1. Nov. 17, 2005Fermi Lab AP Seminar AC Dipole Based Diagnostics Mei Bai, C-A Department

2. Fermi Lab AP Seminar Nov. 17, 2005 Outline Introduction of ac dipole AC dipole based beam diagnostics  beam dynamics  spin manipulation RHIC AC dipole system Summary

3. Fermi Lab AP Seminar Nov. 17, 2005 Abstract after a short introduction of the system. In recent years, there has been growing interests in developing non-destructive beam diagnostic tools for high energy accelerators. AC dipole as a tool to adiabatically excite large amplitude coherent betatron oscillations without emittance blowup is very useful in exploring the beam dynamics. This technique was first tested in the Brookhaven AGS with Au beam. It was then used in the AGS polarized proton operation to overcome strong intrinsic spin resonances by inducing a full spin flip. Two AC dipoles were also installed in RHIC for linear optics measurement as well as non-linear resonance driving term measurement. The vertical ac dipole in RHIC can also be resonated close to half of the revolution frequency for spin manipulations. This talk will overview the ac dipole applications

4. Fermi Lab AP Seminar Nov. 17, 2005 Introduction of ac dipole Beam becomes unstable if  m = z 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 adiabatically ramping up the ac dipole strength, this driven oscillation is well under control and prevent the beam size from being blown up

5. Fermi Lab AP Seminar Nov. 17, 2005 Ac dipole amplitude ramps up in 1000 turns and then kept constant for 1000 turns. The ac dipole amplitude then ramps down to zero in another 1000 turns. 1000 particles in Gaussian before and after the ac dipole excitation. The blue dots are the beam distribution in the rotating frame when the ac dipole amplitude is constant. Dipole field strength Time Introduction of ac dipole Beam emittance gets preserved before and after the excitation as long as the ac dipole excitation is turned on adiabatically

6. Fermi Lab AP Seminar Nov. 17, 2005 First test results of ac dipole driven oscillation Ac dipole in the Brookhaven AGS. The ac dipole was first ramped up its maximum amplitude in 1000 turns. The amplitude was then kept constant for another 1000 turns and the ac dipole oscillation amplitude was ramped to zero in the final 1000 turns Experimental results in the Brookhaven AGS Before excitation after excitation Measured rms beam size [mm]

7. Fermi Lab AP Seminar Nov. 17, 2005 Ac dipole driven coherent oscillation with non-zero detuning

8. Fermi Lab AP Seminar Nov. 17, 2005 Applications of AC dipole Linear optics measurement  Measure beta function and phase advance  Measure beta function at interaction point  Linear coupling measurement Local coupling measurement Non-linear driving term measurement Dynamic aperture measurement Spin manipulation

9. Fermi Lab AP Seminar Nov. 17, 2005 Beam diagnostic applications using AC dipole Linear optics measurement  Measure beta functions as well as phase advances Beta function and phase advance ring wide Beta function at interaction point

10. Fermi Lab AP Seminar Nov. 17, 2005 Beam diagnostic applications using AC dipole Linear optics measurement BPM 1 BPM 2BPM 3

11. Fermi Lab AP Seminar Nov. 17, 2005 Measured phase advance between bpms Measured beta functions between bpms Beta function and phase advance measurement in RHIC

12. Fermi Lab AP Seminar Nov. 17, 2005 Measure beta function at interaction point Dx(L) Dx(R) (  L,  L,  L ) (  R,  R,  R ) Length S*

13. Fermi Lab AP Seminar Nov. 17, 2005 First test at the end of IP2 Beta Squeeze experiment Fulvia, Todd Nikolay, Steve Mei

14. Fermi Lab AP Seminar Nov. 17, 2005 IP24681012 Data 11.953574.858380.896821.013642.531815.85059 Data 21.835124.862530.886350.997432.524095.862 Data 31.863034.85470.873480.990462.514535.87384 Data 41.886024.856480.874071.002042.536286.11184 Average 1.884 ±0.051 4.858 ±0.0034 0.883 ±0.011 1.000 ±0.0097 2.527 ±0.0095 5.924 ±0.125 design2.05.00.85 3.05.0 First test at the end of IP2 Beta Squeeze experiment

