20130214 Effect of Ebeam Rotation During Quad Scan

Without coupling correction it is possible and likely that the beam will be coupled coming into the laser-wire focusing magnets. Therefore, the magnets at a slight rotation with respect to the beam would have a skew quadrupole effect on the beam. This would mean that as the strength of QM14FF vertical focusing magnet is changed during a quad scan, the beam will rotate during the quad scan. This is ok for OTR which is an intrinsic measurement, however, the laser-wire is a projected measurement and so the measured size by the laser-wire will be affected by a change in angle of the electron beam. This of course depends on the dimensions of the electron beam. In the current electron beam optics configuration, we have an approximately 1 micron vertical by approximately 200 micron horizontal electron beam. Therefore, only a small angle of the electron beam with respect to the laser-wire will increase the measured vertical size greatly.

The projected vertical sigma was calculated for a range of small angles (+-50mrad) for different aspect ratio electron beams. Here, the horizontal size was kept at 230 microns and the vertical size was varied from 0.5 - 5.0 microns.

The vertical scan is calculated using:

So, if the electron beam were to rotate throughout the quadrupole scan, this shape would be convoluted with the normal parabolic curve expected from the change vertical focussing. However, the laser-wire may not (and in fact probably won't) be at a zero angle with respect to the electron beam at the focus, which would offset this curve from the focussing parabolic. This could account for a measured focus at a different location.

The laser is aligned by eye to the chamber aperture with the chamber and (0,0) before operation. This is however, not exactly where the vertical centre of collisions are found due to alignment imperfections, laser alignment imperfections and different electron beam orbits. However, currently the vertical position of the laser-wire scans is usually within 100 microns of the chamber 0. This would mean at a focal length / distance of 56.6mm, the 100 micron offset would mean the laser was at an angle of 1.7mrad, which is actually non negligible! Although this assumes a rather simple ray approach to the laser propagation which is of course not accurate.

The alignment uncertainty of the laser beam with respect to the chamber aperture is probably about 0.5mm.

To investigate the effect on the quad scan, data was generated assuming a linear variation in angle through the quad scan. The electron beam was given an angle of 0 at a different current from the focus of the quad scan as there is no need for these to be the same in reality and the also, either the laser-wire or the electron beam may have an arbitrary angular offset with respect to the lab. Three couplings were chosen.

A quad scan should give a parabolic dependence on current for the measured size. Two simple parabolas were generated with scalings to give a possible laser-wire quadrupole scan.

For comparison, the projected sigmas for the above quad scans with the three different coupling models were generated.

The cyan curve in the weaker 0.02 um/A2 quad scan is remarkably similar to what we have observed in the laser-wire scans. No coupling measurement or correction was performed on recent shifts so it is likely there is still some residual coupling. It would make sense that there would be some coupling. However, the laser-wire scans do not have the best signal to noise ratio with the recent poor performance of the laser. Additionally, no dispersion measurement or correction was done so the conditions at subsequent scans aren't quite the same and some variation is observed that increases the uncertainty on several fits. Hopefully, these measurements and corrections in combination with more laser energy should provide better or more ideal quad scan results.

The maximum angles used here are about 1.2 degrees which is below the angular resolution of the OTR to confirm this.

It still remains to be found out whether tilts of such angles are of a scale that could occur in the extraction line or if they are far too small in which case, this will have been in jest.