1. Development of the SRF Cavity Design for the Cooler ERL
JLEIC Collaboration Meeting Spring 2016
F. Marhauser
29. March 2016

2. ERL Baseline Conceptual Design Parameters
from Haipeng Wang’s slides, Nov/2015
MEIC-ERL1 for Electron Cooler, 952.6MHz
Five-cell, Iris diameter = 100mm, Low Loss (LL) shape cavity design
JLab High Current (HC) for FEL-ERL
Five-cell, Iris diameter = 70/140 mm (1497/748.5 MHz)
10/9/2018

3. ERL Baseline Conceptual Design Parameters
from Haipeng Wang’s slides, Nov/2015
On Crest Full Energy Gain 50
MeV
Full energy 55
Acceleration phase (0 on crest)
-20
deg.
Deceleration phase (0 on crest)
159
Dechirper/rechirper RF peak voltage
1.8 MV
Dechirper/rechirper beam phase (0 on crest)
-90/90
Linac beam pass 2
Injector CW beam current
200, 20, 2… mA
Bunch charge
420 pC
SRF cavity frequency
952.6
MHz
# of cells per cavity 5
# of cavities per cryomodule 6
Operating field at full energy gain (Eacc)
10.6
MV/m
10/9/2018

4. ERL Baseline Conceptual Design Parameters
from Haipeng Wang’s slides, Nov/2015
On Crest Full Energy Gain 50
MeV
Full energy 55
Acceleration phase (0 on crest)
-20
deg.
Deceleration phase (0 on crest)
159
Dechirper/rechirper RF peak voltage
1.8 MV
Dechirper/rechirper beam phase (0 on crest)
-90/90
Linac beam pass 2
Injector CW beam current
200, 20, 2… mA
Bunch charge
420 pC
SRF cavity frequency
952.6
MHz
# of cells per cavity 5
# of cavities per cryomodule 6
Operating field at full energy gain (Eacc)
10.6
MV/m
Iris diameter/radius
100/50 mm
10/9/2018

5. Comparison of Different Cavity Shapes on ERL Projects
from Haipeng Wang’s slides, Nov/2015
BERLinPro-ERL uses Cornell-ERL cavity shape
r/l
50mm radius for 952.6MHz
0.5
z/(bl)
10/9/2018

6. What is an Optimum Elliptical SRF Cavity Shape?
There is no optimum elliptical cell shape, but trade-off between performance parameters acceptable for machine
Crucial parameters that determine optimization process for SRF cavities:
Iris radius  strongly impacts achievable operational parameters:
Cutoff of beam tube (number trapped HOMs)
Surface peak fields (quench limit  Bpk/Eacc, field emission onset  Epk/Eacc)
Cell-to-cell coupling (kcc)  coupling of trapped modes to HOM dampers in beam tubes
Number of cells
Sensitivity of field amplitudes in cell with fabrication tolerances (δAcell ~ N2/kcc* δfcell,error)
N2/kcc should be small to minimize possible confinement of HOMs in cells
Equator/iris ellipses and wall inclination
Low Loss (LL)  small Bpk/Eacc
High Gradient (HG)  small Epk/Eacc
Minimize cryogenic (dynamic) losses  maximize R/Q*G
Equatorial cell region  Impact energy for resonant multipacting electrons
Wall inclination (low loss vs. rigidity of cell)  Lorentz Force detuning
10/9/2018

7. What are the Main Operational Constraints?
Given: Eacc = 10.6 MV/m (CW)  comparably low MV/m CW, spec’d for CEBAF upgrade (with contingency) 16 MV/m CW spec’d for LCLS-II MV/m spec’d for Eu X-FEL (pulsed)
 Quench limitation should/will not be the problem  Can sacrifice Bpk/Eacc
Field Emission (FE) is prevalent issue in machines (e.g. contamination during clean room assembly)  Do not sacrifice much on Epk/Eacc
HOM damping important (strong requirement)  Do not sacrifice much on cell-to-cell coupling  With given radius favors High Current (HC) design, i.e. straight walls, but original HC design has a comparably larger tube/iris ID, thus strong cell-to-cell coupling
10/9/2018

