Impact of Impedance effects on beam chamber specifications - PowerPoint PPT Presentation

FREQUENCY RANGE OF INTEREST u Cut-off frequency (above which modes are propagating) 10 lowest [GHz] ≈ f cut − off b [cm] § N.A. for LHC: b ≈ 2 cm => f cut-off ≈ 5 GHz u Lower limit => First Unstable (transverse) Betatron Line: ( ) f rev f FUBL = n − Q § N.A. for LHC: (1 - 0.31) × 11245 ≈ 8 kHz Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

FREQUENCY RANGE OF INTEREST u Bunch length and bunch 0 ALBA spectrum SOLEIL - 10 20 Log H 10, A ê A 0 L @ dB D DLS NSLS - 20 PETRA-III § N.A. for LHC: τ b (4 σ ) - 30 LHC ≈ 1 ns PEP-II - 40 - 50 - 60 0 10 20 30 40 50 f @ GHz D Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

FREQUENCY RANGE OF INTEREST u Bunch length and bunch 0 ALBA spectrum SOLEIL - 10 20 Log H 10, A ê A 0 L @ dB D DLS NSLS - 20 PETRA-III § N.A. for LHC: τ b (4 σ ) - 30 LHC ≈ 1 ns PEP-II - 40 - 50 - 60 0 10 20 30 40 50 f @ GHz D u Some higher-order modes can also be m 0 Power spectrum = excited and lead to longitudinal and/or m 1 = transverse instabilities m 2 = Extends up to ~ ± 1 / τ b f Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

FREQUENCY RANGE OF INTEREST u Bunch length and bunch 0 ALBA spectrum SOLEIL - 10 20 Log H 10, A ê A 0 L @ dB D DLS NSLS - 20 PETRA-III § N.A. for LHC: τ b (4 σ ) - 30 LHC ≈ 1 ns PEP-II - 40 - 50 - 60 0 10 20 30 40 50 f @ GHz D u Some higher-order modes can also be m 0 Power spectrum = excited and lead to longitudinal and/or m 1 = transverse instabilities m 2 = Extends up to ~ ± 1 / τ b f => For LHC: from 8 kHz to few GHz Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u Keep the resistivity as low as possible for 3 reasons Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u Keep the resistivity as low as possible for 3 reasons § Power loss => High-frequency Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u Keep the resistivity as low as possible for 3 reasons § Power loss => High-frequency § Transverse Coupled-Bunch (Resistive-Wall) Instability: TCBI => Low-frequency Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u Keep the resistivity as low as possible for 3 reasons § Power loss => High-frequency § Transverse Coupled-Bunch (Resistive-Wall) Instability: TCBI => Low-frequency § Transverse Mode-Coupling Instability: TMCI => High-frequency Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 1) Power loss => Due to real part of the longitudinal impedance Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 1) Power loss => Due to real part of the longitudinal impedance 2 ⎛ ⎞ 2 π R Γ 3 1 ⎛ ⎞ ⎟ M N b e c ρ Z 0 G , RW ,1layer = − 3/2 ≈ 101mW/m P σ t ⎜ ⎟ ⎜ loss / m ⎝ 4 ⎠ b 2 π 2 ⎝ ⎠ Euler gamma function ⎛ ⎞ 3 ⎟ = 1.23 Γ ⎜ 4 ⎝ ⎠ N b = 1.15 × 10 11 p/b M = 2808 σ t = 0.25 ns 20 K ,7TeV = 7.7 × 10 − 10 Ω m LHC circumference = L ρ Cu = 2 π R = 26658.883 m b = beam screen half height = 36.8 / 2 = 18.4 mm Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 1) Power loss => Due to real part of the longitudinal impedance § For SS for instance, the power loss would be ~ 30 times more § Thickness of Cu (20 K, 7 TeV) coating => 1 (few) µm enough Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 1) Power loss => Due to real part of the longitudinal impedance § For SS for instance, the power loss would be ~ 30 times more § Thickness of Cu (20 K, 7 TeV) coating => 1 (few) µm enough 1000 ρ ( ) = f δ SkinDepth SS: ρ = 0.7 µ Ω m π µ 0 f 100 Skin depth [ mm ] 10 Graphite: ρ = 10 µ Ω m 1 0.100 Copper (room temp.): ρ = 17 n Ω m 0.010 Copper (20 K, 7 TeV): ρ = 0.77 n Ω m 0.001 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 1) Power loss => Due to real part of the longitudinal impedance § For SS for instance, the power loss would be ~ 30 times more § Thickness of Cu (20 K, 7 TeV) coating => 1 (few) µm enough 1000 ρ ( ) = f δ SkinDepth SS: ρ = 0.7 µ Ω m π µ 0 f 100 Skin depth [ mm ] 10 Graphite: ρ = 10 µ Ω m 1 0.100 Copper (room temp.): ρ = 17 n Ω m 0.010 Copper (20 K, 7 TeV): ρ = 0.77 n Ω m 0.001 10 5 10 8 100 f [ Hz ] Power loss and TMCI Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 1) Power loss => Due to real part of the longitudinal impedance § For SS for instance, the power loss would be ~ 30 times more § Thickness of Cu (20 K, 7 TeV) coating => 1 (few) µm enough 1000 ρ ( ) = f δ SkinDepth SS: ρ = 0.7 µ Ω m π µ 0 f 100 Skin depth [ mm ] 10 Graphite: ρ = 10 µ Ω m 1 0.100 Copper (room temp.): ρ = 17 n Ω m 0.010 Copper (20 K, 7 TeV): ρ = 0.77 n Ω m 0.001 10 5 10 8 100 f [ Hz ] TCBI Power loss and TMCI Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 2) TCBI => Due to real part of the transverse impedance Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 2) TCBI => Due to real part of the transverse impedance γ Q y µ 0 τ y ≈ ⎡ ⎤ ( ) M N b r p Re Z y 2 π f FUBL ⎢ ⎥ 2 π R Instability rise-time ⎣ ⎦ (in the thick-wall regime) Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 2) TCBI => Due to real part of the transverse impedance γ Q y µ 0 τ y ≈ ⎡ ⎤ ( ) M N b r p Re Z y 2 π f FUBL ⎢ ⎥ 2 π R Instability rise-time ⎣ ⎦ (in the thick-wall regime) § Previous plot reveals why in this case few tens / hundreds of µm are needed (at low frequency, IF we are in the thick-wall regime) § This thick-wall regime is for instance not the case with the LHC collimators … Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

