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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
Advanced Photon Source Upgrade (APS-U) project
ICFA mini-Workshop on Deflecting/Crabbing Cavities
2Advanced Photon Source Upgrade (APS-U) project
Outline
Bellows requirement Bellows options Low impedance formed bellows design studies Test plan Summary
2
3
SPX bellows requirement
SPX0 Bellows at these temperatures– Warm to cold transition between shield 5K-300K
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Advanced Photon Source Upgrade (APS-U) project
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
4
SPX Cryomodule Layout
Advanced Photon Source Upgrade (APS-U) project4
5
Bellows options
KEK style shielded bellows Low loss formed bellowsDaphne shielded bellows
BNL style shielded bellows
Cornell ERL RF absorbing bellows
Except low loss formed bellows, all other bellows generate particulates and are hard to clean.
Jlab niobium bellows
7
Bellows design flow chart
Beam impedance calculations
Mechanical movement analysis
Mechanical design
RF analysis
Thermal analysis
9
ABCi Simulation
9
Parameter Value
R1 0.6 mm
R2 1.3 mm
R3 1.5 mm
d1 0.1 mm
d2 1.2 mm
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 = 119.05 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
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Basic Wake Property of Bellows
10
Wake impedance of bellows
Loss factor spectrum of bellows
2
22
2
21
d
p
R
xmnmnp
52.4405.2
2
1010
Rf
38.10520.5
2
1020
Rf
• 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.
Slide from Jaeho Jang
11
Volume Changes at Convolution Part
11
Loss factor when NC is changed
Loss factor when R2 is changed, NC = 6.
3-3 DUD structure and parameters
• Constraints to reduce the number of cases
mm
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.
02
0.212
0.432
d
RR
RR
Slide from Jaeho Jang
12
Inserting Straight Section
12
Loss factor when l1 is changed
Frequency spectrum for 3-3 UDU structure, l1 = 40, 80 and 120 mm
• 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).Slide from Jaeho Jang
13
Optimized Options
13
BOA Mark IV Option 1 Option 2
l1 (mm) 48.53 80 130
R2 (mm) 0.99 1.0 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
Bellows Bunch length [mm]
Nominal loss factor Kloss [mV/pC]
Shield
APS 3 64 Yes
SOLEIL 3 20 Yes
SPEAR3 3 67 Yes
NSLS-II 3 18 Yes
American BOA IV 3 455 No
American BOA IV 10 1.517 No
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.
American BOA Mark IV
A design has been selected earlier based on ANL/JLAB design and adapted to American BOA manufacturing procedure
16
American BOA Mark IV
Field concentrated at 4.5GHz, 6 GHz and 8 GHz
17
Loss Factor: 1.517V/nC
American BOA Mark IV
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Determination of Mesh Size
18
• 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
Convolution Spacing
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Stress distribution of 3-3 (left) and 2-2-2 (right) UDU structures
• 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.
20
Pitch Radius
20
• 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
21
Advanced Photon Source Upgrade (APS-U) project
0 50000 100000 150000 200000 250000 300000 350000 400000 450000 5000001.00E-03
1.00E-02
1.00E-01
1.00E+00
1.00E+01
Time [ps]
Su
rfac
e cu
rren
t [A
]
Considering single bunch only. ABCi multi-bunch calculation showed similar result.
22
0.00E+00
1.00E-02
2.00E-02
3.00E-02
4.00E-02
5.00E-02
6.00E-02
7.00E-02
8.00E-02
Su
rfac
e re
sist
ance
[o
hm
]
22
Advanced Photon Source Upgrade (APS-U) project
RF heating calculation ABCi approach
𝛿=√ 2𝜎𝜇𝜔
𝑅𝑠=1𝜎𝛿
Rs = 0.038 ohm
Rs = 0.046 ohm
Rs = 0.052 ohm
Rs = 0.061 ohm
RF surface loss changes almost linearly, or changes in a non-dramatic fashion.
𝑅𝑠∝𝜎0.5𝜔0.5
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 0.23
Average heat flux (W/m2) 12 13 13 13 12
Sampling period: 5 ps
23/11
Slide from Sang-Hoon Kim Jan. 2012
2727
Advanced Photon Source Upgrade (APS-U) project
Thermal analysis examples
An example of RF surface heating for phosphor bronze
1 Watt with center 5K cooling 0.25 Watt without center 5K cooling
Data from J. Feingold
1/8 of actual model
2828
Advanced Photon Source Upgrade (APS-U) project
Thermal analysis examples
Temperature rise is moderate.
Maximum temperature [K] for the bellows under different thermal loads
Data from J. Feingold
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
29
Stand alone bellows test
Advanced Photon Source Upgrade (APS-U) project29
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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
30
Advanced Photon Source Upgrade (APS-U) project
Test setup with cooling mechanism needs to be designed.
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
31
Advanced Photon Source Upgrade (APS-U) project