Correcting the Calibration Constant

The other idea mentioned was to find a new calibration constant which would, on one hand, match the measured data to the theoretical predictions and, on the other hand, give us new understandings of the corrector magnets, i.e. correct values of the properties that lead to the calibration constant (e.g. number of turns of coil, current, dimensions of the vacuum chamber, etc.). The implementation is fairly simple: The measured data is plotted again, but under the assumption that the used calibration factor is not known accurately. Assume that the measured tune-shift is exact and find what kick a certain measured tune-shift corresponds to. This leads to several values for the calibration constant. These different values can then be plotted against each other and if they are close enough the mean value gives you an an idea of the realistic calibration constant. Figure 11 shows the calculated calibration constants with respect to the original constant (which was assumed wrong). The mean value of the calculated values is plotted as well.

Figure 11: Calculated calibration constants corresponding to measured tune-shifts.

Even if one uses the calculated mean value as the calibration constant and compares the predicted theoretical values with the measured and converted values, there is no obvious match (see figure 12). The parabolas meet in the region of zero kick, but their slopes are different as soon as one starts to raise the kick value. Therefore this method of correcting the calibration constant has to be abandoned as well.

Figure 12: Calculated mean calibration constant used to compare experimental data with theoretical predictions.

Up to now, no satisfying explanation for the deviation of experimentally acquired tune-shifts from the theoretically predicted values could be found. The investigation of this question will continue. Unfortunately the calculated values are very far apart from each other which of course lets doubt arise if building the mean really leads to a realistic value. Even worse -- the mean value of the calculated constants lies at a value about five times greater than expected. Even taking into account that inaccuracies occur during measurement of the magnet properties, there is no possibility of the calibration constant being so high. Cross-checks done by other SLS members using various measurement techniques have proven the estimated factor to not be off by a factor of five.