1. Low Impedance Bellows for High Current SRF Accelerators
G. Wu, R. Rimmer, J. Feingold, H. Wang, J. Mammosser, G. Waldschmidt, A. Nassiri, J. H. Jang, S.H. Kim, K-J. Kim, and Y. Yang
ICFA mini-Workshop on Deflecting/Crabbing Cavities
Advanced Photon Source Upgrade (APS-U) project

2. Outline Bellows requirement Bellows options
Low impedance formed bellows design studies
Test plan
Summary
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3. SPX bellows requirement
SPX0 Bellows at these temperatures
Warm to cold transition between shield 5K-300K
SPX0 bellows mechanical specs
5-inch total length
7-inches to cavities
Horizontal +/-1.0mm
Vertical +/-0.5mm
Low impedance
No trapped mode
Easy to clean
Particulate free operation
Cavity length is ~380mm
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4. SPX Cryomodule Layout
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5. Bellows options BNL style shielded bellows
Cornell ERL RF absorbing bellows
Jlab niobium bellows
KEK style shielded bellows
Daphne shielded bellows
Low loss formed bellows
Except low loss formed bellows, all other bellows generate particulates and are hard to clean.

6. Daphne
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7. Bellows design flow chart
Beam impedance calculations
Mechanical movement analysis
Mechanical design
RF analysis
Thermal analysis

8. Tasks Beam impedance simulation for both bellow options.
CST, GdFidl, ABCi verification
Mechanical analysis
RF simulations
Thermal analysis
Prototyping
Niobium
Titanium
Phosphor Bronze
Stainless Steel/Superconducting coating/copper coating
Beam test at APS
Low impedance formed bellows
Temperature: 77K and room temperature
Forced air cooled, water cooled or liquid nitrogen cooled
Space requirement: 30-inches
Diagnostics: temperature monitoring, BPM
We are here !

9. ABCi Simulation Parameter Value R1 0.6 mm R2 1.3 mm R3 1.5 mm d1
Geometric parameters at convolution part (left) and their values of the initial model (right)
Applied conditions in this ABCi simulation study
Radius of beam tube = 25.4 mm (fixed)
Length of beam tube = mm (from convolution part to end of bellows)
Mesh size = 0.2 mm, beam size = 10 mm (obtained from feasibility study)
Monopole wakefield up to 200 m from the source bunch
The calculation time: ~ 1 hour in a PC with 4 CUPs of 3.4 GHz each
Slide from Jaeho Jang

10. Basic Wake Property of Bellows
Resonance frequencies of right circular cylindrical resonator:
Broad-band spectrums above 4.5 GHz:
Sharp peaks about 10.4 GHz:
※ Mesh size (0.2 mm) and beam size (10 mm) are chosen from this study.
Wake impedance of bellows
Loss factor spectrum of bellows
Slide from Jaeho Jang

11. Volume Changes at Convolution Part
3-3 DUD structure and parameters
Loss factor when NC is changed
Constraints to reduce the number of cases mm
Increase of NC and R2 means the increase of volume at convolution part.
Large geometric variation, which wakefield can stay more in the structure, causes large loss factor.
Loss factor when R2 is changed, NC = 6.
Slide from Jaeho Jang

12. Inserting Straight Section
Total length is changed according to l1.
Minimum loss factor when l1 = 80 mm for both UDU and DUD structures.
For no or small spacing (ex. 40 mm)
Broad-band spectrum of loss factor by the irregular shape of convolution part
For optimum spacing (ex. 80 mm)
The straight section acts like a resonant cavity.
Optimum spacing can be obtained by choosing small amplitude of spectrum and small total loss factor.
The overall values of DUD structures are slightly lower than UDU structure (volume difference).
Loss factor when l1 is changed
Frequency spectrum for 3-3 UDU structure,
l1 = 40, 80 and 120 mm
Slide from Jaeho Jang

13. Optimized Options BOA Mark IV Option 1 Option 2 l1 (mm) 48.53 80 130
R2 (mm)
0.99
1.0
d2 (mm)
2.17
2.0
2.5
Loss factor (V/nC)
1.52
1.04 (68%)
1.56 (103%)
Max. von-Mises stress (MPa)
314
223 (71%)
127 (40%)
Max. principal stress (MPa)
361
257
146
Slide from Jaeho Jang

14. Comparison to shielded bellows
Bunch length [mm]
Nominal loss factor Kloss [mV/pC]
Shield
APS 3 64
Yes
SOLEIL 20
SPEAR3 67
NSLS-II 18
American BOA IV
455 No 10
1.517
A. Blednykh et al, Impedance calculation for the NSLS-II storage ring, PAC2009
Low impedance unshielded bellows may work since APS beam has forgivingly long bunches.

