1. LEIR IMPEDANCE AND INSTABILITY MEASUREMENTS
N.Biancacci, E.Métral, M.Migliorati, T. Rijoff
Injectors MD days, 24 March 2017
Acknowledgement: H. Bartosik, G. Favia, A. Haushauer, J.Lacroix, M.Paoluzzi, R. Scrivens, L.Teofili, G.Tranquille and SPS/LEIR OP team.

2. Outline Motivation LEIR impedance model
Measurements of transverse impedance
Measurements of transverse coasting beam instability
Conclusions and next steps

3. Outline Motivation LEIR impedance model
Measurements of transverse impedance
Measurements of transverse coasting beam instability
Conclusions and next steps

4. Motivation
Within the LIU project, the LEIR intensity will rise to 8e10 charges/bunch (reached already in 2016).
High intensities are not limited by coherent instabilities at present thanks to the action of the transverse feedback.
Nevertheless a fast transverse instability in coasting beam is observed if we set the transverse feedback off.
How much margin we have?
Questions to be answered with MDs:
Which kind of instability develops w/o damper?
How good is the transverse impedance model?

5. Outline Motivation LEIR impedance model
Measurements of transverse impedance
Measurements of transverse coasting beam instability
Conclusions and next steps

6. LEIR transverse impedance model
Elements considered so far:
Dipoles

7. LEIR transverse impedance model
Elements considered so far:
Dipoles
Quadrupoles

8. LEIR transverse impedance model
Elements considered so far:
Dipoles
Quadrupoles
Kickers

9. LEIR transverse impedance model
Elements considered so far:
Dipoles
Quadrupoles
Kickers
Other elements:
Short Dipole correctors
Stripline Pick ups
Septa
Vacuum tubes ….
septum

10. LEIR transverse impedance model
Elements considered so far:
Dipoles
Quadrupoles
Kickers
Other elements:
Short Dipole correctors
Stripline Pick ups
Septa
Vacuum tubes ….
Under study:
Finemet cavities

11. LEIR transverse impedance model
Elements considered so far:
Dipoles
Quadrupoles
Kickers
Other elements:
Short Dipole correctors
Stripline Pick ups
Septa
Vacuum tubes ….
Under study:
Finemet cavities
Electron cooler

12. LEIR transverse impedance model
Elements considered so far:
Dipoles
Quadrupoles
Kickers
Other elements:
Short Dipole correctors
Stripline Pick ups
Septa
Vacuum tubes ….
Under study:
Finemet cavities
Electron cooler
Segmentation on kickers

13. LEIR transverse impedance model
Elements considered so far:
Dipoles
Quadrupoles
Kickers
Other elements:
Short Dipole correctors
Stripline Pick ups
Septa
Vacuum tubes ….
Under study:
Finemet cavities
Electron cooler
Segmentation on kickers
Total accounted length: 68m (~85% of LEIR)

14. Transverse impedance Quadrupoles Kickers Dipoles Dipoles
Bunch spectrum up to few MHz range
Real part dominated by dipoles and kickers.
Imaginary part dominated by dipoles (60%) and quadrupoles (20%) indirect space charge contribution.
No details on Higher Order Modes (yet…)

15. Outline Motivation LEIR impedance model
Measurements of transverse impedance
Measurements of transverse coasting beam instability
Conclusions and next steps

16. Tune shift (coasting beam)
Measurement procedure:
Coasting beam accumulated (damper on, ecooler on)
Intensity scan: beam scraping through instability with damper off.
Ecooler function unchanged to have reproducible momentum distribution and avoid tune shift due to chromaticity.
Δ 𝑄 𝑦 = −3.3±0.4 ⋅ 10 −4
80%
Δ 𝑄 𝑡ℎ =−2.7⋅ 10 −4

17. Tune shift (bunched beam)
Measured tune shift of peak line density with BBQ
Past result shown (details in M. Migliorati’s LIU-IONS PS Injectors 19/07/2016)
Δ 𝑄 𝑦 = −2.0±0.1 ⋅ 10 −3
80%
Δ 𝑄 𝑡ℎ =−1.6⋅ 10 −3 (scaling with bunching factor from a coasting beam)
On the good path considering the impedance model partially developed…!

18. Outline Motivation LEIR impedance model
Measurements of transverse impedance
Measurements of transverse coasting beam instability
Conclusions and next steps

19. Transverse coasting beam instability
Studied the coasting beam instability occurring w/o damper on the vertical plane
Trace recorded as sequence of sampled windows of TFB pickup 41
Mode at 1.9 MHz develops first.
Beam spectral lines are every 𝑛+ 𝑄 𝑦 𝑓 0 , i.e. n=-8 is unstable with growth rate of 40 s^-1/1e10 charges
1/tau = 40 s^-1

20. Transverse coasting beam instability
Predictions from the impedance model
n=-8
n=-3
n=-3 -> 𝒔 −𝟏
n=-8 -> 0.1 𝒔 −𝟏
The measurement is ~150 times faster than max predicted growth rate (resistive wall)!
Do we have an HOM? Need to determine fr, R and Q:
Resonance frequency fr would be ~1.9 MHz
Shunt impedance R would be proportional to the growth rate
What about the Q factor?

