Varying Sextupole Strength

As stated above, the first derivative corresponds to the sextupole terms and so the first approach is to reduce the sextupole magnet strength in order to reduce the slope of the parabola until data and theoretical values match. If applicable this procedure can be used to obtain new and more precise values of the sextupole strength. Figure 8 shows a comparison between the original 100% strength and the reduced 90% strength sextupoles. One sees clearly that the slope of the parabola is reduced. Unfortunately this reduction is not sufficient to match theoretical hypothesis with our data (see figure 9). Another attempt to match both is presented in figure 10: After reducing sextupole strength by 50% (!) we achieve a satisfactory match in the region of zero perturbation; but nevertheless, further away from this point the slopes are very different. Even taking into account that magnetic field measurement is not completely precise, it has a higher confidence level than the 50% sextupole strength error would allow. Therefore this procedure of finding a new value for the sextupole strength has to be given up in favor of finding the error in the calibration factor.

Figure 8: Comparison (theoretical prediction) between the original and reduced sextupole strengths.

Figure 9: Comparison between the theoretical (90% reduced sextupoles) and measured tune-shifts.

Figure 10: Comparison between the theoretical (50% reduced sextupoles) and the measured tune-shifts.