The Measurement of Chromaticity by Head-Tail Phase Shift Analysis

1. The Measurement of Chromaticityby Head-Tail Phase Shift Analysis CARE Workshop on Schottky Measurement and Tune, Coupling & Chromaticity Measurement & Feedback Chamonix 11th - 13th December 2007 Rhodri Jones CERN Beam Instrumentation Group

2. Outline • The Head-Tail measurement principle • The Head-Tail monitor of the SPS (2000) • Improvements & simulations since • Results from the Tevatron • Head-Tail: impedance & higher order terms • Conclusions Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

3. The Head-Tail Principle I • The Principle: • Apply single transverse kick & observe resulting motion • Chromaticity will determine the pattern of this motion • By following the time evolution of any two positions within the bunch a phase-difference is obtained from which the chromaticity can be calculated • Assumptions used in the Theory: • The displacement due to the kick is much larger than the betatron oscillations performed by the particles in the unperturbed bunch • when the kick is applied all particles assumed to have the same initial betatron phase • The synchrotron frequency is the same for all particles in the bunch • assumption holds for measurements are performed close to centre of bunch • The presence of higher order fields such as octupolar fields not taken into consideration Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

4. The Head-Tail Principle II Positive Chromaticity (above transition) Negative Chromaticity (above transition) Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

5. The Head-Tail Principle Response for Zero Chromaticity Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

6. The Head-Tail Principle Response for Non-Zero Chromaticity Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

7. The Head-Tail Principle V Tail Head Time 1 Synchrotron Period Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

8. The Head-Tail Principle V Tail Head Time 1 Synchrotron Period Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

9. The Head-Tail Equation • For g >> gt chromaticity depends only on • Maximum phase shift measured between head and tail • The separation between the head & tail measurements Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

10. CERN-SPS System Set-up Sum Difference Bunch Synchronous Trigger GPIB link Fast (2GS/s per channel) Digital Oscilloscope SPS Tunnel Hybrid Straight Stripline Coupler Beam Pipe Beam VME Acquisition via GPIB UNIX User Interface Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

11. The Initial CERN-SPS Head-Tail Monitor D Signal Coupler too short for bunch length Coupler long enough for bunch length Time Signal and Reflection NOT fully resolved Signal and Reflection fully resolved Reflected Signal Pick-up • Straight stripline coupler - 37cm long • Completely resolves a bunch < 2.5ns in length • NOT the case in the CERN-SPS where bunch length is ~4ns Useable signal ~2.5ns  measure head & centre NOT head & tail Real response Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

12. Measuring Q’ Qs-1 = 97 turns Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

13. Measuring Q’ Qs-1 = 230 turns Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

14. Measuring Q’ Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

15. Measuring Q’’ and Q’’’ Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

16. Improvements and Developments • Added 60cm long coupler • can fully resolve bunches up to 4ns in length • Added low loss cables & reduced cable length • increase in the overall system bandwidth • Performed more complete simulations (Stephane Fartoukh) • originally intended to find source of missing factor • Turned out to be due to hardware bandwidth limitations • Added better cables and introduced deconvolution algorithm to eliminate this factor • developed into a robustness study for the technique • Effect of accelerating buckets • Effect of Q’’ and Q’’’ Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

17. Measuring Q’ (long coupler) Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

18. Understanding the Scaling Factor Factor down from 2.2 to 1.4 From 2000 to 2001 Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

19. Signal Output – Bandwidth Limitations Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

20. Signal Output - Deconvolution Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

21. Effect of Acceleration Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

22. Use of Kicked Head-Tail in the Tevatron • Intensity of 2.5-3x1011 particles per bunch with 3ns bunch rms length (coalesced bunches) • Main instrument for chromaticity measurement on the Tevatron ramp • RF modulation not feasible • change in RF required to resolve the chromaticity causing losses during the ramp • tune moved a lot during snapback & RF frequency modulation too slow to resolve chromaticity Courtesy of Vahid Ranjbar Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

23. Use of Kicked Head-Tail in the Tevatron • Calibration with RF modulation at injection energy • Head-Tail measurements at the start of the ramp Courtesy of Vahid Ranjbar Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

24. Effects of Impedance & Higher Order Terms • Addition of higher order terms • Octupoles induce tune spread • Coherence maintained for much shorter time • Phase difference over 1 synchrotron period more difficult to extract Courtesy of Vahid Ranjbar Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

25. Effects of Impedance & Higher Order Terms • Effect of impedance observed early on in the SPS • Phase shift at low energy depended on single bunch intensity Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

26. Effects of Impedance & Higher Order Terms • Effect of impedance confirmed by data & simulations at FNAL • Results of multi-particle simulation • N=1000 particles with resistive wall wake field 4.4x105cm-1 (Zeff = 7 MWm-1) • The behaviour is almost identical to measured response Courtesy of Vahid Ranjbar Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

27. Effects of Impedance & Higher Order Terms Measured data Courtesy of Vahid Ranjbar • Adding second order chromaticity results in even better fits Fit with impedance Fit with impedance & Q’’ Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007

28. Conclusions Experimental • Operational Head-Tail Q’-Measurement system demonstrated • Used for studies in SPS • limited to use at high energy due to impedance • Used routinely in the Tevatron • Deconvolution required to remove perturbations due to hardware bandwidth limitations (mainly cables) • Useful instrument for other applications • Routinely used in the SPS for transverse instability studies Theoretical • Method applicable for both stationary and accelerating buckets • Experimentally verified with the constraint that the measurement be performed symmetrically about the bunch centre • Data can be used to fit for other machine parameters • Good agreement between simulations and measurements in the Tevatron • Allows estimate of • Resistive wall impedance • Second order chromaticity Rhodri Jones – CERN Beam Instrumentation Group CARE Meeting – Chamonix 2007