Using ac dipoles to localize sources of beam coupling impedance

The beam coupling impedance is one of the main sources of beam instabilities and emittance blow up in circular accelerators. A refined machine impedance evaluation is therefore required in order to understand and model intensity dependent effects and instabilities that may limit the machine performance. For this reason, many impedance source localization techniques have been developed. In this work we present the impedance localization technique based on the observation of phase advance versus intensity at the beam position monitors using ac dipoles to force betatron oscillations. We present analytical formulas for the interpretation of measurements together with simulations to benchmark and illustrate the equations. Studies on the method accuracy for different Fourier transform algorithms are presented as well as first exploratory measurements performed in the LHC.

Figure 1

Typical excitation pattern of a driven oscillation at frequency $Q_d$ as simulated in HEADTAIL.

Figure 2

Simulated spectrum of the transverse beam signal on the ac dipole plateau showing driven $Q_d$ and natural $Q_{\text{nat}}$ tunes.

Figure 3

Natural horizontal phase advance beating versus intensity calculated with HEADTAIL simulations of a broadband impedance placed close to the IP7 in the LHC at 20 km. An horizontal kick is used as excitation.

Figure 4

Driven horizontal phase advance beating versus intensity calculated with HEADTAIL simulations of a broadband impedance placed close to the IP7 in the LHC at 20 km. An ac dipole is used as excitation.

Figure 5

Uncertainty in the tune determination with NAFF, FFT and SUSSIX versus number of turns calculated up to $N\simeq {10}^4$ turns considering amplitude Gaussian noise of $\mathrm{NSR}=5\%$. Dots are the simulated data, lines are the fits. SUSSIX and NAFF both implement a hanning window.

Figure 6

Uncertainty in phase advance determination with NAFF, FFT and SUSSIX versus number of turns calculated up to $N\simeq {10}^4$ turns considering amplitude Gaussian noise of $\mathrm{NSR}=5\%$. Dots are the simulated data, lines are the fits.

Figure 7

Scraping of a single bunch during multiturn data acquisition with an ac dipole during the machine fill 3338 on 28-11-2012.

Figure 8

Phase advance slope uncertainty in the LHC machine. Black dots represent the measured uncertainty for $N=2200$ turns and $M=14$ measurements over an intensity scan from $N_b={10}^{11}$ to $N_b=3\times {10}^{11}\mathrm{ppb}$. Red dots represent the predicted uncertainty with Eq. (31). Horizontal lines are the signal amplitudes expected from the horizontal (in blue) and vertical (in black) collimators. The uncertainty line shows the uncertainty attainable over NSR for average measurement parameters.