LHC beam pipe: round, 20 mm radius, 1 m long 10 7 Im 10 5 Z y [ Ω / m ] Re 1000 Copper: ρ = 17 n Ω m 10 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

LHC beam pipe: round, 20 mm radius, 1 m long Re 10 7 Im Graphite: ρ = 10 µ Ω m 10 5 Z y [ Ω / m ] 1000 Copper: ρ = 17 n Ω m 10 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

LHC beam pipe: round, 2 mm radius, 1 m long Re 10 7 Im 10 5 Z y [ Ω / m ] Copper: ρ = 17 n Ω m 1000 10 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

LHC beam pipe: round, 2 mm radius, 1 m long Graphite: ρ = 10 µ Ω m 10 7 10 5 Z y [ Ω / m ] Copper: ρ = 17 n Ω m 1000 Re 10 Im 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

LHC beam pipe: round, 1 m long Graphite: ρ = 10 µ Ω m, Im b = 2 mm 10 7 10 5 Z y [ Ω / m ] Re 1000 Copper: ρ = 17 n Ω m, 10 b = 20 mm 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

LHC beam pipe: round, 1 m long Graphite: ρ = 10 µ Ω m, Im ) = j Z 0 b = 2 mm ( Z y f → 0 10 7 2 π b 2 10 5 Z y [ Ω / m ] Re 1000 Copper: ρ = 17 n Ω m, 10 b = 20 mm 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

LHC beam pipe: round, 1 m long b 2 × 1 f max,Re ≈ ρ π µ 0 Graphite: ρ = 10 µ Ω m, Im ) = j Z 0 b = 2 mm ( Z y f → 0 10 7 2 π b 2 10 5 Z y [ Ω / m ] Re 1000 Copper: ρ = 17 n Ω m, 10 b = 20 mm 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

