Spin Flipper Effectiveness: A simple simulation

1. Spin Flipper Effectiveness:A simple simulation Stephen Pate New Mexico State University RSC Meeting 15-May-2009

2. Uncertainties in Double Spin Asymmetries Usual statistical uncertainty; our FOM is essentially the inverse of this number. Systematic uncertainty due to relative luminosity. The quantity dR can be significant if the balance between L++ and L+- is noisy. The biggest source of noise is the bunch-to-bunch intensity variation. The spin flipper makes the systematic term smaller by balancing L++ and L+- in every bunch crossing in every fill. The spin flipper can also make the statistical term larger if it depolarizes the beam or reduces the luminosity. We need to find the right compromise, depending on the actual spin flipper performance. RSC Meeting 15-May-2009

3. Relative Luminosity Asymmetry RSC Meeting 15-May-2009

4. How the simulation works RSC Meeting 15-May-2009

5. How the simulation works RSC Meeting 15-May-2009

6. Accelerator Operation Effects • Fill-to-fill luminosity variations: the accelerator is not filled, and does not operate, the same each fill. => Vary the mean bunch-crossing luminosity from fill to fill, using a +/- 5% Gaussian distribution. • Bunch-to-bunch intensity variations: not every bunch has the same number of protons. => Vary the bunch-crossing luminosity within a fill using a +/- 5% Gaussian distribution. • Even/odd effect: we observe that every other bunch crossing has a different luminosity, in a regular pattern. => Increase the luminosity of “even-numbered” bunch crossing by 1%, reduce that of “odd-numbered” bunch crossings by 1%. RSC Meeting 15-May-2009

7. Spin Flipper Operation Effects • Depolarization => reduce the polarization by 1% (relative) each time the spin is flipped. (i.e. Pafter = 0.99 * Pbefore). • Reduction in luminosity --- not included in simulation yet. RSC Meeting 15-May-2009

8. An example of what the spin flipper can do for you 5% fill-to-fill, 5% bunch-to-bunch, and 1% even/odd variations turned on. No depolarization effect (yet). 100 fills, 40 1/pb. The bunch-to-bunch intensity variations produce significant noise in A_lumi from fill to fill. In this example the Blue beam spin is flipped every ten minutes during each fill. The noise in A_lumi is eliminated; the remaining width is almost purely statistical. RSC Meeting 15-May-2009

9. Effectiveness vs. number of spin flips It seems that flipping just once per hour (about 8 flips) would be sufficient to reduce the systematic uncertainty by a factor of 10. RSC Meeting 15-May-2009

10. 8 Flips in a 9 hour fill (no depolarization effect) Without spin flipper: Alumi = (23 +/-13) x 10-4 With spin flipper: Alumi = (2.8 +/-1.6) x 10-4 RSC Meeting 15-May-2009

11. Effectiveness vs. number of spin flips: Now including 1% depolarization at each flip. Flipping just once per hour (about 8 flips) still ok, but beyond that the FOM is decreased enough to begin to increase the total uncertainty. RSC Meeting 15-May-2009

12. 8 Flips in a 9 hour fill (now with depolarization effect) Without spin flipper: Alumi = (-11 +/-13) x 10-4 With spin flipper: Alumi = (1.3 +/-1.7) x 10-4 RSC Meeting 15-May-2009

13. Summary • Spin Flipper can remove noise in the relative luminosity caused by fill-to-fill, bunch-to-bunch, and even/odd intensity variations. • Not necessary to flip as rapidly as possible; flipping once per hour should be sufficient. • Can tolerate some depolarization. • Still need to investigate the effect of luminosity losses. RSC Meeting 15-May-2009