8. Field Emission
10/9/2018

9. Field Emission C100/R100: Epk/Eacc = 2.17 Epk = 30 MV/m 10/9/2018

10. What are the Main Operational Constraints?
Given: Eacc = 10.6 MV/m (CW)  comparably low MV/m CW, spec’d for CEBAF upgrade (with contingency) 16 MV/m CW spec’d for LCLS-II MV/m spec’d for Eu X-FEL (pulsed)
 Quench limitation should/will not be the problem  Can sacrifice Bpk/Eacc
Add 30 % contingency  Eacc = 13.8 MV/m
Peak field not to exceed Epk = 30 MV/m  Epk/Eacc = 2.17
by chance equal to CEBAF LL design
10/9/2018

11. How to make sure that one has obtained an optimum cell shape given all the trade-offs to make ?
10/9/2018

12. JLEIC Design Optimization
All cells scaled to MHz and iris ID = 100 mm
> 400 cell shapes
Epk/Eacc = 2.17
10/9/2018

13. JLEIC Design Optimization
All cells scaled to MHz and iris ID = 100 mm
> 400 cell shapes
Epk/Eacc = 2.17
10/9/2018

14. JLEIC Design Optimization
All cells scaled to MHz and iris ID = 100 mm
Epk = 30 MV/m
Bpk < 60 mT
Epk < 30 MV/m
Eacc = 10.6 MV/m + 30% = 13.8 MV/m
10/9/2018

15. JLEIC Design Optimization
All cells scaled to MHz and iris ID = 100 mm
Eacc = 10.6 MV/m + 30% = 13.8 MV/m
Parameter
Unit
Value
cavity type
LHeC study
CEBAF HC
LCLS-II
(TESLA)
CEBAF OC
CEBAF LL
JLEIC
(JG)
(FM)
kcc %
2.14
3.12
1.89
3.15
1.49
2.81
2.37
N2/kcc
11.71
8.01
42.97
7.94
32.89
8.90
10.57
10/9/2018

16. New JLEIC Cavity Cell Multipacting Barrier
10/9/2018

17. Elliptical Cavity Cell Multipacting Barriers
10/9/2018

18. HOM Excitation Excitation lines from Haipeng Wang’s slides, Nov/2015
476.3MHz
952.6MHz
1.9052GHz
476.3MHz rep. rate
200 mA injection current
10/9/2018

19. Higher Order Mode (HOM) Studies
Including 3 waveguide dampers (plus coaxial coupler)
10/9/2018

20. Higher Order Mode (HOM) Studies
Including 3 waveguide dampers (plus coaxial coupler)
10/9/2018

21. Higher Order Mode (HOM) Studies
Including 3 waveguide dampers (plus coaxial coupler)
tube = 100 mm
Ql~5e7
10/9/2018

22. Higher Order Mode (HOM) Studies
Trapped dipole mode pair close to beam tube cutoff
MHz, TM111 /5-mode
Ql~4.9e7
MHz, TM111 /5-mode
Electrical field (logarithmic scale)
Ql~5.1e7
Electrical field (logarithmic scale)
10/9/2018

23. Tuning Sensitivity & Stiffness (Frederic Fors)
3D FE models have been created and analyzed in ANSYS Workbench 16.1, based on previous analysis work by Gary Cheng
Tuning sensitivity:
One end face of cavity is fixed with constraints in all directions (yellow)
Other end face is displaced 1 mm in the axial direction, other DOF’s constrained. (red)
Reaction force is obtained from constrained end surface to calculate cavity stiffness.
C100 helium vessel end discs and end cell stiffener rings added
10/9/2018

24. Tuning Sensitivity & Stiffness (Frederic Fors)
5-cell cavity with 3mm wall thickness with end cell stiffeners
Stiffening ring radius (mm) c
f1 (MHz)
f2 (MHz)
Δf (Hz)
df/dL
(kHz/mm)
Tuning Force
(N)
Tuning Stiffness (lbf/in)
72.5
949.38
949.67
295.79
2861.9
16342 80
949.37
949.68
307.26
4601.9
26278 85
949.69
315.43
6410.2
36603 90
949.70
324.37
8672.5
49521
100
949.71
332.15
73482
5-cell cavity with 4mm wall thickness
Stiffening ring radius (mm) c
f1 (MHz)
f2 (MHz)
Δf (Hz)
df/dL
(kHz/mm)
Tuning Force
(N)
Tuning Stiffness (lbf/in)
949.37
949.64
266.47
2565.0
14647
72.5
949.66
298.10
4748.3
27114 80
949.67
307.23
6386.1
36465 90
949.68
317.98
9147.1
52231
100
949.69
323.00
66828
110
320.54
76090
120
315097
315.10
80942
130
311.55
84381
10/9/2018

