmetry. Significant DoLP with small change in DoCP Now L/R states have opposite sign linear components. In the photocathode, there is a preferred axis: Quantum Efficiency is higher for light that is polarized along that axis This is the  phase

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts Measuring analyzing power Voltage change of 58 Volts, added to both the + and - voltages, would zero the asymmetry. A rotatable /2 waveplate downstream of the P.C. allows arbitrary orientation of DoLP A simplified picture: asymmetry=0 corresponds to minimized DoLP at analyzer Perfect DoCP Scanning the Pockels Cell voltage = scanning the retardation phase = scanning residual DoLP Intensity Asymmetry (ppm) Pockels cell voltage  offset (V)

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts maximum analyzing power minimum analyzing power Intensity Asymmetry using RHWP 4  term measures analyzing power*DoLP (from Pockels cell) Electron beam intensity asymmetry (ppm) Rotating waveplate angle

PAVI ’06 Milos May 20, 2006 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. Medium charge asymmetry Large  Medium  Small  Big charge asymmetry Small charge asymmetry Gradient in charge asymmetry creates a beam profiles with helicity- dependent centroid. 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 Intensity asymmetry is proportional to the phase . 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. Optics-table data looking at asymmetries while translating Pockels cell

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts Position Differences using RHWP Electron beam position difference (micron) Rotating waveplate angle 4  term measures: analyzing power*(gradient in DoLP) + (gradient in analyzing power)*DoLP Position differences also follow “2  /4  ” fit. To minimize all effects, keep DoLP small and stay at small effective analyzing power Large DoLP -> large position difference -> Gradient in cathode analyzing power Electron beam position difference (micron) With Large  voltage offset Rotating waveplate angle

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts Beam Divergence and Fine Alignment of Cell Laser spot centroid difference, after linear polarizer (maximum “analyzing power”) Vertical position difference (  m) Yaw Angle (mrad) IHWP OUT IHWP IN 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. New! Off-axis beam mixes index of refraction between optic and extraordinary axes Divergent beam couples  -phase to divergence angle a position-sensitive  -phase Beam divergence couples angle to position, resulting in a position-sensitive  -phase

PAVI ’06 Milos May 20, 2006 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 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. 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)!

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: Helicity signal deflecting the beam through electronics “pickup” Large beam deflections even when Pockels cell is off Helicity signal to driver reversed Helicity signal to driver removed Problem clearly identified as beam steering from electronic cross-talk Tests verify no helicity- correlated electronics noise in Hall DAQ at sub ppb level Large position differences mostly cancel in average over both detectors, cancels well with slow reversal X Angle BPM Raw ALL Asymetry micron ppm AT 3 GeV!

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts Injector Position Differences for 2005 HAPPEX-H Electron beam vertical position difference (micron) Location in Injector After configuration: position differences in injector had maximum around 200 nanometers Additional suppression from slow reversal and adiabatic damping 200 nm -200 nm

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 helicity- correlated position differences to get smaller The critical parameter in position difference isn’t sqrt(emittence) The projection along each axis is sensitive to coupling. If the coupling develops, it is difficult to remove… To take advantage of adiabatic damping, keep machine close to design to minimize undesired correlations. Design transport Bad match to design transport X X’

PAVI ’06 Milos May 20, 2006 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-PZT (Source) Y-PZT (Source) X-BPM (mm)Y-BPM (mm) 1C-Line X-BPM (mm)Y-BPM (mm) 1C-Line without with Factor between 5-30 observed during HAPPEX-H

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts Hydrogen 2005 position differences xxxx  x’  y’ yyyy  micron 4*ppm Degradation of source setup at end of run but good adiabatic damping Run Averaged: Energy: ppb X Target: 1 nm X Angle: 2 nm Y Target : 1 nm Y Angle: <1 nm

PAVI ’06 Milos May 20, 2006 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 Magnitude depends on product of: Nonlinear response in apparatus, and Size modulation at f rev in beam No significant JLab bounds on Δ, Δ, Δ, Δ, Δ, or Δ. (“Significant” means they haven’t been proven to be smaller than 1 ppm.) XiXi XiXi Simple breathing. Same,, Different Interaction between scraping and intensity feedback. Same,, Different time Differential intensity bounce. Same,, Different Based on slides by Dave Mack Examples of currently invisible : How big are these terms? Do these effects cancel under half- wave plate reversal? (also, no significant JLab bounds on the 15 unique Δ.)

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts Phase Trombone 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 60 o while vertical stays fixed Figures from Beck, PAVI’04 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

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts PhaseTrombone, Results from First Test in Hall A 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 (0 o,0 o ) (30 o,0 o ) (-30 o,0 o ) (30 o,30 o ) Data from 2004 (Bogacz and Paschke): 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 Fast RF phase shifter /2 /2 /4 atten steering mirror Fiber-based laser p-polarized s-polarized s and p polarized 60 degree optical delay line Fast phase shifter moves beam IN/OUT of slit; Downside: extract 2x required beam current Slide from M.Poelker

PAVI ’06 Milos May 20, 2006 Kent Paschke – University of Massachusetts 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?