LHC beam pipe: round, 1 m long b 2 × 1 f max,Re ≈ ρ π µ 0 Graphite: ρ = 10 µ Ω m, Im ) = j Z 0 b = 2 mm ( Z y f → 0 10 7 2 π b 2 10 5 Z y [ Ω / m ] When Re = Im Re => Classical thick-wall 1000 regime Copper: ρ = 17 n Ω m, Z 0 10 ( ) = 1 + j ( ) ( ) Z y f f 2 π b 3 δ SkinDepth b = 20 mm 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

SS beam pipe with 20 mm radius and 0 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

SS beam pipe with 20 mm radius and 1 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

SS beam pipe with 20 mm radius and 5 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

SS beam pipe with 20 mm radius and 10 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

SS beam pipe with 20 mm radius and 50 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

SS beam pipe with 20 mm radius and 1000 µm = 1 mm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Graphite beam pipe with 2 mm radius and 0 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Graphite beam pipe with 2 mm radius and 1 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Graphite beam pipe with 2 mm radius and 5 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Graphite beam pipe with 2 mm radius and 10 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Graphite beam pipe with 2 mm radius and 50 µm copper coating (room temp.) 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Copper (room temp.) beam pipe with 20 mm radius and 0 µm graphite coating 10 Re 5 Im 1 0.50 Ratio 0.10 0.05 0.01 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Copper (room temp.) beam pipe with 20 mm radius and 1 µm graphite coating Re Im 20 10 Ratio 5 2 1 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Copper (room temp.) beam pipe with 20 mm radius and 5 µm graphite coating Re Im 20 10 Ratio 5 2 1 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Copper (room temp.) beam pipe with 20 mm radius and 10 µm graphite coating Re Im 20 10 Ratio 5 2 1 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Copper (room temp.) beam pipe with 20 mm radius and 50 µm graphite coating Re Im 20 10 Ratio 5 2 1 10 5 10 8 100 f [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? u 3) TMCI => (Mainly) due to i m a g i n a r y p a r t o f t h e transverse impedance Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COPPER COATING: WHY AND WHICH THICKNESS? 1.0 u 3) TMCI => (Mainly) due to 0.5 Re ( ω - ω y ) / ω s i m a g i n a r y p a r t o f t h e 0.0 transverse impedance - 0.5 § Example case (~ LHC) - 1.0 - 1.5 - 2.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] - j Z ϵ 1.0 Im ( ω - ω y ) / ω s 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017 - j Z ϵ

COPPER COATING: WHY AND WHICH THICKNESS? 1.0 u 3) TMCI => (Mainly) due to 0.5 Re ( ω - ω y ) / ω s i m a g i n a r y p a r t o f t h e 0.0 transverse impedance - 0.5 § Example case (~ LHC) - 1.0 - 1.5 - 2.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] - j Z ϵ Mode-coupling between 1.0 modes 0 and -1 Im ( ω - ω y ) / ω s 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017 - j Z ϵ

COPPER COATING: WHY AND WHICH THICKNESS? 1.0 u 3) TMCI => (Mainly) due to 0.5 Re ( ω - ω y ) / ω s i m a g i n a r y p a r t o f t h e 0.0 transverse impedance - 0.5 § Example case (~ LHC) - 1.0 § Approximation to find the - 1.5 - 2.0 threshold => When tune 0.0 0.5 1.0 1.5 2.0 shift of mode 0 is ~ - Q s N b - j Z ϵ 1.0 From Sacherer Im ( ω - ω y ) / ω s 0.5 formula 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017 - j Z ϵ

