The angle of the kick can be described by:
where is the number of turns of coil, the current in the coils and is the size of the vacuum chamber. Therefore the kick can be expressed as a linear function of the current:
In a given accelerator where energy and magnet properties are known, this can be reduced to:
This calibration allows comparison of the model with the measured tune-shift resulting from a corrector kick. Figure 5 shows the theoretically resulting tune-shift from various (horizontal) kicks. As expected the dependency is parabolic. Using the above mentioned conversion scheme (from a current in A to a kick in rad on a corrector magnet) one can now look at measured tune-shift vs. kick on a (horizontal) corrector magnet. This is done in figure 6.
Figure 7 shows a comparison between the model and the measured tune-shifts. One can see easily that the curves have the same shape, but a different slope, which is very bothering. The slope, i.e. the first derivative results from the sextupole terms, so an obvious idea would be to change the sextupole strength until the slopes are equal. This is basically an experimental check of the assumed value of sextupole strength. Another idea is to find a new calibration constant (see equation 5) for the conversion in the corrector magnets. It is possible, that due to inaccuracies in magnetic field measurement the original calibration constants were wrong. Both ideas were pursued and the results will be presented in the next two sections.