15. Fermi Lab AP Seminar Nov. 17, 2005 Linear coupling measurement Beam diagnostic applications using AC dipole Skew quadrupole strength y amp /x amp x amp /y amp

16. Fermi Lab AP Seminar Nov. 17, 2005 Courtesy of Rama Coupling matrix C changes along the ring and it can be shown that the determinant of C jumps at a coupling source. One turn transfer matrix T Beam diagnostic applications using AC dipole Local coupling measurement

17. Fermi Lab AP Seminar Nov. 17, 2005 Courtesy of Rama Beam diagnostic applications using AC dipole Local coupling measurement

18. Fermi Lab AP Seminar Nov. 17, 2005 Courtesy of Rama Beam diagnostic applications using AC dipole Local coupling measurement  Data taken at injection in Yellow ring  The average coupling strength over the ring varied with different local skew quad settings  The quality of the data is compromised due to the bpm problems  the continuous linear increase of coupling strength in the middle of arc is against the expectation that the local coupling in RHIC mainly comes from the triplets

19. Fermi Lab AP Seminar Nov. 17, 2005  Normal form with free 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)  Beam diagnostic applications using AC dipole Measure non-linear resonance driving term

20. Fermi Lab AP Seminar Nov. 17, 2005 Non-linear driving term measurement in RHIC First 3 rd order resonance driving term measurement in RHIC with ac dipole Rogelio, Wolfram Rama, Mei, …

21. Fermi Lab AP Seminar Nov. 17, 2005 Dynamic aperture measurement  Limitation of the traditional DA technique is the tune meter kicker strength at store  With ac dipole, the idea is to drive the beam with a well controlled ramping strength and record the beam oscillation amplitude. In principle, the amplitude of the coherent oscillation saturates when the DA is reached.  One can also extract the frequency spectrum as a function of oscillation amplitude from the million turn bpm data Beam diagnostic applications using AC dipole

22. Fermi Lab AP Seminar Nov. 17, 2005 Spin manipulation – measure spin tune How to use spin flipper to measure spin tune?  Spin motion nearby a spin depolarization resonance  Induce a coherent spin precession with spin flipper. Measure the turn by turn spin precession. Calculate the precession amplitude of the vertical and radial component. Currently, we are focusing on analyzing the RHIC pp 2004 spin flipping data y x z beam direction

23. Fermi Lab AP Seminar Nov. 17, 2005 Spin manipulation -- Spin flipping spin flipping efficiency in Blue is 66% yellow got depolarized possibly because yellow spin tune is too close to the spin flipper tune

24. Fermi Lab AP Seminar Nov. 17, 2005 RHIC AC dipole system Magnet  Air core with Litz wire  Ceramic beam pipe with an dimension of  Two aluminum strips outside the beampipe provide a path for image current Location

25. Fermi Lab AP Seminar Nov. 17, 2005 RHIC AC dipole system Inductance of the magnet:  In parellel: 26.362 uH  In series: 104.32 uH Current achieved  In series: 50 Amp ~ 67 Gm  In parallel: 160 Amp ~ 106 Gm This corresponds to a 1.4  coherence at RHIC store energy The bottom figure shows the vertical 1024 turn by turn beam position data in the middle of the arc. The black solid circles are the measured turn-by-turn beam position data and the red open circles are the fitted turn-by- turn data. The top plot is the phase plot at the same location.

26. Fermi Lab AP Seminar Nov. 17, 2005 RHIC AC dipole circuit

27. Fermi Lab AP Seminar Nov. 17, 2005 Experience from RHIC AC dipole based beam experiments Reliable turn by turn data from BPMs are very critical Sharing magnets between Blue and Yellow makes it very difficult on using ac dipole independently in the two rings The strength of the spin flipper is kind of marginal, esp. for the spin tune measurement. The current RHIC ac dipole only provides a resonance strength of a few units of 10 -4

28. Fermi Lab AP Seminar Nov. 17, 2005 Summary AC dipole has been demonstrated to be a powerful tool to induce long lasting coherent oscillations. Large coherent oscillations are often needed for measuring the machine optics parameters as well as for studying the non-linear behavior of the beam. This technique has been routinely applied in the Brookhaven RHIC to measure the phase advances as well beta functions. It has also been demonstrated in RHIC to use ac dipole to measure the non-linear resonance driving terms.