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Agenda

- Previous RF measurements
- Attempts to simulate the complex ZS geometry
- Replacing the wires with a solid on a simplified model
- Studying the full geometry
- Frequency domain simulations

- What can we conclude?

Measurements of Fritz presented by Elena at Chamonix 2001

40 MHz

2001

2012

0

16

5

0

0

0

0

8 (new)

4

5+1

3

2

1

1

1 TCE + 1 TCSP

Other elements to consider?

Replacing the wires with a solid on a simplified model

With wire (spacing

between wires =20 mm, larger than in reality)

Wire replaced by a solid (much easier for the code)

Replacing the wires with a solid:real longitudinal impedance

Im(Zlong/n) ~14 mOhm

It seems we can model the wires as solids for the longitudinal impedance.

Wakefields were not damped, hence the

Replacing the wires with a solid:Imaginary vertical impedance

Im(Zy_eff)=40(/5mm)=8 kOhm/m for this simplified model

Replacing the wires with a solid:Imaginary horizontal impedance

Different amplitudes for both models can be due to different wake lengths

Im(Zx_eff)= 12 Ohm (/5mm)= 2.4 kOhm/m for this simplified model

As a conclusion from these studies, the ZS wires do not seem to be contributing significantly to the ZS impedance (at frequencies < 1GHz).

Simplified vs full geometry

Simplified geometry generated from the drawing

Full geometry imported from CATIA

steel

Perfect conductor

dielectric

ZS longitudinal impedance (real):

Quite different behaviour, in particular above 500 MHz!

ZS longitudinal impedance (real):

These harmonics of ~40 MHz should be linked to the length of the ZS (3.2 m)

43 MHz

35 MHz

The smaller frequency for the full structure could be due to the presence of the dielectric rods.

ZS longitudinal impedance (imaginary):

Similar effective longitudinal impedance at low frequency is therefore predicted for the full and for the simplified geometry

Frequency domain (eigenmode) simulationslongitudinal modes with the simplified geometry and stainless steel materials

43 MHz

44 MHz

43 MHz

44 MHz

44 MHz

44 MHz

Abs(H)

Abs(H)

f=257 MHz

f=290 MHz

Full vs simplified: imaginary vertical impedance

Very different behaviour.

Full structure: Im(Zeff_y)~40 KOhm/m

Simplified structure: Im(Zeff_y)~10 KOhm/m

Transitions between ZS (question from Jan)

Effective impedances at low frequency

Im(Zlong/n)~ 7 mOhm

Im(Zx)~ 2 kOhm/m

Im(Zy)~ 8 kOhm/m

1.18 GHz

Rs=1.1 MOhm (stainless steel)

Q=14000 (stainless steel)

900 MHz

What can we conclude for now?

- With the current simulations:
- From the transverse effective impedance point of view, the 6 ZS seem to contribute to ~ 1% of the total imaginary effective vertical impedance
(6 ZS (6*40 mOhm/m) +7 transitions (7*8 kOhm/m)~300 kOhm/m, i.e. ~1.5% of the SPS transverse effective imaginary impedance).

- From the longitudinal effective impedance point of view, the 6 ZS seem to contribute to 1% of the imaginary effective longitudinal impedance (6 ZS (6*14 mOhm) +7 transitions (7*7 mOhm)~130 mOhm, i.e. ~1.3% of the SPS longitudinal effective imaginary impedance Z/n).
- The impact of the ZS longitudinal harmonics of ~40 MHz reaching 100 kOhm should be studied in detail to know if they represent an issue.
- If the large modes at around 1.1 GHz of the ZS transitions are an issue for longitudinal stability, these transitions should be optimized.
- The ZS wires do not seem to contribute significantly to the impedance of the ZS (at frequencies below 1 GHz)

- From the transverse effective impedance point of view, the 6 ZS seem to contribute to ~ 1% of the total imaginary effective vertical impedance

Questions that remain to be answered:

- Effect of voltage applied to ion traps
- Effect of connection of the ion traps
- Can we understand the reason for the burst behaviour around 700 MHz and 1.1 GHz in the full model? Can that be a numerical problem?
- Study and impact of transverse modes
- Should we remeasure the ZS?
More studies are needed, and the new powerful PCs are helping greatly.

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