1. C. Zannini, G. Rumolo, V.G. Vaccaro
Update on the kicker impedance model and measurements of material properties
C. Zannini, G. Rumolo, V.G. Vaccaro
Thanks to: N. Biancacci, A. Danisi, H. Day, G. De Michele, E. Metral, B. Salvant

2. Penetration depth in ferrite

3. Overview Kicker impedance model Wire measurements
Measurements of material properties

4. Simplified kicker model
Courtesy T. Kroyer
A kicker is a special type of magnet designed to abruptly deflect the beam off its previous trajectory, for instance to inject/extract the beam to a transfer line or to a beam dump. Among all the SPS elements, the kickers are suspected to contribute to a significant amount of the transverse impedance of the SPS. In the first picture at the top we can see the drawing of the transverse cross-section of an SPS MKE kicker (on the left) and 7 assembled ferrite cells of an MKE kicker mounted with the hot and cold conductors (on the right). In the picture at the bottom we can see some simplified model of kickers for impedance calculations. Recently we used the Tsutsui model with good results.

5. Simulation models
C-magnet model x y

6. Comparing the two models
Real horizontal quadrupolar impedance calculated at x=1 cm
Using the C-magnet model in the transverse horizontal impedance a high peak at 40MHz appears. At low frequency the Tsutsui model is not able to estimate correctly the kicker impedance. The two models are in good agreement at high frequency (>400MHz).

7. Comparing the two models
Real longitudinal impedance
We can see the peak also in the longitudinal and vertical impedance
Real vertical detuning impedance calculated at y=0.5cm
Impedance [Ohm]

8. C-magnet and Frame magnet
Frame Magnet model
C-magnet model x y

9. C-magnet and Frame magnet

10. Penetration depth in ferrite

11. Calculation of the impedance for the C-Magnet model
Where is the low frequency impedance in a C-Magnet kicker model calculated using the Sacherer Nassibian formalism and is the impedance calculated using the Tsutsui formalism.
The Tsutsui impedance is calculated in H. Tsutsui. Transverse Coupling Impedance of a Simplified Ferrite Kicker Magnet Model. LHC Project Note 234, Instead we have to spend some word about the Sacherer Nassibian impedance.
This impedance is defined as:
Where l is the length of the magnet, x0 the beam position, L the inductance of the magnet and Zg is the impedance seen by the kicker

12. Comparing with theoretical results
Horizontal driving impedance calculated at x=1cm: MKP
The simulations of the C-magnet model are in agreement with a theoretical prediction based on Sacherer-Nassibian and Tsutsui formalism
Frame Magnet model
Horizontal dipolar impedance

13. External circuits EK PSB
The green curve depends from the cable properties (propagation and attenuation constants)

14. MKP: horizontal transverse impedance
The segmentation seems to affect strongly the low frequency peak

15. Overview Kicker impedance model Wire measurements
Measurements of material properties

16. Measurements of the coupling impedance using the coaxial wire method
The measured quantity is the transmission S21
cut-off frequency ≠0
cut-off frequency =0
TEM Propagation losses
Measured Losses = True Losses + Propagation losses
For resonant structures:

17. MKP: Comparing measured and simulated longitudinal impedance
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18. Measurements of the coupling impedance using the coaxial wire method
cut-off frequency =5.74 GHz
Superfish

19. Measurements of the coupling impedance using the coaxial wire method

20. Overview Kicker impedance model Wire measurements
Measurements of material properties

21. Electromagnetic characterization of materials
We characterize the material at high frequency using the waveguide method
Coaxial line method

22. Status of the measurements
We (me and G. De Michele) did measurements for some SiC in the ranges 10 MHz-2GHz and GHz and for the ferrite 8C11 in the range 10MHz-10GHz The elaboration of the results will take at least one month (simulation time of the measurement setups)

23. Ferrite Model
The ferrite has an hysteresis loop

24. The hysteresis effect in this measurementsμ H
In this measurements for the coaxial ferrite sample we have: