Impedance due to laser treatment Sergey Arsenyev FCC-hh collective effects meeting on 07.02.2017

Should we care about impedance due to laser treatment? At what frequencies impedance is important? Strict approach (Sacherer’s formula) S. Arsenyev 09.02.2017

Should we care about impedance due to laser treatment? At what frequencies impedance is important? Approximations (inspired by X. Buffat, FCC meeting on 10.06.2016) 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 09.02.2017

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 09.02.2017

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 09.02.2017

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 09.02.2017

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 09.02.2017

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 1.26 2 =1.58 at room T. For STFC sample 𝜌 𝑙𝑎𝑦𝑒𝑟 increases by 4.24 2 =17.97 at room T. S. Arsenyev 09.02.2017

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 1.26 2 =1.58 at room T. For STFC sample 𝜌 𝑙𝑎𝑦𝑒𝑟 increases by 4.24 2 =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 359.4 for STFC. Waiting for results with the quadrupole resonator at cryogenic T. S. Arsenyev 09.02.2017

Should we care about impedance due to laser treatment? Yes. S. Arsenyev 09.02.2017

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 09.02.2017

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 09.02.2017

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 09.02.2017

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 09.02.2017