COPPER COATING: WHY AND WHICH THICKNESS? u 3) TMCI => (Mainly) due to i m a g i n a r y p a r t o f t h e Weighted by the bunch transverse impedance spectrum (mode 0), which also depends on § Example case (~ LHC) bunch length … § Approximation to find the threshold => When tune shift of mode 0 is ~ - Q s τ b = 1ns = 2E - 3 = 7E12 ( ) τ b Q s ) max = 4 π E t / e ( ) < Im Z y ( eff eff Im Z y av N b e β y ≈ 134 M Ω /m = R / Q y = 71.5 m 1.15E11 p/b Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER u A (bunch by bunch) resistive transverse damper is usually used to damp the TCBI => IF instability rise-time is longer than ~ 10 turns Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER u A (bunch by bunch) resistive transverse damper is usually used to damp the TCBI => IF instability rise-time is longer than ~ 10 turns u Depending on Q’ (chromaticity) and the transverse damper gain, a certain amount of non-linearities (Landau octupoles) is also needed to stabilize the single-bunch instabilities by Landau damping Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER u A (bunch by bunch) resistive transverse damper is usually used to damp the TCBI => IF instability rise-time is longer than ~ 10 turns u Depending on Q’ (chromaticity) and the transverse damper gain, a certain amount of non-linearities (Landau octupoles) is also needed to stabilize the single-bunch instabilities by Landau damping u Recent studies revealed that for Q’ = 0 the resistive transverse damper is destabilising (for the single bunch) and shed a light on the physical mechanism Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER u Destabilising effect of the resistive transverse damper (in red below) 1.0 0.5 Re ( ω - ω y ) / ω s 0.0 - 0.5 - 1.0 - 1.5 - 2.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] - j Z ϵ 1.0 Im ( ω - ω y ) / ω s 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] - j Z ϵ Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER u Destabilising effect of the resistive transverse damper (in red below) 1.0 0.5 § This is the interaction Re ( ω - ω y ) / ω s 0.0 between modes - 1 and 0 - 0.5 through the damper which creates the instability - 1.0 - 1.5 - 2.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] - j Z ϵ 1.0 Im ( ω - ω y ) / ω s 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] - j Z ϵ Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER u Destabilising effect of the resistive transverse damper (in red below) 1.0 0.5 § This is the interaction Re ( ω - ω y ) / ω s 0.0 between modes - 1 and 0 - 0.5 through the damper which creates the instability - 1.0 - 1.5 § The “coupling” between the - 2.0 0.0 0.5 1.0 1.5 2.0 2 modes pushes apart the N b [a.u.] - j Z ϵ instability growth rates and 1.0 as the lowest one is 0, it Im ( ω - ω y ) / ω s becomes negative 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] - j Z ϵ Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER § Considering only the 2 modes 0 and - 1 yields With the transverse damper gain used before 1.0 Im ( ω - ω y ) / ω s 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] x = - j Z ϵ Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER With the transverse damper gain used before / 2 1.0 Im ( ω - ω y ) / ω s 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] x = - j Z ϵ Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER With the transverse damper gain used before / 4 1.0 Im ( ω - ω y ) / ω s 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] x = - j Z ϵ Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER With the transverse damper gain used before / 10 1.0 Im ( ω - ω y ) / ω s 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] x = - j Z ϵ Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER With the transverse damper gain used before / 100 1.0 Im ( ω - ω y ) / ω s 0.5 0.0 - 0.5 - 1.0 0.0 0.5 1.0 1.5 2.0 N b [a.u.] x = - j Z ϵ Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER u The consequences on the Landau damping are currently under investigation (as the assumption of independent modes cannot be made anymore) Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