15. American BOA Mark IV
A design has been selected earlier based on ANL/JLAB design and adapted to American BOA manufacturing procedure

16. Field concentrated at 4.5GHz, 6 GHz and 8 GHz
American BOA Mark IV
Field concentrated at 4.5GHz, 6 GHz and 8 GHz

17. American BOA Mark IV
Loss Factor: 1.517V/nC

18. Determination of Mesh Size
Calculation result mainly depends on the element size at convolution part (edge 1) and the number of layers
By above feasibility study, the following conditions are chosen
8 layers / Edge 1 = 0.1 mm
Edge 2 = Edge 3 = 2.0 mm
Run time: ~ 3 hours with 4 CPU of 3.4 GHz

19. Stress distribution of 3-3 (left) and 2-2-2 (right) UDU structures
Convolution Spacing
Large spacing
 small slope of straight section
 reduced bending angle
2-2-2 structure
has same number of convolutions with 3-3 structure,
but middle part cannot share the stress with both side.
Stress distribution of 3-3 (left) and (right) UDU structures

20. Bellows geometry with smooth edge at R1
Pitch Radius
Similar values of R2 and R3
 sharing the stress evenly
 reducing maximum stress
Same constraints with wake analysis cause the drastic increase of stress.
Smooth edge condition is needed when R2 = 2 mm.
Bellows geometry with smooth edge at R1

21. RF heating calculation ABCi approach
APS beam 153 nS spacing, 30nC bunch charge averaged at 200mA
Considering single bunch only.
ABCi multi-bunch calculation showed similar result.
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22. RF heating calculation ABCi approach
Rs = ohm
𝛿= 2 𝜎𝜇𝜔
Rs = ohm
𝑅 𝑠 = 1 𝜎𝛿
Rs = ohm
𝑅 𝑠 ∝ 𝜎 0.5 𝜔 0.5
Rs = ohm
RF surface loss changes almost linearly, or changes in a non-dramatic fashion.
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23. Dissipation Power (BOA IV)
Zone1
Zone2
Zone3
Zone4
Zone5
Dissipation energy per bunch (nJ) 35
8.7 15
8.6 36
Average heating power (W)
0.23
0.057
0.10
0.056
Average heat flux (W/m2) 12 13
Sampling period: 5 ps
Slide from Sang-Hoon Kim Jan. 2012

24. RF heating calculation ABCi approach
Assumptions:
Single bunch, monopole
Bellows ends with open boundaries
Constant RMS surface current (Averaged through time integration)
Constant surface current around the bellows surface area
Geometric factor of 0.5 applied toward surface field distribution heating
Single frequency based on loss factor spectrum
Room temperature
Phosphor bronze (8.7 µ.cm at room temperature)
Anomalous skin depth effect makes the cold temperature of copper or bronze to be 6 fold decreasing instead of (RRR) 50 or 100 decreasing.
American BOA bellows surface RF heating <~ 1 W, Beam power loss = 9 W
To be verified with ACE3P
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25. RF heating calculation frequency domain approach
Geometric factor of 0.5 is not very accurate
Beam loss factor appears “discreet” from frequency spectrum plot
𝑃 𝑏𝑒𝑎𝑚 =𝑞𝐼 𝐾 𝑙𝑜𝑠𝑠 (𝑓)
q = 30 nC, I = 200 mA
RF heating calculated in HFSS through Q0 and Qloaded for each main frequency
RF heating can be integrated by peaks in frequency domain
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26. RF heating calculation frequency domain approach
An example of RF surface loss.
f = GHz, Q0 = , Qloaded = 143
P_RF loss = W/GHz at 10 GHz
American BOA bellows surface RF heating <~ 0.16 W
Beam power loss = 9 W. (To be verified with ACE3P)
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27. Thermal analysis examples
1/8 of actual model
1 Watt with center 5K cooling
0.25 Watt without center 5K cooling
An example of RF surface heating for phosphor bronze
Data from J. Feingold
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28. Thermal analysis examples
Maximum temperature [K] for the bellows under different thermal loads
Material
0.25 W
0.5 W
1.0 W
Stainless steel, no center cooling 32 44 61
Stainless steel, center 5K cooling 19 26 36
Bronze, no center cooling 25 35 50
Bronze, center 5K cooling 15 21 29
Temperature rise is moderate.
Data from J. Feingold
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29. Stand alone bellows test
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30. Test setup with cooling mechanism needs to be designed.
Further development
Simulation by ACE3P at SLAC
Beam impedance, surface heating for complete model with cavities and bellows.
Manufacturing bellows prototype
Stainless Steel
Phosphor Bronze
Copper coating
Q measurement at room temperature and 77K
In ring test
Free air
Forced air cooling
Water cooling
Liquid nitrogen cooling
Test setup with cooling mechanism needs to be designed.
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31. Summary – a low impedance bellow is feasible
Low impedance formed bellows is preferred option for particulate free operation and ease of cleaning
Formed bellows needs prototype to confirm mechanical analysis
Low impedance formed bellows needs beam test to verify impedance analysis
Final design requires trade off between beam physics, SRF, and mechanical alignment ranges
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