1. Closing remarks of “Session 3: Impedance measurements and control”
Iaia Masullo & Andrea Passarelli
22/09/2017

2. What should we keep in mind… from 3rd session
A reliable impedance model of the machine to understand the impedance source
Very precise laboratory measurements
Very accurate simulations (2D &3D codes)
It is also important to study the EM behaviour of the coupled system
Separate elements can behave differently when you take into account their coupling (coupled resonators….)
We need lab measurements to validate the simulations
We always need two out of the three
for a very accurate design of the machine !!!!!
Models need constantly to evolve over the years
A reliable impedance model of the machine to understand and find means to mitigate instabilities
Very precise and accurate measurements with the real beam
Very accurate simulations (2D &3D codes)
Many machines requires updates of the design because of new experimental requirements

3. Challenges and pitfalls for impedance measurements in the lab
Impedance measurements in laboratory: some recipes from Andrea Mostacci
Challenges and pitfalls for impedance measurements in the lab
ATTENTION
Distributed impedance: coaxial wire method
Data interpretation formulae
Matching issues
Pitfalls
Some examples:
as LHC collimator
Low impedance devices
Complicated devices
Challenges
High frequency
Small aperture devices
Resonant impedance: bead pull technique
Bead pull methods are not suitable to characterize heavily dumped mode, e.g. with low Q and/or with resonance shift not clearly measurable.
(Alesini et al, PRST , 2004)
RF deflectors

4. 2D and 3D collimator impedance modeling and experimental measurements-Nicolò Biancacci
Example of 2D code : comparison with measurements
Example of 3D code : comparison with measurements

5. HOM Load Power Computations Based on Single-Bunch Wake Simulations
Continuous-Wave
HOM Load Power Computations
Based on Single-Bunch Wake Simulations
Hans-Walter Glock
CST does it 
how much HOM power in the loads ??
BESSY-VSR, bERLinPro operate CW !!
How do we get the multi-bunch port/mode power Ppm (averaged over ΔT) from the single-bunch exited port/mode amplitude Apm ?
Compute for each frequency step j the excitation-scaled, frequency-domain port / mode amplitude:
Ãpm = beam-spectrum / gauss-spectrum ∙ αpm(j)
Ppm(j) = Ãpm(j) ∙ Ã*pm(j) , j = 1... Nmax
BESSY-VSR-Upgrade: W

6. Needs and Solutions for Machine Impedance Reduction- Christine Vollinger
Usual approach is to calculate the contribution of separate machine elements, although in some cases this is insufficient, due to interaction/ coupling of the different elements.
find RF-solutions to mitigate existing beam impedances, and
provide input for macroparticle codes by means of impedance calculation so that beam dynamics simulation can be carried out to predict, e.g., intensity thresholds, etc.
Example: SPS Vacuum Pipe Flanges
Attention not only to impedance requirements but also to other constrains in the realization as costs!!
Example: reworking a machine section

7. Beam measurements of the impedance – Alexandre Lasheen
The frequency characteristics of the impedance can be probed by measuring the effective impedance varying the bunch spectrum (bunch length)
𝑍 1 =−2𝜋 −∞ ∞ 𝑆 𝑓 Im𝑍 𝑓 𝑓 𝑑𝑓
Adding a resonator at 𝑓 𝑟 =350 MHz with 𝑅/𝑄=3 kΩ (Q=1-10), missing impedance source in SPS impedance model?

8. Beam-based impedance measurement techniques in light sources – Ryutaro Nagaoka
Impedance tends to grow larger with narrower vacuum chamber needed to reach ultra-low emittance and to achieve higher ID fields;
High single and multibunch current required for users.
Precise orbit control and bunch-by-bunch feedback, both indispensable for modern LS rings, provide ways to precisely measure the machine impedance and impedance-induced coherent motions.
Example1: Transverse kick factor measurement --Orbit distortion generated by bunch displacement can be measured to quantify () and so (ImZ)eff , Z is generally distributed around
Example2: BPM’s turn-by-turn mode
Using the defocusing behaviour of transverse (inductive) impedance its effective focusing strength Keff can be measured locally using BPM’s turn-by-turn mode
Good agreement achieved with expectations (CST, GdfidL)
Contribution from Elettra, ESRF, SOLEIL, DIAMOND and MAXIV

9. Comparison of machine impedance calculation with beam based measurements – Karl Bane
Can a “bottom-up” approach to a pseudo-Green function wake calculation hope to obtain the broad-band impedance of a modern, complicated storage ring such as KEKB and SuperKEKB (SKEKB)? Or do we need to resort to e.g. a Q= 1 resonator model with the parameters obtained by machine measurements?
Very accurate calculations are required !
Beam phase measurement at KEKB LER
This plot suggests that we can!
For KEK LER ring, the following impedance sources are included:
Geometric wakes
Coherent synchrotron radiation +
Resistive wall
Coherent wiggler radiation
No fitting parameters are used!
Very good agreement.

10. Precise Impedance Determination from Simultaneously Measured Tunes of Unequally Charged Bunches–
Boris Podobedov
A fast and precise technique for measuring the transverse impedance (kick factor) of storage ring element from tune measurements
They measured the difference between the betatron tunes of several individual bunches simultaneously stored in the ring with an accuracy of 10-6 !!!!!!!!
getting kick factors as low as 10 V/pC/m
Simultaneous measurements eliminates harmful effects of machine drifts (virtually) and also other large systematic effects, unrelated to the impedance
REQUIREMENTS: high-resolution BPMs capable of accurate tune measurements. Many BPMs to improve the resolution further.
BPMs must be capable of resolving turn-by-turn positions of two (or more) individual bunches, with low-current bunch(es) used as a reference.

11. An improved method to measure beam impedance with rotating wire
Theoretical and simulation results – Olav Berring
We need only 8 parameters!
If we want have only long. impedance
Use a collimator with a sextupole shape!
No-hybrid configurations are required.
We need two wires single ended measurements !!!!