Plan for the next three months

1. Plan for the next three months Shinji Machida ASTeC/STFC/RAL 16 December 2010

2. Main tasks • Acceleration/deceleration needs the following tasks • Phase adjustment of individual cavity (longitudinal). • Orbit correction (transverse). • Attempt at extraction (if possible). • Hopefully all the BPM (42 between QD and QF) will be ready by January 2011.

3. Phase adjustment of individual cavity

4. Possible methods • Without beam • Relative phase between LLRF and monitor port. • With beam • Beam loading signal at monitor port. • Horizontal displacement at BPM. • Synchrotron oscillation amplitude and frequency. • With and without cavity detuning

5. Request and assumption • An issue of “random new angle after a sweep” must be resolved before any beam based measurements.

6. Beam loading signal at monitor port (1) • This is done with multiple turns only. • No need to detune other cavities. • Phase slippage (questioned by Jamison) may not be a problem because cavity is tuned to revolution frequency (and self bunching). • Accuracy is not clear.

7. Beam loading signal at monitor port (2) • Can be improved if we can choose a shot with similar number of turns. • Is it possible to take beam loading signal and BPM signal of the same shot through EPICS?

8. Horizontal displacement at BPM (1) • A beam is deflected by different angle with different momentum. • Dispersion function tells a rough estimate. e.g. 120 kV energy gain at a cavity dispersion function of 60 mm • All the cavity except one has to be detuned.

9. Horizontal displacement at BPM (2) • Betatron oscillation is excited at cavity #4 because of a sudden jump of equilibrium orbit. • Osc. amplitude is ~0.7 mm (full) with 120 kV. cavity #4 Red: +120 kV Green: 0 V Blue: -120 kV

10. Horizontal displacement at BPM (3) • In reality, injection error excites another betatron oscillation at the beginning. • Have to measure small difference. Red: +120 kV Green: 0 V Blue: -120 kV

11. Horizontal displacement at BPM (4) • Multiple passage gives more energy gain and larger displacement. • This is nothing but synchrotron oscillation observed through dispersion function. Red: +120 kV Green: 0 V Blue: -120 kV 0 turns 100 turns

12. Synchrotron oscillation (1) • Assume that all the cavity except one is detuned. • Synchrotron oscillation amplitude depends on the initial phase. Initial phase Red: 270 deg. Green: 340 deg. Blue: 350 deg.

13. Synchrotron oscillation (2) • When vector sum becomes the maximum, it gives the maximum synchrotron oscillation frequency. • No need to detune cavities. • Maximize synchrotron frequency by sweeping individual cavity phase. • Simulation is in progress.

14. Plan for phase adjustment • My preference of “with beam” measurement is the following order. • Beam loading measurement synchronized with BPM signal. • Synchrotron frequency measurement. both do not need detuning • Synchrotron amplitude measurement. • Measurement of displacement at BPM. need detuning

15. Orbit correction

16. Source of COD (1) • Assume the observed COD comes only from misalignment of QD (red) and QF (green). • It needs rather large misalignment. horizontal vertical

17. Source of COD (2) • Vertical corrector is suspicious although a simple model with different integrated gradient was not enough to explain the COD. • Field calculation has been done (Shepherd.) • More detailed simulation including field distribution has not finished yet.

18. Source of COD (3) • QF41 shifted longitudinally by 6.5 mm. • This could be a source although simple hard edge model was not enough to explain the COD. • Field calculation has been done (Giboudot.) • More detailed simulation including field distribution has not been done yet.

19. Correction (1) • Setup a model lattice which has a similar COD in vertical direction. • Use vertical misalignment of 84 quadrupoles. Red cross: observed COD Green: COD reconstructed

20. Correction (2) • Correct COD by SVD using 16 V-corrector. • Decelerate in serpentine channel. Green: before correction Red: after correction COD Tracking results

21. Correction (3) • Identify tune where beam amplitude grows. Green: before correction Red: after correction Red: horizontal tune Greed: vertical tune Tracking results deceleration 7 6 5 Qz=8

22. Correction (4) • Harmonic analysis before and after COD correction with SVD. Green: before correction Red: after correction COD

23. Correction (5) • COD after removing harmonic of 8. Green: all harmonics Red: after removing h=8 COD

24. Correction (6) • Amplitude growth is suppressed after removing h=8. Green: all harmonics Red: after removing h=8 COD Tracking results

25. Correction (7) • Tracking simulation shows eliminating one harmonic component is more effective than reducing orbit deviation on average by SVD. • Eliminating harmonic component of integer part of tune (4 to 11 for vertical) seems to be a way of orbit correction in a linear nonscaling FFAG.

26. Possible explanation • If a lattice has harmonic of n, integer tune of n becomes systematic resonance. • Tune change per periodic unit decreases by a factor of 42/n. For example, with harmonic of n=8, crossing speed becomes one order lower. • With harmonic of n, it is equivalent to have n times smaller ring with n times more turns. • …

27. Plan for orbit correction • Measure COD at several different momenta to identify error source or harmonics of errors at least. • Apply harmonic correction. • If necessary, move some of quadrupole magnets vertically.