CNI P-Carbon 500GeV polarization profile simple test

      As Carbon targets in PC polarimeters are very thin, so they can be used to measure the beam polarization profile.

    Usually the beam polarization has a gaussian distribution and the beam intensity also has a gaussian distribution. Under this condition, the average polarization for each fill is not just the average value of all runs in this fill. It should consider the beam intensity.

    So the polarization profile procedure is as follows:

   1, to collect the polarization, beam intensity data at the same target position for each run. eg, fig1. Left is beam intensity vs target position, right is polarization vs target position.

   2, to fit the polarization vs L/L_max plots to get the P_max and R=(sigma_I/sigma_P)^2. eg, fig2. Simple average value eg, fig3.

   3, the average polarization using polarization profile is P=P_max/sqrt(1+R) with considering one direction polarization profile.

   4, compare the polarization profile values with average polarization values to check correction. eg, fig4 which is polarization (%) vs fill using several fills for test and also need QA.

   In attachment are just using blue 1 polarimeters. There are 4 polarimeters in CNI P-Carbon polarimeters.