Polarization Correlations in the SLC Final Focus

At the SLC, the electron beam polarization (P) is measured by a Compton poharimeter downstream of the Interaction Point. This measurement averages over the entire beam distribution and must be corrected for various correlations to calculate the luminosity (L) weighted polarization. Because the spin rotation in the ARC is energy dependent, off energy particles have lower polarization. These particles may also be poorly focused and contribute less luminosity due to the higher order chromatic optics of the final focus. The small vertical p function at the interaction point also causes an hour-glass -effect, where particles at the head and tail of the bunch have less luminosity. Since there is an energy-z correlation due to the compensation of longitudinal wakefields in the linac, these particles may also have lower polarization. The correlations are: z <---> E (linac), E <---> P (ARC), z <--> L (hour-glass) and E <--> L (chromaticity). The contributions from the z <---> E and z <--> L correlations are discussed.