Controlling Helicity-Correlated Asymmetries in a Polarized Electron Beam

1. Controlling Helicity-Correlated Asymmetries in a Polarized Electron Beam Kent Paschke University of Massachusetts, Amherst Some slides adapted from G. Cates, PAVI ‘04 Kent Paschke – University of Massachusetts

2. 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 Kent Paschke – University of Massachusetts

3. 208Pb 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) Kent Paschke – University of Massachusetts

4. 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.) Kent Paschke – University of Massachusetts

5. 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*. Kent Paschke – University of Massachusetts

6. 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. Kent Paschke – University of Massachusetts

7. 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 Kent Paschke – University of Massachusetts

8. 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) Kent Paschke – University of Massachusetts

9. The piezoelectric Pockels Cell acts as “active” lens X position diff. (um) Y position diff. (um) Translation (inches) Red, IHWP Out Blue, IHWP IN Piezoelectric Steering • Signature of steering: • scales with lever arm • not related to beam polarization • does cancel on slow reversal Kent Paschke – University of Massachusetts

10. Now L/R states have opposite sign linear components. This couples to “asymmetric transport” in the optics system to produce an intensity asymmetry. Significant DoLP with small change in DoCP 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 Kent Paschke – University of Massachusetts

11. Perfect DoCP A simplified picture: asymmetry=0 corresponds to minimized DoLP at analyzer Intensity Asymmetry (ppm) Pockels cell voltage D offset (V) 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 Kent Paschke – University of Massachusetts

12. minimum analyzing power maximum analyzing power Intensity Asymmetry using RHWP Electron beam intensity asymmetry (ppm) Rotating waveplate angle 4q term measures analyzing power*DoLP (from Pockels cell) Kent Paschke – University of Massachusetts

13. Big charge asymmetry Large D Medium charge asymmetry Medium D Small charge asymmetry Small D 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 -> position difference) can be created by constant linear polarization but gradient inCathode Analyzing Power Kent Paschke – University of Massachusetts

14. 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. Kent Paschke – University of Massachusetts

15. With Large D voltage offset Large DoLP -> large position difference -> Gradient in cathode analyzing power Electron beam position difference (micron) Rotating waveplate angle 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 Kent Paschke – University of Massachusetts

16. Vertical position difference (mm) IHWP IN IHWP OUT Yaw Angle (mrad) 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. Kent Paschke – University of Massachusetts

17. 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. Kent Paschke – University of Massachusetts

18. 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 AT 3 GeV! X Angle BPM micron Raw ALL Asymetry ppm Problem: Helicity signal deflecting the beam through electronics “pickup” Helicity signal to driver reversed Helicity signal to driver removed Large beam deflections even when Pockels cell is off 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*. Kent Paschke – University of Massachusetts

19. Electron beam vertical position difference (micron) Location in Injector 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 Kent Paschke – University of Massachusetts

20. 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. X 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 Kent Paschke – University of Massachusetts

21. X-BPM (mm) Y-BPM (mm) without X-PZT (Source) 1C-Line 1C-Line with X-BPM (mm) Y-BPM (mm) Y-PZT (Source) 1C-Line 1C-Line 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 Kent Paschke – University of Massachusetts

22. Hydrogen 2005 position differences 5*Dx’ Dx micron micron Dy 5*Dy’ micron micron 4*DE/E Run Averaged: Energy: -0.25 ppb X Target: 1 nm X Angle: 2 nm Y Target : 1 nm Y Angle: <1 nm 4*ppm • Degradation of source setup at end of run but good adiabatic damping Kent Paschke – University of Massachusetts

23. 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. Kent Paschke – University of Massachusetts

24. Backup Kent Paschke – University of Massachusetts

25. Non-linearity in Beam Corrections Based on slides by Dave Mack Magnitude depends on product of: Nonlinear response in apparatus, and Size modulation at frevin 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>.) How big are these terms? Do these effects cancel under half-wave plate reversal? Examples of currently invisible <xi2>: Simple breathing . Same <x>, <I>, Different <x2> Interaction between scraping and intensity feedback. Same <x>, <I>, Different <x2> Differential intensity bounce. Same <x>, <I>, Different <I 2> Kent Paschke – University of Massachusetts Xi Xi time

26. 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 • 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 Kent Paschke – University of Massachusetts Figures from Beck, PAVI’04

27. PhaseTrombone, Results from First Test in Hall A 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 Kent Paschke – University of Massachusetts

28. s-polarized l /4 s and p polarized p-polarized l /2 Polarized beam without PC Slide from M.Poelker 60 degree optical delay line steering mirror atten Fiber-based laser l /2 atten Fast RF phase shifter Fast phase shifter moves beam IN/OUT of slit; Downside: extract 2x required beam current Kent Paschke – University of Massachusetts

29. Position differences at the end of H-2005 Kent Paschke – University of Massachusetts

30. 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? Kent Paschke – University of Massachusetts