Download - Impedance of Y-Chamber for SPS Crab cavity
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IMPEDANCE OF Y-CHAMBER FOR SPS CRAB CAVITYBy Phoevos KardasopoulosThanks to Benoit Salvant, Pei Zhang, Fred Galleazzi, Roberto Torres-Sanchez and Alick MacPherson
Impedance MeetingDate: 14/04/14
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Contents• Overview• Methodology• Review Existing Y-Chamber (COLDEX)• Evaluation of Designs for Crab Cavities
• Presentation of recommended impedance design
• Issues Related to Bellows• Conclusions
Objective of this talk: Present revised Y-chamber design for SPS crab cavity installation and seek approval from impedance group, so that the design can proceed to fabrication by the vacuum group.
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Contents• Overview• Methodology• Review Existing Y-Chamber (COLDEX)• Evaluation of Designs for Crab Cavities
• Presentation of recommended impedance design
• Issues Related to Bellows• Conclusions
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Overview• Y-Chamber’s purpose to switch objects in and out of the
beam line.
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Overview• Y-Chamber’s purpose to switch objects in and out of the
beam line.
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Overview• Current Y-Chamber:
• Used by COLDEX. • Opening angle: 12 degrees.• Transverse displacement: 340mm.
• Crab Cavities:• Opening angle: 16 degrees.• Transverse displacement: 510mm.• Expected number of cycles(in and out) = O(1000).
• Redesign needed:• Mechanical redesign needed to accommodate Crab Cavities.• Take opportunity to redesign Y-Chamber to reduce impedance.• Mechanical design must have required reliability.
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Previous Research• Previous research has been conducted:
• B. Spataro et al• Impedance of the LHC recombination chambers. LHC Project Note 254.
03/05/2001• On trapped modes in the LHC recombination chambers: experimental
results. LHC Project Note 254. LHC Project Note 266. 14/08/2001
• LHC Recombination chamber.• Possibility of trapped modes above the cut off frequency.
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Contents• Overview• Methodology• Review Existing Y-Chamber (COLDEX)• Evaluation of Designs for Crab Cavities
• Presentation of recommended impedance design
• Issues Related to Bellows• Conclusions
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Methodology• Initial 12o Y-chamber model received from Benoit.
• CST used to perform simulations on the models.
• Selection criteria: Based on CST simulations • High frequency : Frequency domain Eigenmode solver.• Low frequency: Time domain Wakefield solver
• Results for new designs compared to baseline results of initial Y-chamber model.
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Methodology – High Frequency• Look at high frequency modes excited by the beam.
• Evaluate shunt impedances.• Eigenmode solver.• Shunt impedances – CST post processing
• Circular convention 2.
• Evaluate impedance of transverse modes • Panofsky-Wenzel theorem – Only true for symmetric structures.
• d = transverse displacement of integration path in cavity axis• Integration path offset by: d = ±5mm, ± 7mm, and ± 10mm.
• MATLAB script to fit a parabolic shape, and take the coefficient of the linear term.
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Methodology – Low Frequency• Use time domain solver and look at imaginary part of
impedance for different source-wake bunch configurations• Separate simulations for the monopole, dipole, and quadrupole.
(1) (2) (3) (4) (5)
1)Monopole - Beam and test beam on the beam axis2)Horizontal Dipolar - Beam offset from the beam axis in x3)Horizontal Quadrupolar - Test beam offset from the beam axis in x4)Vertical Dipolar - Beam offset from the beam axis in y5)Vertical Quadrupolar - Test beam offset from the beam axis in y
Source bunchwake bunch
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Methodology – Low Frequency• Effective longitudinal impedance:
• n= f/frev
• Effective transverse impedance:
• Transverse impedance needs to be weighted by :• =0.65
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Contents• Overview• Methodology• Review Existing Y-Chamber (COLDEX)• Evaluation of Designs for Crab Cavities
• Presentation of recommended impedance design
• Issues Related to Bellows• Conclusions
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Current Y-Chamber• 12 degree version currently installed at COLDEX at SPS LSS4
• There are 3 of these currently in the SPS.• Two at LSS4, COLDEX(Crab Cavity) testing area.
• Legacy design: Reasons behind design are unclear.
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Current Y-ChamberTwo Models:
.