EFFECT OF THE (RESISTIVE) TRANSVERSE DAMPER u The consequences on the Landau damping are currently under investigation (as the assumption of independent modes cannot be made anymore) u However, with a sufficiently strong (and low noise) transverse damper, the TCBI (low frequency) should not be a problem anymore => Particular attention should be paid to the high frequency (single- bunch) regime Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COATING (e.g. a-C) OR SURFACE TREATMENT (e.g. LESS) TO FIGHT AGAINST E-CLOUD Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COATING (e.g. a-C) OR SURFACE TREATMENT (e.g. LESS) TO FIGHT AGAINST E-CLOUD u This will increase the resistivity (or roughness) at high frequency => Mainly the imaginary parts of the longitudinal and transverse impedances Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COATING (e.g. a-C) OR SURFACE TREATMENT (e.g. LESS) TO FIGHT AGAINST E-CLOUD u This will increase the resistivity (or roughness) at high frequency => Mainly the imaginary parts of the longitudinal and transverse impedances § Increase of imaginary part of longitudinal impedance at high frequency => More critical for the loss of longitudinal Landau damping Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COATING (e.g. a-C) OR SURFACE TREATMENT (e.g. LESS) TO FIGHT AGAINST E-CLOUD u This will increase the resistivity (or roughness) at high frequency => Mainly the imaginary parts of the longitudinal and transverse impedances § Increase of imaginary part of longitudinal impedance at high frequency => More critical for the loss of longitudinal Landau damping = τ b f rev = 1ns × 11245.5 Hz 16 MV 35640 max ∝ h 3 ˆ ( ) ( ) 5 Z l n ≤ Z l n V RF B 0 n n N b e f rev eff eff n = f / f rev Weighted by the bunch spectrum Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COATING (e.g. a-C) OR SURFACE TREATMENT (e.g. LESS) TO FIGHT AGAINST E-CLOUD § Increase of imaginary part of transverse impedance at high frequency => More critical for TMCI Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COATING (e.g. a-C) OR SURFACE TREATMENT (e.g. LESS) TO FIGHT AGAINST E-CLOUD § Increase of imaginary part of transverse impedance at high frequency => More critical for TMCI • Example case of FCC-hh, where laser treatment was proposed as baseline for SEY reduction Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COATING (e.g. a-C) OR SURFACE TREATMENT (e.g. LESS) TO FIGHT AGAINST E-CLOUD § Increase of imaginary part of transverse impedance at high frequency => More critical for TMCI • Example case of FCC-hh, where laser treatment was proposed as baseline for SEY reduction Dotted line Sergey Arsenyev Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

COATING (e.g. a-C) OR SURFACE TREATMENT (e.g. LESS) TO FIGHT AGAINST E-CLOUD § Increase of imaginary part of transverse impedance at high frequency => More critical for TMCI • Example case of FCC-hh, where laser treatment was proposed as baseline for SEY reduction Dotted line Sergey Arsenyev => Measurements at low temperature and high magnetic field are required (and planned) Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

HTS COATING for FCC-hh: YBCO (from Sergio Calatroni) Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

HTS COATING for FCC-hh: YBCO (from Sergio Calatroni) 1 10 - 1 10 - 4 10 - 7 Ratio Vs. copper at injection 10 - 10 10 - 13 Re Im 10 - 16 10 4 10 6 10 8 10 10 1 100 10 9 Frequency [ Hz ] Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

HTS COATING for FCC-hh: YBCO (from Sergio Calatroni) 1 10 - 1 10 - 4 10 - 7 Ratio Vs. copper at injection 10 - 10 10 - 13 Re Im 10 - 16 10 4 10 6 10 8 10 10 1 100 10 9 Frequency [ Hz ] § Much better at low and intermediate frequencies Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

HTS COATING for FCC-hh: YBCO (from Sergio Calatroni) 1 10 - 1 10 - 4 10 - 7 Ratio Vs. copper at injection 10 - 10 10 - 13 Re Im 10 - 16 10 4 10 6 10 8 10 10 1 100 10 9 Frequency [ Hz ] § Much better at low and intermediate frequencies § Pay attention to higher frequencies as it could impact TMCI Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Beam screen tube (Stainless-Steel) Copper coating Longitudinal weld 2 b Saw teeth ~
40
 µ m
 ~
500
 µ m
 Longitudinal weld Pumping slots Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Beam screen tube (Stainless-Steel) Copper coating Longitudinal weld 2 b Saw teeth ~
40
 µ m
 ~
500
 µ m
 Longitudinal weld Pumping slots ◆ Increased factor deduced from 3D CST simulations with 50 µm of copper on top of SS and assuming a 2 mm high weld in SS Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017

Beam screen tube (Stainless-Steel) Copper coating Longitudinal weld 2 b Saw teeth ~
40
 µ m
 ~
500
 µ m
 Longitudinal weld Pumping slots ◆ Increased factor deduced from 3D CST simulations with 50 µm of copper on top of SS and assuming a 2 mm high weld in SS Carlo Zannini Elias Métral, workshop "Beam Dynamics meets Vacuum, Collimation and Surfaces", Karlsruhe, Germany, 08-10/03/2017