20120525 Sig Ey M2 Dependence Data Analysis

• How accurately do we need to know M2?

Horizontal Fitting

• Need accurate horizontal measurement of the electron beam to fix that parameter in the fit.
• Horizontal measurement from the same shift in file 20120522_0258_lws.dat
• Not entirely compete, but reasonable.

• Horizontal Fit Charge Normalised Only:
  

Horizontal Chamber Scan - Charge Normalised Only

Horizontal Chamber Scan - Charge & Laser PD Normalised

• These fits both indicate a horizontal size of around 235um. This is inline with the OTR measurement that was 230 (don't have exact value).

• Use 235um for horizontal size in fits.

Fitting

Use 20120522_0548 as a sample data file. It was taken at QM14FF = -88.26A - the nominal setting in the quad scan at the end of the shift on 20120522. This may not be the smallest scan, but it is suitable for fitting.

• Fix m2, e_x=230um, amplitude, offset, centre, e_y free

• (1) Minuit did not converge on this - 'inversion of matrix fails' - used last values - errors estimated

Plots

Below are some of the plots from the fits that converged.

20120522_0548_lws_xy_fit_plot3.pdf

20120522_0548_lws_xy_fit_plot4.pdf

Sumamry

The M2 directly determines the measured size of the electron beam as they are both of a similar size. Obviously, there are further questions as to the validity of using the M2 model, but in the meantime, it clearly determines our main results. Below, the ratio of the laser size to the quadrature sum as a function of laser size with the electron beam size fixed at 1um is shown.