Measurement of global and local resonance terms

Recently, resonance driving terms were successfully measured in the CERN SPS and the BNL RHIC from the Fourier spectrum of beam position monitor (BPM) data. Based on these measurements a new analysis has been derived to extract truly local observables from BPM data. These local observables are called local resonance terms since they share some similarities with the global resonance terms. In this paper we derive these local terms analytically and present experimental measurements of sextupolar global and local resonance terms in RHIC. Nondestructive measurements of these terms using ac dipoles are also presented.

Figure 1

Segment of an accelerator lattice. BPMs and multipoles are shown with their relevant Twiss parameters.

Figure 2

Amplitude of the spectral line with frequency $-2{\nu }_x$ [line $(-2,0)$] from the Fourier spectrum of $\chi (N)$ versus $\sqrt{2I_x}$.

Figure 3

Measurement of $|{\chi }_{3000}|$ from kick data. The top plot shows the beta beating. The middle plot shows $|{\chi }_{3000}|$ around the ring with a comparison to the model. The bottom plot shows the sextupolar components of the ring.

Figure 4

Measurement of $|f_{3000}^{\prime }|$ with an ac dipole. The bottom plot shows the sextupolar components of the ring.

Figure 5

Measurement of $|{\chi }_{3000}|$ with an ac dipole. The bottom plot shows the sextupolar components of the ring.