Local transverse coupling impedance measurements in a synchrotron light source from turn-by-turn acquisitions

Transverse beam coupling impedance is a source of beam instabilities that limits the machine performance in circular accelerators. Several beam based techniques have been used to measure the transverse impedance of an accelerator, usually based on the optics distortion produced by the impedance source itself. Beam position monitor turn-by-turn analysis for impedance characterization has been usually employed in large circumference machines, while synchrotron light sources have mainly used slow orbit based techniques. Instead, the work presented in this paper uses for the first time turn-by-turn data at ALBA to advance the measurement technique into the range of the typically small impedance values of modern light sources. We have measured local impedance contributions through the observation of phase advance versus bunch charge using the betatron oscillations excited with a fast dipole kicker. The ALBA beam position monitor system and the precision of the turn-by-turn analysis allowed to characterize the main sources of transverse impedance, in good agreement with the model values, including the impedance of an in-vacuum undulator.

Figure 1

Betatron functions and location of the major transverse impedance sources in the ALBA storage ring. The ring nominal lattice has a fourfold symmetry, where each quadrant is composed by two Chasman-Green cells surrounded by two matching cells. The injection section is between two matching cells where the vertical betatron function reaches higher values.

Figure 2

Turn-by-turn vertical beam position measurements for the standard operation and zero chromaticity lattice. In the standard operation case (upper plot) a fast damping along with the characteristic pulsating amplitude is observed while the zero chromaticity case (lower plot) has an almost purely exponential decay.

Figure 3

Histogram of the vertical tune measured by 120 BPMs for 100 acquisitions. The measurement shows an overall standard deviation of $1.1\times {10}^{-4}$, on the other hand looking at one single acquisition (in red) the spread is strongly reduced presenting a standard deviation of only $2.1\times {10}^{-6}$.

Figure 4

Two different filling patterns used during the measurements. A low charge per bunch filling pattern (top) composed by a train of 45 buckets, each one filled with 0.20 nC each on average. A high charge filling pattern (bottom) composed by only two bunches carrying around 4.4 nC each. Only the first 50 buckets out of the total 448 are shown. The temporal structure of the magnetic kicker field is also shown, displaying a rather flat profile in the region where the bunches are located.

Figure 5

In red, measured change in the focusing kick for different QH01 setpoints. Each measurement is obtained averaging over data sets containing 100 acquisitions each. The error bars represent the standard deviation of the estimated focusing kick due to the acquisition to acquisition fluctuations. In black, the expected kick based on magnetic calibrations.

Figure 6

In red, measured change in the defocusing kick per current unit due to the transverse impedance of the vertical scraper for different gaps with respect to the scraper at nominal position (9.5 mm). Each measurement is obtained averaging over data sets containing 500 acquisitions each. The error bars represent the standard deviation of the estimated focusing kick due to the acquisition to acquisition fluctuations. In black, the predicted values from the impedance computation calculated as kick differences of the considered gap to the nominal scraper gap.

Figure 7

Measured phase beat for each BPM along with the one computed from the nominal machine model including the two measured defocusing kick produced by the beam pipe and the injection section.

Figure 8

In red, the defocusing kick strength per current unit obtained from the fit including the beam pipe and the injection section. Each measurement is obtained averaging over data sets containing 500 acquisitions each. The error bars represent the standard deviation of the estimated focusing kick due to the acquisition to acquisition fluctuations. In black, the predicted value from the impedance computation.

Figure 9

Measured phase beat for each BPM along with the one computed from the high ${\beta }_v$ model including the three measured defocusing kicks produced by the beam pipe, the injection section and the IVU located at the high vertical beta position.

Figure 10

Vertical betatron functions for the nominal and modified ALBA lattices. The average vertical betatron function has been increased from 1.2 m to 6.5 m at the location of one IVU.

Figure 11

In blue the defocusing kick strength per current unit obtained from the fit including the beam pipe, the injection section and the IVU located at the high vertical beta spot. Each measurement is obtained averaging over data sets containing 500 acquisitions each. The error bars represent the standard deviation of the estimated focusing kick due to the acquisition to acquisition fluctuations. In black is the predicted value from the impedance computation while red bars represent the defocusing kick obtained from the previous measurement (Fig. 8) where the nominal lattice was employed.