25. Tuning Sensitivity (Frederic Fors)
10/9/2018

26. Tuning Stiffness (Frederic Fors)
Horizontal lines indicate levels without stiffener rings
10/9/2018

27. Pressure Sensitivity (Frederic Fors)
Tuning sensitivity:
One end face of cavity is constrained in the axial direction (yellow)
Pressure load of 1 bar applied over the outer surface of the cavity (red)
Spring representing a stiff tuner connects the two end surfaces of the cavity (Ktuner = kN/mm ( lbf/in))
10/9/2018

28. Pressure Sensitivity (Frederic Fors)
5-cell cavity with 3mm wall thickness with end cell stiffeners
Stiffening ring radius (mm) c
f1 (MHz)
f2 (MHz)
Δf (Hz)
df/dP
(Hz/torr)
(Hz/mbar)
Smax (excl. cav ends) (MPa)
72.5
949.33
949.32
-11.04
-8.28
13.87 80
949.31
-13.77
-10.33
14.41 85
-15.11
-11.33
14.89 90
949.34
-15.8
-11.85
15.19
100
-15.69
-11.77
23.59
5-cell cavity with 4mm wall thickness
Stiffening ring radius (mm) c
f1 (MHz)
f2 (MHz)
Δf (Hz)
df/dP
(Hz/torr)
(Hz/mbar)
Smax (excl. cav ends) (MPa)
949.3
949.26
-56.95
-42.71
8.52
72.5
949.31
949.27
-54.87
-41.16
14.46 80
-49.95
-37.46
16.73 90
949.28
-41.33
-31.00
16.55
100
-33.72
-25.29
19.71
110
949.29
-28.52
-21.39
12.65
120
-19144
-25.52
-19.14
8.802
130
-24.2
-18.15
8.827
10/9/2018

29. Pressure Sensitivity (Frederic Fors)
10/9/2018

30. Modal Analyses (Frederic Fors)
Comparison between the first 6 modes of the unstiffened 4 mm cavity and the 3 mm cavity with 6x 85 mm stiffener rings
Modes marked in yellow will be suppressed by the use of a spider stiffener on the middle cell
5-cell cavity with 4mm wall thickness,
no stiffeners
5-cell cavity with 3mm wall thickness
with end cell stiffeners (6 x 85 mm rings)
Mode No.
f (Hz)
Description 1
30.8
1st order bending 2
104.9
2nd order bending 3
137.6
1st order axial 4
187.5
3rd order bending 5
249.7
4th order bending 6
269.4
2nd order axial
Mode No.
f [Hz]
Description 1
71.075
1st order bending 2
236.01
Axial 3
240.39
2nd order bending 4
433.54
3rd order bending 5
467.96
2nd order axial 6
742.5
4th order bending
Findings:
The end rings added to the 3 mm cavity increases its axial stiffness and lowers the pressure sensitivity
85 mm rings are chosen to keep the tuning stiffness under lbf/in
However, the smaller 85 mm rings makes the cavity weak in bending, and the modal performance is therefore worse than for the 3mm cavity with 4x110 mm rings

32. Backup Slides
10/9/2018

33. Comparison of Cavity Parameters for Existing Designs
Unit
Value
cavity type
LHeC study
CEBAF HC
LCLS-II
(TESLA)
CEBAF OC
CEBAF LL
frequency
MHz
802
748.5
1300
1497
number of cells 5 9 7
Lactive mm
922.14
1000
500
700
R/Q = Veff2/(ω*W) Ω
583.4
518.8
1036.0
482.5
868.9
R/Q/cell
116.7
103.8
115.1
96.5
124.1 G
273.2
278.3
270.0
274.0
280.3
R/Q∙G/cell
 Ω2
31877
28876
31080
26441
34793
Eq. Diameter
323.12
352.73
206.60
187.03
173.99
Iris Diameter
115
140 70 53
Tube Diameter 78
Eq./Iris ratio
2.81
2.52
2.95
2.67
3.28
Wall angle (mid-cell)
deg.
13.31
 8.10
Epeak/Eacc (mid cell)
2.07
2.44
1.98
2.56
2.17
Bpeak/Eacc (mid cell)
mT/(MV/m)
4.00
4.24
4.17
4.56
3.74
kcc %
2.14
3.12
1.89
3.15
1.49
N2/kcc
11.71
8.01
42.97
7.94
32.89
cutoff TE11
GHz
1.53
1.25
2.25
2.51
cutoff TM01
1.996
1.64
2.94
10/9/2018

