1. AC dipole for LHC Mei Bai Collider Accelerator Department Brookhaven National Laboratory

2. LARP, 2005 What’s ac dipole and its technique for beam diagnostic AC dipole: a dipole magnet with oscillating field. AC dipole: a dipole magnet with oscillating field. By driving the ac dipole at a frequency at the vicinity of beam betatron frequency, a coherent oscillation can be excited. The size of this excited coherent oscillation is proportional to the strength of the ac dipole. The closer the ac dipole frequency to the beam betatron frequency, the stronger the driven coherent oscillation By driving the ac dipole at a frequency at the vicinity of beam betatron frequency, a coherent oscillation can be excited. The size of this excited coherent oscillation is proportional to the strength of the ac dipole. The closer the ac dipole frequency to the beam betatron frequency, the stronger the driven coherent oscillationThe closer the ac dipole frequency to the beam betatron frequency, the stronger the driven coherent oscillationThe closer the ac dipole frequency to the beam betatron frequency, the stronger the driven coherent oscillation The technique of using an ac dipole to achieve a long lasting coherent oscillation in the hardon machine was first developed in the Brookhaven AGS. The technique was also tested the CERN SPS using a transverse damper The technique of using an ac dipole to achieve a long lasting coherent oscillation in the hardon machine was first developed in the Brookhaven AGS. The technique was also tested the CERN SPS using a transverse damper coherent oscillation coherent oscillation The Brookhaven AGS beam experiment also demonstrated the beam emittance can be restored if the excitation of ac dipole gets ramped up/down adiabatically. The Brookhaven AGS beam experiment also demonstrated the beam emittance can be restored if the excitation of ac dipole gets ramped up/down adiabatically.beam emittance can be restored beam emittance can be restored

3. LARP, 2005 AC dipole applications: Linear Optics measurement BPM 1 BPM 2BPM 3 Use the coherent oscillation driven by an ac dipole to measure the betatron functions and phase advances between bpms Use the coherent oscillation driven by an ac dipole to measure the betatron functions and phase advances between bpms

4. LARP, 2005 AC dipole applications: Linear Optics measurement Measured phase advances Measured betatron functions

5. LARP, 2005 Driven coherent oscillation with non-zero coupling Driven coherent oscillation with non-zero coupling AC dipole applications: Linear coupling measurement Driven oscillation amplitude with horizontal ac dipole x amp

6. LARP, 2005 AC dipole applications: Linear coupling measurement The measured ratio of amplitudes for horizontal (top) and vertical (bottom) AC dipole excitation with different skew quadrupole settings. Skew quadrupole strength y amp /x amp x amp /y amp

7. LARP, 2005 AC dipole applications: Non-linear resonance measurement Non-linear resonance driving term Non-linear resonance driving term Normal form with free oscillation Normal form with free oscillation Normal form with driven coherent oscillation Normal form with driven coherent oscillation Non-linear resonance driving term Normal form of particle motion under the influence of an ac dipole, R. Tomas, Phys. Review ST-AB, Vol. 5, 054001 R. Bartolini and F. Schmidt, LHC Project Note 132, 1998 Spectral line @ (1-j+k, m-l)resonance @ (j-k, l-m) 

8. LARP, 2005 AC dipole applications: Non-linear resonance measurement First 3 rd order resonance driving term measurement in RHIC with ac dipole Courtesy of R. Tomas

9. LARP, 2005 Why AC dipole for LHC Critical to measure Critical to measure Linear optics measurement including beta* measurement Linear optics measurement including beta* measurement Non-linearity could be a concern for high energy collider’s luminosity and being able to measure the non-linear resonance will be critical Non-linearity could be a concern for high energy collider’s luminosity and being able to measure the non-linear resonance will be critical Other transverse beam parameters Other transverse beam parameters Disadvantage of using transverse kicker Disadvantage of using transverse kicker Long lasting coherence is critical for the transverse measurements. However, it is hard to maintain coherent oscillation induced by a kicker due to the tune spread Long lasting coherence is critical for the transverse measurements. However, it is hard to maintain coherent oscillation induced by a kicker due to the tune spread The budget for emittance growth in LHC is rather limited The budget for emittance growth in LHC is rather limited Large amplitude coherence is desired for measuring the non- linearity. However, to kick the beam to high amplitude may require a very strong kicker Large amplitude coherence is desired for measuring the non- linearity. However, to kick the beam to high amplitude may require a very strong kicker The ac dipole technique has been tested in SPS using the SPS transverse damper The ac dipole technique has been tested in SPS using the SPS transverse damper

10. LARP, 2005 Summery AC dipole has demonstrated to be a powerful tool to induce long lasting coherent oscillation which is necessary for measuring the machine optics parameters as well as studying the non-linear behavior of the beam. It has been routinely applied in the Brookhaven RHIC to measure the phase advances as well as betatron functions. AC dipole has demonstrated to be a powerful tool to induce long lasting coherent oscillation which is necessary for measuring the machine optics parameters as well as studying the non-linear behavior of the beam. It has been routinely applied in the Brookhaven RHIC to measure the phase advances as well as betatron functions.

11. LARP, 2005 Active non-destructive technique: AC dipole Amplitude of driven coherent oscillation in a linear machine Amplitude of driven coherent oscillation in a linear machine O. Berrig, W. Hoflem, R. Jones, J. Koopman, J-P. Koutchouk, F. Schmidt, SL-Note-00-062 MD, Nov. 2003 M. Bai et al., Physical Review E. Vol 5, (1997) Beam becomes unstable if  m = z

12. LARP, 2005 Active non-destructive technique: AC dipole Driven coherent oscillation with non-linear detuning Driven coherent oscillation with non-linear detuning

13. LARP, 2005 Active non-destructive techniques: AC dipole Adiabatic excitation allows the particles in the beam to follow the external driving force so that the beam distribution gets restored after the excitation. Adiabatic excitation allows the particles in the beam to follow the external driving force so that the beam distribution gets restored after the excitation. Dipole field strength Time

14. LARP, 2005 Active non-destructive technique: AC dipole Ac dipole driven coherent oscillation in the Brookhaven AGS Ac dipole driven coherent oscillation in the Brookhaven AGS

15. LARP, 2005 Active non-destructive techniques: AC dipole Beam size measurement results of the beam experiment with ac dipole in the Brookhaven AGS Beam size measurement results of the beam experiment with ac dipole in the Brookhaven AGS Experimental results in the Brookhaven AGS Before excitation after excitation Measured rms beam size [mm]