Application of independent component analysis to ac dipole based optics measurement and correction at the Relativistic Heavy Ion Collider

Correction of beta-beat is of great importance for performance improvement of high energy accelerators, like the Relativistic Hadron Ion Collider (RHIC). At RHIC, using the independent component analysis method, linear optical functions are extracted from the turn by turn beam position data of the ac dipole driven betatron oscillation. Despite the constraint of a limited number of available quadrupole correctors at RHIC, a global beta-beat correction scheme using a beta-beat response matrix method was developed and experimentally demonstrated. In both rings, a factor of 2 or better reduction of beta-beat was achieved within available beam time. At the same time, a new scheme of using horizontal closed orbit bump at sextupoles to correct beta-beat in the arcs was demonstrated in the Yellow ring of RHIC at beam energy of 255 GeV, and a peak beta-beat of approximately 7% was achieved.

Figure 1

Measured beta-beat with error bars in the horizontal (bottom) and vertical (top) plane for both rings at RHIC. A peak beta-beat of approximately 15% is observed in the horizontal plane for both rings. A 30% vertical peak beta-beat is found in the Blue ring and 60% in the Yellow ring.

Figure 2

Relative changes of quadrupole integrated strength as a function of quadrupole locations in the Blue ring.

Figure 3

Simulated evolution of tunes and rms beta-beat along a ramp-up process of the computed correction for the Blue ring. The measured rms beta-beat with error bars at 100% correction strength is also shown.

Figure 4

Baseline and corrected horizontal (bottom) and vertical (top) beta-beat with error bars for the Blue ring. Horizontal peak beta-beat was corrected from 15% to 8%, while vertical peak beta-beat from 40% to 14%.

Figure 5

Relative changes of quadrupole integrated strength as a function of quadrupole locations in the Yellow ring for the first iteration (hollow bars) and second iteration (solid bars), respectively.

Figure 6

Simulated evolution of tunes and rms beta-beat along a ramp-up process of the computed first iteration of corrections for the Yellow ring. The measured rms beta-beat with error bars at 100% of correction strength is also shown.

Figure 7

Baseline and corrected horizontal beta-beat with error bars for the Yellow ring. The peak beta-beat was reduced from 15% to 12% after the first iteration of correction, and further reduced to 10% after the second iteration.

Figure 8

Baseline and corrected vertical beta-beat with error bars for the Yellow ring. The peak beta-beat was reduced from 60% to 20% after the first iteration of correction, and further reduced to 10% after the second iteration.

Figure 9

Simulated evolution of tunes and rms beta-beat along a ramp-up process of the computed second iteration of corrections for the Yellow ring. The rms measured beta-beat with error bars at 100% of correction strength is also shown.

Figure 10

Baseline and corrected horizontal (bottom) and vertical (top) relative phase-beat with error bars for the Yellow ring. The reduction of relative phase-beat after correction of beta-beat is evident.

Figure 11

Measured and computed horizontal closed orbit for correction of arc beta-beat in the Yellow ring. A maximum excursion of 8.5 mm was observed in the arc between IP6 and IP8.

Figure 12

Horizontal (bottom) and vertical (top) residual beta-beat with and without the horizontal closed orbit bump displayed in Fig. 11 for the Yellow ring. The peak beta-beat was reduced to 7% for both planes with the closed orbit bump.

Figure 13

Estimation of rms errors ${\sigma }_{\beta }/\beta$ and ${\sigma }_{\Delta \psi }$ with various BPM random calibration errors ${\sigma }_{\mathrm{cal}}$. The estimation at each random calibration error ${\sigma }_{\mathrm{cal}}$ is made by repeating the measurement of $\beta$ and $\Delta \psi$ 500 times with random Gaussian calibration errors added to each BPM. The error bars reflect the standard deviations at corresponding noise levels.

Figure 14

Estimation of rms errors ${\sigma }_{\beta }/\beta$ and ${\sigma }_{\Delta \psi }$ with various random noise levels ${\sigma }_{\mathrm{noise}}$. The estimation at each noise level ${\sigma }_{\mathrm{noise}}$ is made by repeating the measurement of $\beta$ and $\Delta \psi$ 500 times with white Gaussian random noises added to each BPM. The error bars reflect the standard deviations at corresponding noise levels.

Figure 15

Histogram of BPM noise levels estimated from a total of 37 turn by turn BPM data. In each set of data there are 68 arc BPMs and 88 other BPMs on average.