1. Reminder on longitudinal modes of the SPS BPMs and ZS pumping ports Benoit Salvant for the impedance team

2. Context Hunt for significant longitudinal modes above 1 GHz – ZS pumping modules simulated for the ZS review – SPS BPMs simulated in 2008/2009

3. Transitions between ZS Effective impedances at low frequency Im(Zlong/n)~ 7 mOhm Im(Zx)~ 2 kOhm/m Im(Zy)~ 8 kOhm/m 900 MHz 1.18 GHz Rs=1.1 MOhm (stainless steel) Q=14000 (stainless steel)

4. SPS BPMs Reference: – http://cdsweb.cern.ch/record/1208424/files/CERN-ATS-2009-046.pdf http://cdsweb.cern.ch/record/1208424/files/CERN-ATS-2009-046.pdf – Talk at SPSU in March 2011 with improved model – Note: mistake in computing shunt impedance of transverse mode was discovered 106 BPH and 96 BPV in the SPS Low frequency imaginary impedance for a BPH : Zlong/n ~ 1 mΩ, Zx=- 0.1 kΩ/m and Zy=2 kΩ/m. Separate simulations for a BPV: Zlong/n~0.5mΩ, Zy= 0.1 kΩ/m and Zx= 0.2 kΩ/m.

5. Modelled structure for the BPH All materials are perfect conductors (except the ceramic spacers) In fact: - Electrodes + pipe should be in Stainless Steel - Casing should be in Anticorodal Ultrarelativistic beams CST convention: Rs=|V|^2/Plosses  to be used for beam dynamics, the Rs values should be divided by 2 (work ongoing to clarify this and establish procedures)

6. BPH longitudinal (with material losses) fres (GHz) Q Rs (“center”) in Ohm Rs/Q In Ohm 0.26526317666.7 0.8854822750.6 0.8924933740.8 1.05277330133.9 1.06277335914.6 1.5986728041.2 1.6136861127416.4 1.85989655676.2

7. Why don’t we see the first mode? fres (GHz) Q Rs (“center”) in Ohm Rs/Q In Ohm 0.26526317666.7 0.8854822750.6 0.8924933740.8 1.05277330133.9 1.06277335914.6 1.5986728041.2 1.6136861127416.4 1.85989655676.2 ?

8. 8 Effect of matching the impedance at electrodes coaxial ports in Particle Studio simulations (BPH) Electrode coaxial port Modes are damped by the “perfect matching layer” at the coaxial port Short bunch (1 cm rms) SPS bunch (20 cm rms) Importance to match the BPM electrodes!

9. Note: BPH vertical (with material losses) to correct the mistake fres (GHz)Q Rs RtRt/Q (“center”)(y=2mm) in Ohm in Ohm/m 0.5284650521.18E+062529 0.532483092.02E+05418 1.20612760212.08E+05163 1.2587640109.49E+04124 1.271688054.70E+0468 1.41415140685.74E+05379 1.61368611274113394.81E+05702 1.66512230674.81E+05393 1.859896556755901.48E+05165 I did a mistake in 2009 in computing the transverse Shunt impedance at that time: it should be Significant transverse modes (100 of these BPHs!)  to be added to the model and used in beam dynamics simulations

10. BPV

11. From PhD thesis…

12. BPV (with material losses) Longitudinalvertical horizontal fresQ Rs (“center”) Rs(center)/ Q In Ohm Rs (y=2mm) vertical Rs in Ohm/m vertical Rs/Q in Ohm/m Rs (x=2mm) horizontal Rs in Ohm/m horizontal Rs/Q in Ohm/m In Ohm 0.293239900.4931.22E+055129000 0.29824115956.615950015964.01E+04166 0.70452500000172.88E+05549 0.7155480000071.17E+05213 1.0696549451.4943-2.23E+04-349483.35E+0451 1.09266711881.81185-3.28E+04-4911913.28E+0449 1.1856102410.42541.31E+05215235-6.05E+04-99 1.215624260431.67E+0526825-9.83E+03-16 1.5774500000000 1.5767240000021.52E+0421 1.6177300000000 1.6616860000017.19E+0310 1.871287300000000 1.91243000000000 1.96199315030.815093.66E+04181501-1.22E+04-6

13. Outlook There are many resonances beyond 1 GHz for most SPS equipment due to the large pipe apertures Single shunt impedances can reach 1 MOhm! Which one is harmful for longitudinal dynamics?