21. Q factor determinatin
Changing the tune, we move the coasting beam line around the HOM frequency: 𝒇 𝒏 = 𝑛+ 𝑄 𝑦 𝑓 0
Max: ~40 𝑠 −1
Min: ~20 𝑠 −1
For 𝑸 𝒚 >𝟎.𝟕𝟓 large error bars due to additional incoherent losses.
Growth rate halved if Δ𝑄=0.05 →Δ𝑓≃50 𝑘𝐻𝑧 →𝑄= 𝑓 𝑟 2Δ𝑓 ≃20

22. HOM equivalent model From the measurements we derive: fr ~1.9 MHz
HOM source? -> developing an HOM LEIR impedance model starting from large and dispersive elements (e-cooler, cavities, segmented kickers, ….)

23. Effect of chromaticity
Coasting beam stabilization can be provided by betatron spread 𝑆 𝑝 with chromaticity: 𝑺 𝒑 = 𝑓 𝑛 + 𝑸′ 𝜂 𝑓 0 𝜂 Δ𝑝 𝑝
Having η<0 at injection, 𝑆 𝑝 passes a minimum for specific values of 𝑛.
Spread assuming Δ𝑝 𝑝 = 1e-3 and injection energy.
1.9 MHz
Theory: unstable only around Q’ ~ 5
Measurement: unstable for Q’ < 7.5
Discrepancy to be further investigated (Q changes with Q’?)

24. Outline Motivation LEIR impedance model
Measurements of transverse impedance
Measurements of transverse coasting beam instability
Conclusions and next steps

25. Conclusions and next steps
The developed LEIR impedance model can explain so far ~80% of the machine observed tune shift both in coasting and bunched beam.
The observed fast vertical instability is not currently predicted by the model and it is ~150 times faster than resistive wall.
HOM equivalent resonator model can be derived with parameters:
fr ~1.9 MHz | R ~28 𝑀Ω 𝑚 | Q ~ 20
From theory the growth rate of the instability is predicted only for Q’ around 5 but it is currently not clear why , for Q’<5 the measurements still show instability.
MD time:
Measurements took place from 23/07/2016 to 16/12/2016:
86 MD slots of 6h (516h requested)
50%: cycle set-up (injection efficiency, e-cooler optimization, …)
20%: script debugging (in view of systematic scans in intensity, tune, chromaticity)
30%: data acquisition
Overall, enough time to learn the machine (and profit from having learnt!)
Next steps:
Offline resonant mode identification.
Confirm (or not) the measured Q’ dependence accounting for Q variations.
Measure Δ𝑝/𝑝 for coasting beam and corresponding growth rate scan.
Measure stability diagram with BTF (hint of additional effects like amplitude detuning and space charge)

26. Thanks for your attention!

27. Appendix

28. Longitudinal impedance model

29. Transverse impedance model

30. Effect of chromaticity
Coasting beam w/o damper w/o cooling
Q’ scan from -10 to 10 units (knob value)
Q’ < -7.5: incoherent losses

31. Effect of chromaticity
Coasting beam w/o damper w/o cooling
Q’ scan from -10 to 10 units (knob value)
1/tau = 40 s^-1
Q’ < -7.5: incoherent losses
-5 < Q’ < 7.5: coherent losses: instability of n = -8 line (1.9 MHz)

32. Effect of chromaticity
Coasting beam w/o damper w/o cooling
Q’ scan from -10 to 10 units (knob value)
Q’ < -7.5: incoherent losses
-5 < Q’ < 7.5: coherent losses: instability of n = -8 line (1.9 MHz)
Q’ > 7.5: n = -8 stabilizes, higher frequency lines unstable (8 to 12 MHz).
Discrepancy with theory -> to be further investigated (Q changes with Q’?)

33. Stability diagrams
Momentum spread translates to Landau damping for each specific line ad we can draw the corresponding stability diagram*.
Q’=3
Q’=5
Q’=8
Stability diagram can currently only explain why we are stabilized above Q’=5.
Landau damping only from momentum spread here
Contribution of amplitude detuning + space charge may lead to important stability diagram modifications.
* Details in e.g. J.L.Laclare, Coasting beam instabilities, 1992 CAS Jyväskylä, CERN 94-01, pp. 349)