1 Missing impedance from synchrotron frequency shift s LIU-SPS Beam Dynamics Working Group 04/08/2016A. Lasheen, T. Bohl, E. Shaposhnikova Acknowledgments: BR section, OP team, MD coordinators

2 Missing impedance ? The comparison of simulations and measurements suggest that ImZ/n~2 Ohm is missing from the impedance model… (Space charge in Q26: ImZ/n~ -1.3 Ohm) Other sources of discrepancies are being evaluated (distribution, etc…)

3 Outline Correction of the measurement line transfer functionNew measurements results and analysis in the Q20 optics Estimation of the missing impedance in Q26 and Q20

4 Measurement line transfer functionThe measurement line transfer function (TF) is altering the measured longitudinal profile and is composed of: Longitudinal pick-up Cables and fiber-optic link up to the BA3 Faraday cage The TF was obtained from pulse measurements (deconvolution of a perturbed pulse w.r.t. a reference one) Data > 3GHz is unphysical and may introduce some corrections errors (mainly for bunch length < 1ns, and for the tails distribution) 𝜆 meas = ℱ −1 𝜎 bunch 𝒵 TF

5 Measurement line transfer functionBlue: the original bunch profile => 𝜆= 𝜆 0 1−4 𝑡 𝜏 full Green: the perturbed profile Red: the fitted profile from the perturbed one The perturbation is small, the bunch is slightly lengthened (+ some extra tails)

6 Bunch lengthening from TFThe bunch length is defined as 𝜏 4𝜎 =4 𝜎 RMS (computed from the fitted profile) The bunch lengthening is around ps depending on the input bunch length which corresponds to 5% to 10% lengthening (results are uncertain bellow 1ns due to the TF noisy data above 3GHz)

7 Measurements in Q20 ImZ/n [au] Average Bunch length [ns]Slope b [ 10 −10 Hz] ImZ/n [au] Average Bunch length [ns] Average Bunch length [ns] Measurements done in Q20 with V = 2.6 MV (same acceptance as for Q26 studies A~0.46eVs), after data analysis the actual RF voltage appeared to be V=2.8MV Results are very similar to Q26 after rescaling with: 𝐼𝑚𝑍 𝑛 fit = 𝑏 𝑎 𝜔 0 2 𝜏 3 𝑉 𝑅𝐹 ℎ 6𝑒 2 𝑓 𝑠0 corresponding to V=2.8MV Origin a [Hz] 𝑓 2𝑠 0 𝜏 ≈2 𝑓 𝑠0 1− 𝜔 𝑅𝐹 𝜏 Average Bunch length [ns]

8 Comparison with simulationsQ26 Q20 The data analysis is including the corrections of the TF. Simulations were done by taking each acquisition and using the exact same line density, and generating a mismatched bunch to have the same peak-to- peak bunch length oscillations. Measurements in Q20 and Q26 give very similar results/pattern, except at 1.8 ns (may be more sensitive to the bunch distribution and coherent effects for bigger bunch lengths) In both cases, comparing measurements (black) with simulations (blue) show that some little impedance is missing.

9 Evaluation of the missing impedanceQ26 Q20 Simulations were done by adding a pure inductive impedance and scanning ImZ/n from -0.5 to 2 Ohm. For each bunch length, the necessary ImZ/n to add to have a perfect agreement was estimated. The missing impedance is around Ohm for bunch length <1.4ns, for bunch length > 1.4ns an increasing inductive impedance is missing (resonator at low frequency)

10 Impact of the various impedance sourcesTWC200 TWC800 Kickers ImZ/n [au] Average Bunch length [ns] Average Bunch length [ns] Average Bunch length [ns] Flanges (1.4GHz) Remaining impedances ImZ/n [au] Average Bunch length [ns] Average Bunch length [ns] The influence of each impedance group was tested one by one to better evaluate the frequency dependence of the missing impedance

11 Impact of the various impedance sourcesQ26 – 1 resonator 300MHz Q26 – 1 resonator 400 MHz ImZ/n [au] ImZ/n [au] Average Bunch length [ns] Average Bunch length [ns] A single resonator is used for the simulations and its parameters 𝑓 𝑟 and 𝑅 𝑄 were scanned (the results are independent with Q) To obtain the expected missing impedance pattern, the range of 𝑓 𝑟 is around MHz

12 Adding a single resonatorQ26 Q20 A better agreement can be found by adding to the full impedance model a resonator with 𝑓 𝑟 =350 MHz (±100 MHz) and 𝑅 𝑄 =3 kΩ (±1 kΩ) Q was set to 10

13 Adding a single resonatorThe extra resonator is this small bump Z [Ohm] f [Hz]

14 Possible candidates ? E. Shaposhnikova – LIU-SPS Coordination meeting 03/08/2016 Low freq resonances flanges Beam dump gaps T. Roggen – LIU-SPS Beam Dynamics Working Group meeting 16/04/2015 TWC200 HOM Non conform pumping ports

15 Conclusions In overall, some impedance seem still to be missing.Including the corrections of the measurement line transfer function, around ImZ/n~ Ohm (instead of ImZ/n~2 Ohm without the correction) The measurements uncertainty and the high amount of parameters to control lead to big error bars, making difficult to estimate the missing impedance. Nevertheless, the bunch length dependence of the missing impedance indicates that to reach a better agreement a resonance sitting around in the range of MHz would be required.