• Simplified model.• Received from Benoit• Imported from Catia.
• Realistic model.• Drawn in SolidWorks,
imported as ACIS.
Baseline model. As-Installed
Stainless Steel BoundariesAll Beam pipe connection inner diameter = 155 mm
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Current Y-ChamberTwo Models:
• Simplified model.• Received from Benoit• Imported from Catia.
• Realistic model.• Drawn in SolidWorks,
imported as ACIS.• >200 reduced curvature
elements.
Baseline model. As-Installed
Stainless Steel BoundariesAll Beam pipe connection inner diameter = 155 mm
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
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Shu
nt im
peda
nce
in k
Ohm
Frequency in GHz
Modes for the Y-Chamber 12
Eigenmode Results – Simple Y-Chamber
Frequency (GHz) Shunt Impedance (KOhms) Q Factor0.696 93.76 74020.910 44.66 84151.067 14.15 79791.078 22.50 78121.155 17.43 66621.232 15.02 58721.343 13.72 7823
1 Transverse mode identified48 kOhms/m at 1.40 GHz
Cut off frequency at 1.48 GHzWaveguide theory, Pipe radius 77.5mm
Results from Eigenmode Simulations
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-500
0
500
1000
1500
2000
Re(Z)
Frequency in GHz
12 Y-Chamber - Time Domain
Wakefield Solver - Simple Y-Chamber
Frequency (GHz) Shunt Impedance (KOhms) Q Factor0.696 93.76 74020.910 44.66 84151.067 14.15 79791.078 22.50 78121.155 17.43 66621.232 15.02 58721.343 13.72 7823
Results from Eigenmode Simulations
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35-19
-18
-17
-16
-15
-14
-13
-12
-11
Im(Zx)
Frequency in GHz
12 Y-Chamber - Effective Low Frequency Transverse X Impedance
MonopolarDipolarQuadrupolar
Low Frequency Transverse
𝑍 𝑥=𝑍 𝑥 (dip)−𝑍𝑥 (𝑚𝑜𝑛𝑜)
𝑑 +𝑍 𝑥 (quad )−𝑍𝑥 (𝑚𝑜𝑛𝑜)
𝑑(d=5mm)
𝑍 𝑥=16.9−14.40.005 +
14.4−14.30.005
0.5 kOhms/m 𝐙𝐱(𝐄𝐟𝐟𝐞𝐜𝐭𝐢𝐯𝐞)=𝟎 .𝟑𝟑𝐤𝐎𝐡𝐦𝐬 /𝐦
CST Convention: Inductive impedance is -ve
Bunch length = 300Charge =1e-9
Wakelength = 20000Direct Testbeams
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35-5
-4
-3
-2
-1
0
1
2
3
Im(Zy)
Frequency in GHz
12 Y-Chamber - Effective Low Frequency Transverse Y Impedance
MonopolarDipolarQuadrupolar
Low Frequency Transverse
𝑍 𝑦=𝑍 𝑦 (dip )−𝑍 𝑦(𝑚𝑜𝑛𝑜)
𝑑 +𝑍 𝑦 (quad )−𝑍 𝑦(𝑚𝑜𝑛𝑜)
𝑑𝑍 𝑦=
2.3−0.00.005 +
0.1−0.00.005
= 0.48 kOhms/m 𝐙𝐲(𝐄𝐟𝐟𝐞𝐜𝐭𝐢𝐯𝐞)=𝟎 .𝟑𝟏𝐤𝐎𝐡𝐦𝐬 /𝐦
Bunch length = 300Charge =1e-9
Wakelength = 20000Direct Testbeams
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Low Frequency Longitudinal
Y-Chamber ≈ 2.8 ± 0.2 mOhms
0 0.05 0.1 0.15 0.2 0.25 0.3 0.350
0.5
1
1.5
2
2.5
3
3.5x 10
-3
Im(Zk)n
Frequency in GHz
12 Y-Chamber - Effective Low Frequency Impedance
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12 Degree Model Comparison
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
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Shu
nt im
peda
nce
in k
Ohm
Frequency in GHz
Comparison of 12 Degree Longitudinal Impedances
BaselineUndulated
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
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Tran
vers
e im
peda
nce
in k
Ohm
/m
Frequency in GHz
Comparison 12 Degree Transverse Impedances
BaselineUndulated
12 Degree Model Comparison
SPS ≈ 20 MOhms/m
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12 Degree Model Comparison
Model ZL (mOhms)
Zx (kOhms/m)
Zy (kOhms/m)
Baseline 12o 2.8 ± 0.2 0.33 0.31
Undulated 12o 2.8 ± 0.2 0.33 0.31
SPS: Total Longitudinal 5 Ohms Total Transverse 20MOhms/m
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Contents• Overview• Methodology• Review Existing Y-Chamber (COLDEX)• Evaluation of Designs for Crab Cavities
• Presentation of recommended impedance design
• Issues Related to Bellows• Conclusions
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Alternate Designs Analysed
• Scaled up of 12 degree.• Provided by F. Galleazzi.
