1. Impedance due to laser treatment
Sergey Arsenyev
FCC-hh collective effects meeting on

2. Should we care about impedance due to laser treatment?
At what frequencies impedance is important?
Strict approach (Sacherer’s formula)
S. Arsenyev

3. Should we care about impedance due to laser treatment?
At what frequencies impedance is important?
Approximations
(inspired by X. Buffat, FCC meeting on )
Strict approach (Sacherer’s formula)
1) 𝑍 𝜔 is a smooth function for frequency
steps of Ω 0 ≈3 𝑘𝐻𝑧
2) Only consider mode 0 as the most unstable
For 𝜏 𝑏 =4𝜎=1.07 𝑛𝑠
S. Arsenyev

4. Should we care about impedance due to laser treatment?
At what frequencies impedance is important?
For a non-treated beam screen:
For 𝜏 𝑏 =4𝜎=1.07 𝑛𝑠
For un-treated resistive wall, 90% of contribution to the tuneshift comes from the frequency range
2 𝑀𝐻𝑧≤𝑓≤0.7 𝐺𝐻𝑧
S. Arsenyev

5. Should we care about impedance due to laser treatment?
Experimental evidence of impedance increase
(Sacherer, 1970-s)
Was measured
Dundee sample (old pattern)
STFC sample
𝑅 𝑠𝑢𝑟𝑓 increases by a factor of 1.26 at room T at 7.8 GHz
𝑅 𝑠𝑢𝑟𝑓 increases by a factor of 4.24 at room T at 7.8 GHz
S. Arsenyev

6. Should we care about impedance due to laser treatment?
Applying the experimental data: the two-layer model
Bulk copper
Layer of increased resistivity
IW2D + DELPHI simulations
S. Arsenyev

7. Should we care about impedance due to laser treatment?
Applying the experimental data: the two-layer model
To convert the measured increase in 𝑅 𝑠𝑢𝑟𝑓 to the layer resistivity, assume
𝑙𝑎𝑦𝑒𝑟 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 ≫ 𝛿 7.8 𝐺𝐻𝑧 ~1𝜇𝑚
S. Arsenyev

8. Should we care about impedance due to laser treatment?
Applying the experimental data: the two-layer model
To convert the measured increase in 𝑅 𝑠𝑢𝑟𝑓 to the layer resistivity, assume
𝑙𝑎𝑦𝑒𝑟 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 ≫ 𝛿 7.8 𝐺𝐻𝑧 ~1𝜇𝑚
Then for Dundee sample (old pattern) 𝜌 𝑙𝑎𝑦𝑒𝑟 increases by =1.58 at room T. For STFC sample 𝜌 𝑙𝑎𝑦𝑒𝑟 increases by =17.97 at room T.
S. Arsenyev

9. Should we care about impedance due to laser treatment?
Applying the experimental data: the two-layer model
To convert the measured increase in 𝑅 𝑠𝑢𝑟𝑓 to the layer resistivity, assume
𝑙𝑎𝑦𝑒𝑟 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 ≫ 𝛿 7.8 𝐺𝐻𝑧 ~1𝜇𝑚
Then for Dundee sample (old pattern) 𝜌 𝑙𝑎𝑦𝑒𝑟 increases by =1.58 at room T. For STFC sample 𝜌 𝑙𝑎𝑦𝑒𝑟 increases by =17.97 at room T.
If 𝜌 𝑙𝑎𝑦𝑒𝑟 does not change with T, we have an additional factor of 20 making it 31.6 for Dundee and for STFC.
Waiting for results with the quadrupole resonator at cryogenic T.
S. Arsenyev

10. Should we care about impedance due to laser treatment?
Yes.
S. Arsenyev

11. Should we care about impedance due to laser treatment?
Yes.
However:
We know that the two-layer model does not really apply to this case (reason: roughness)
We need a better model
We need more experimental data to fit in the model (low T, high B)
S. Arsenyev

12. Ways to include roughness in the impedance model
Alternatives to the two-layer model
Geometrical impedance
Inductive model
Resonator model
Chao, Stupakov:
Bane, Novokhatsky:
Biancacci:
S. Arsenyev

13. Ways to include roughness in the impedance model
Alternatives to the two-layer model
𝐸 ⊥ 𝐻 ⊥ = 𝑍 𝑠𝑢𝑟𝑓
Geometrical impedance
Generalized resistive wall impedance
Inductive model
Resonator model
Hammerstad:
Chao, Stupakov:
Bane, Novokhatsky:
Groiss:
Biancacci:
Snowball model:
(can be simplified to the cannonball model)
Gradient model:
S. Arsenyev

14. Proposal for an experiment
Setup by Caspers et al., 1999
Two-wire method to calculate out the resistivity of the wires.
Cryogenic T
Magnetic field of a dipole
FRESCA test facility:
Inner cryostat’s T is controlled independently
50 cm – 1 m long region on constant B
72 mm sample holder diameter
S. Arsenyev