Overlap Integral Investigation

Overlap integral fits of recent LW data are good fits to the data and represent the shape well, however, this is only true when the horizontal electron beam size is set to around 10 microns. This is clearly wrong as the electron beam optics predict a size of around 200 microns that is verified by the OTR measurements. Although the horizontal electron beam width can be left as a free parameter to get a reasonable looking fit, this should ideally be fixed to give the most accurate answers for the vertical size of the electron beam. The current fits range from an unrealistic 0.7 microns to a more plausible 2 microns for some scans. The vertical size predicted by the OTR is 1.4 microns or close to it. The uncertainty of the overlap integral fits is typically around 0.3 microns.

Below is a typical vertical scan with the current fitting procedure used.

For this fit, a horizontal sigma of 10 microns was used, which is quite different from the measured 200 microns.

Resolution

This problem was resolved. In the end a misplacement of parenthesis in the calculation of the f_r function using the Rayleigh range caused the modelled laser beam size to increase dramatically from the focus. As the overlap integral is a product of both the laser divergence and the horizontal electron beam size, it is unsurprising that reducing the horizontal electron beam size balanced this mistake and improved the fit.

With the correct use of the horizontal electron beam size, the vertical be more accurately determined.