IMPEDANCE OF Y-CHAMBER FOR SPS CRAB CAVITY

By Phoevos KardasopoulosThanks to Benoit Salvant, Pei Zhang, Fred Galleazzi, Roberto Torres-Sanchez and Alick MacPherson

Impedance Meeting

Date: 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

4

Overview• Y-Chamber’s purpose to switch objects in and out of the

beam line.

5

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

14

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-Chamber

Two 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-Chamber

Two 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

10

20

30

40

50

60

70

80

90

100

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

Monopolar

DipolarQuadrupolar

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

Monopolar

DipolarQuadrupolar

Low Frequency Transverse

𝑍 𝑦=𝑍 𝑦 (dip )−𝑍 𝑦(𝑚𝑜𝑛𝑜)

𝑑+𝑍 𝑦 (quad )−𝑍 𝑦(𝑚𝑜𝑛𝑜)

𝑑

𝑍 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

10

20

30

40

50

60

70

80

90

100

Shu

nt im

peda

nce

in k

Ohm

Frequency in GHz

Comparison of 12 Degree Longitudinal Impedances

Baseline

Undulated

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

5

10

15

20

25

30

35

40

45

50

Tra

nver

se im

peda

nce

in k

Ohm

/m

Frequency in GHz

Comparison 12 Degree Transverse Impedances

Baseline

Undulated

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

10

20

30

40

50

60

70

80

90

100

Shu

nt im

peda

nce

in k

Ohm

Frequency in GHz

Comparison 16 Degree Longitudinal Impedances

Baseline 12 Degree

16 Degree

Undulated 16 DegreeElipsoid 16 Degree

Proposed 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

10

20

30

40

50

60

70

80

90

100

Shu

nt im

peda

nce

in k

Ohm

Frequency in GHz

Comparison between Baseline and Proposed Design

Baseline

Proposed

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

5

10

15

20

25

30

35

40

45

50

Tra

nver

se im

peda

nce

in k

Ohm

/m

Frequency in GHz

Comparison of 16 Degree Transverse Impedances

Baseline 12 Degree

16 Degree

Undulated 16 DegreeElipsoid 16 Degree

Proposed 16 Degree

High Frequency Transverse Impedance

Proposed Design - No significant transverse modes why?

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Low Frequency Impedance Comparisons

Model 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

38

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.