To study the effects of these asymmetries on our measured detector asymmetries we periodically turn off the charge feedbacks and purposely induce large beam charge asymmetries.  We induce a few different asymmetries and usually take a few runs at each asymmetry.  We use the data from these runs to make Wells plots--plots of measured detector asymmetry vs. beam charge asymmetry.

January/February 2007
In late January and earlier February we took Wells plot data immediately before and immediately after fixing the "RCS problem."  Figure 1 shows Wells plots for the North American octants.  The upper row shows plots from runs before the RCS fix while the lower row shows plots from runs after the RCS fix.  The plots in the left column show points only for detector asymmetries averaged over all North American octants while the plots in the right column show these points for the average asymmetries as well as points for the asymmetries in each octant.  In these plots the octant 1 points are red, octant 3 points are green, octant 5 points are blue, octant 7 points are yellow and the octant-averaged data points are black.


Figure 1:  Wells Plots for North American Octants, January 07


Figure 2 shows Wells plots for the French octants.  Again, the upper plots show data from before the RCS fix and the lower plots show data from after the RCS fix; the left plots show points only for detector asymmetries averaged over all French octants while the plots in the right column show these points for the average asymmetries as well as points for the asymmetries in each octant.  In these plots the octant 2 points are red, octant 4 points are green, octant 6 points are blue, octant 8 points are yellow and the octant-averaged data points are black.


Figure 2:  Wells Plots for French Octants, January 07


We decided to investigate whether there might be any significant non-linear contributions--especially before the RCS fix.  Figure 3 shows three fits each for the North American octant-averaged data, before and after the RCS fix.  The fit in the first plots is a pure linear fit--A_det=p0*A_q.  The fit in the last plots includes a quadratic term--A_det=p0*A_q+p1*A_q².  The fit in the middle plots includes an x^3/2 term, to check for any dependence between linear and quadratic.


Figure 3:  Wells Plot Fits for North American Octants, January 07


These plots show that the linear contribution dominates the Wells plots--both before and after the RCS fix.  The linear coefficient, p0 in all these plots, is of order 10^-1, so that, with a beam charge asymmetry of order 10³, the first term is of order 10².  The x^3/2 coefficient, p1 in the middle plot, is of order 10^-5 so that, with a beam charge asymmetry of order 10³, the second term is of order 10⁰.  The quadratic coefficient, p1 in the last plot, is of order 10^-7 so that, with a beam charge asymmetry of order 10³, the quadratic term is of order 10^-1.  This means that the x^3/2 term contributes only at the 1% level and that the quadratic term contributes only at the 0.1% level.

After the RCS fix the non-linear coefficients are larger--order 10^-4 for the x^3/2 coefficient and order 10^-7 for the quadratic coefficient.  Still, the x^3/2 term is, at most, of order 10¹ and contributes at the 10% level while the quadratic term is of order 10¹ and contributes at the 1% level.

Figure 4 shows three fits each for the French octant-averaged data, before and after the RCS fix--in the same format as figure 3.


Figure 4:  Wells Plot Fits for French Octants, January 07


Again, these plots show that the linear contribution dominates the Wells plots--both before and after the RCS fix.  The coefficients for the French fits are of the same orders as those for the North American fits.  Therefore, before the RCS fix, the x^3/2 term contributes only at the 1% level and the quadratic term contributes only at the 0.1% level.  After the RCS fix the x^3/2 term contributes at the 10% level while the quadratic term contributes at the 1% level.

March 2007
In March we took data for another Wells plot.  Figure 5 shows plots for the North American octants.  The plots in the left column show points only for detector asymmetries averaged over all North American octants while the plots in the right column show these points for the average asymmetries as well as points for the asymmetries in each octant.  In these plots the octant 1 points are red, octant 3 points are green, octant 5 points are blue, octant 7 points are yellow and the octant-averaged data points are black.  We took only one run (instead of three) with each charge asymmetry so the error bars in these plots are much larger than in the plots from January.

Figure 5:  Wells Plots for North American Octants, March 07


Figure 6 shows Wells plots for the French octants.  Again, the left plots show points only for detector asymmetries averaged over all French octants while the plots in the right column show these points for the average asymmetries as well as points for the asymmetries in each octant.  In these plots the octant 2 points are red, octant 4 points are green, octant 6 points are blue, octant 8 points are yellow and the octant-averaged data points are black.


Figure 6:  Wells Plots for French Octants, March 07

Figure 7 shows a linear fit of the North American octant-averaged data--A_det=p0*A_q.

Figure 7:  Wells Plot Fits for North American Octants, March 07

Figure 8 shows a linear fit for the French octant-averaged data--A_det=p0*A_q.

Figure 8:  Wells Plot Fits for French Octants, March 07

Both of these plots show a slope, p0, of order 10^-1--the same order as the linear slope from the January/February Wells plots.  The slope has, however, switched signs.  We believe this may be because we took the March runs with the insertable half wave plate (IHWP) in whereas we took the January/February runs with the IHWP out.