Low Impedance Bellows for High Current SRF Accelerators G. Wu, R. Rimmer, J. Feingold, H. Wang, J....

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

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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

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SPX Cryomodule Layout

Advanced Photon Source Upgrade (APS-U) project4

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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

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Bellows design flow chart

Beam impedance calculations

Mechanical movement analysis

Mechanical design

RF analysis

Thermal analysis

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ABCi Simulation

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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

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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

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Volume Changes at Convolution Part

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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

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Inserting Straight Section

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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

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Optimized Options

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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

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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

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American BOA Mark IV

Field concentrated at 4.5GHz, 6 GHz and 8 GHz

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Loss Factor: 1.517V/nC

American BOA Mark IV

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Determination of Mesh Size

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• 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

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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.

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Pitch Radius

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• 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

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RF heating calculation ABCi approach

APS beam 153 nS spacing, 30nC bunch charge averaged at 200mA

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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.

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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

]

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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

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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

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Slide from Sang-Hoon Kim Jan. 2012

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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

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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

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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

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Advanced Photon Source Upgrade (APS-U) project

Test setup with cooling mechanism needs to be designed.

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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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Advanced Photon Source Upgrade (APS-U) project