1. Source Systematics PITA - type effects The importance of controlling the analyzer-axis –Two Pockels cells –Half-wave plate Position asymmetries –Lensing effects –Phase gradients –Other Feedback, and its limitations Gordon D. Cates, Jr. University of Virginia Parity Workshop - May 10, 2002

2. Polarization Induced Transport Asymmetries (The PITA effect) Polarization ellipses that result from various phases Right helicityLeft helicity How imperfect circular polarization translates into helicity correlated intensity asymmetries

3. PITA curve from strained GaAs cathode A PITA is plotted as a function of , where  was adjusted using the voltages on the Pockels cell. Here, the analyzing power that caused the asymmetry was not the laser transport system, but rather a strained GaAs crystal. PITA curves are routinely used to set feedback parameters in parity experiments.

4. Matching the polarization ellipse’s to the axis of the analyzing power In a Strained GaAs crystal, there is a preferred axis. Quantum Efficiency is higher for light that is polarized along that axis It is desirable to have a means for orienting your ellipses

5. SLAC polarization control setup

6. Ellipses are rotated using the two PC’s The two Pockels cells have their fast axes set at 45  to one another.

7. The “two-dimensional” PITA effect, formulae for A PITA for two Pockels cells Now there is a line in the space spanned by  and  for which A PITA is zero.

8. The line in phase space that minimizes A PITA PITA is suppressed along the line. Circular polarization is only maximized at one point.

9. Simple PITA-type effects cannot be everything If phase alone were the problem (and not phase gradients), position asymmetries would go to zero at the same time.

10. Gradients in the phase  and position asymmetries Linear gradient in  Across laser beam Left helicity, emitted charge vs. position Right helicity, emitted charge vs. position

11. Laser studies of systematics demonstrating sensitivity to gradients of  across Pockels cell Intensity asymmetry vs.position (averaged over photodiode array) Position asymmetry vs. position (sensitive to the gradient of  Intensity asymmetry vs. position (single photodiode element) Spot size asymmetry vs. position (sensitive to the 2nd derivative of 

12. Feedback’s effect on integrated asymmetries (intensity and position) versus time. Envelopes represent the one sigma statistical error for the quantity measured. In the absence of a systematic, this is the error with which one would expect the distribution to be centered on zero. Feedback causes 1/N convergence toward zero.

13. The effect of inserting and rotating a half- wave plate

14. Asymmetries while rotating half-wave plate

15. Systematics beyond the PITA effect

16. What is needed for the future Continued empirical work is critical. Need to focus on passive suppression as well as feedback. The important problems at JLab could be very different than at SLAC, Bates, Mainz, …

17. Removing helicity correlated angle asymmetries using point-to-point focusing Solid squares indicate data taken without lens and point-to-point focusing. Crosses indicate data taken with lens and point-to-point focusing.

18. Helicity correlated position/angle asymmetries from non-phase related sources The data provides a measure of the helicity correlated changes in the angle of the laser beam as a function of the place on the Pockels cell through which the laser passes.

19. Sources of systematics Failure to produce circularly polarized light due to a non- zero “asymmetric phase  ” –Charge asymmetries - the average value of  –Position asymmetries - the gradients of  –Beam size/shape asymmetries - higher moments of  Beam steering due to lensing/prisming effects from the Pockels cell.