• Scaled up with undulations.
• Ellipsoid Conical. • Proposed.
All Designs: 16 Degree angle, stainless steel boundaries, 155mm pipe diameter
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High Frequency Longitudinal Impedance
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
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Shu
nt im
peda
nce
in k
Ohm
Frequency in GHz
Comparison 16 Degree Longitudinal Impedances
Baseline 12 Degree16 DegreeUndulated 16 DegreeElipsoid 16 DegreeProposed 16 Degree
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High Frequency Longitudinal Impedance
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
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Shu
nt im
peda
nce
in k
Ohm
Frequency in GHz
Comparison between Baseline and Proposed Design
BaselineProposed
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
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Tran
vers
e im
peda
nce
in k
Ohm
/m
Frequency in GHz
Comparison of 16 Degree Transverse Impedances
Baseline 12 Degree16 DegreeUndulated 16 DegreeElipsoid 16 DegreeProposed 16 Degree
High Frequency Transverse Impedance
Proposed Design - No significant transverse modes why?
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Low Frequency Impedance ComparisonsModel ZII (mOhms) Zx (kOhms/m) Zy (kOhms/m)Baseline 12 Degree
2.8 0.33 0.31
16 Degree 3.73 0.27 1.67
16 Degree Undulations
3.69 0.41 0.53
Ellipsoid 1.65 0.25 0.85
Proposed 0.43 0.21 0.85
SPS: 5 Ohms Longitudinal 20MOhms Transverse
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Candidate Design
Question: Is this design acceptable for the impedance working group?Question: What other aspects are important, aperture?Question: Can we proceed to develop mechanical design with vacuum group?
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Contents• Overview• Methodology• Review Existing Y-Chamber (COLDEX)• Evaluation of Designs for Crab Cavities
• Presentation of recommended impedance design
• Issues Related to Bellows• Conclusions
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Bellows
Suggested by Cedric Garion TE-VSC-DLM
Are there issues with the bellows?
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Bellow Impedance
• Analytical Mode l- At high energy
×4
(Valid up to first cut off frequency)
Effective Impedance ≈0.65 mOhms
(http://cdsweb.cern.ch/record/118026/files/p1.pdf)
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Bellow Impedance
Cut off frequency at 1.47 GHzWaveguide theory, Pipe radius 78mm
Effective Impedance ≈0.65 mOhms
Should we be worried at we approach cut-off
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• Transverse Impedance:• (Handbook of Accelerator Physics and Engineering, pg. 258, A. Wu. Choa)
• 3.12 mOhms/m
Bellow Impedance
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Contents• Overview• Methodology• Review Existing Y-Chamber (COLDEX)• Evaluation of Designs for Crab Cavities
• Presentation of recommended impedance design
• Issues Related to Bellows• Conclusions
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Conclusions• Current 12 degree Y-Chamber has been modelled in CST.
• Impedances have been calculated cross checked with previous calc..• Consistency cross check between time and frequency domain.
• Crab cavity Y-Chambers designs• 4 models have been modelled & impedances calculated.
• Results• Scaled up version of current Y-Chamber has increased impedance.• Reducing the volume reduces the impedance.• Candidate design:
• Shunt impedance: • lowest significant: 3.92 kOhms @ 1.12 GHz• Most significant:: 5.25 kOhms @ 1.39 GHz
• No transverse mode below cut off
• Contribution from bellows: TE-VSC Design has negligible Impedance
• Next step: Can impedance working group endorse Y-Chamber design for next step.