34. Comparison of Cavity Parameters for Existing Designs
Unit
Value
cavity type
CEBAF HC
TESLA
(e.g. LCLS-II)
CEBAF OC
CEBAF LL
LHeC study
(FM)
frequency
MHz
748.5
1300
1497
802
number of cells 5 9 7
Lactive mm
1000
500
700
922.14
R/Q = Veff2/(ω*W) Ω
518.8
1036.0
482.5
868.9
583.4
R/Q/cell
103.8
115.1
96.5
124.1
116.7 G
278.3
270.0
274.0
280.3
273.2
R/Q∙G/cell
 Ω2
28876
31080
26441
34793
31877
Eq. Diameter
352.73
206.60
187.03
173.99
323.12
Iris Diameter
140 70 53
115
Tube Diameter 78
Eq./Iris ratio
2.52
2.95
2.67
3.28
2.81
Wall angle (mid-cell)
deg.
13.31
 8.10
Epeak/Eacc (mid cell)
2.44
1.98
2.56
2.17
2.07
Bpeak/Eacc (mid cell)
mT/(MV/m)
4.24
4.17
4.56
3.74
4.00
kcc %
3.12
1.89
3.15
1.49
2.14
N2/kcc
8.01
42.97
7.94
32.89
11.71
cutoff TE11
GHz
1.25
2.25
2.51
1.53
cutoff TM01
1.64
2.94
1.996
Ranking 1 2 3 4 5
10/9/2018

35. Comparison of Cavity Parameters for Existing Designs
Unit
Value
cavity type
CEBAF HC
TESLA
(e.g. LCLS-II)
CEBAF OC
CEBAF LL
LHeC study
(FM)
JLEIC
frequency
MHz
748.5
1300
1497
802
952.6
number of cells 5 9 7
Lactive mm
1000
500
700
922.14
786.8
R/Q = Veff2/(ω*W) Ω
518.8
1036.0
482.5
868.9
583.4
569
R/Q/cell
103.8
115.1
96.5
124.1
116.7
113.8 G
278.3
270.0
274.0
280.3
273.2
273
R/Q∙G/cell
 Ω2
28876
31080
26441
34793
31877
31071
Eq. Diameter
352.73
206.60
187.03
173.99
323.12
272.66
Iris Diameter
140 70 53
115
100
Tube Diameter 78
Eq./Iris ratio
2.52
2.95
2.67
3.28
2.81
2.73
Wall angle (mid-cell)
deg.
13.31
 8.10
Epeak/Eacc (mid cell)
2.44
1.98
2.56
2.17
2.07
2.16
Bpeak/Eacc (mid cell)
mT/(MV/m)
4.24
4.17
4.56
3.74
4.00
4.03
kcc %
3.12
1.89
3.15
1.49
2.14
2.37
N2/kcc
8.01
42.97
7.94
32.89
11.71
10.57
cutoff TE11
GHz
1.25
2.25
2.51
1.53
1.76
cutoff TM01
1.64
2.94
1.996
2.29
10/9/2018

36. Five-Cell Cavity Parameters
Unit
Value
frequency
MHz
952.6 (cold, vacuum with tuner)
952.3 (cold, vacuum VTA)
(warm, vacuum before chemistry)
R/Q (β = 1) Ω
569.04 G
273.01
R/Q *G Ω2
155355
Transit Time Factor
0.720
Epeak/Eacc
2.16
Bpeak/Eacc
mT/(MV/m)
4.03
Lactive mm
786.77
κ=Sqrt(R/Q)/L
√Ω/m
30.32
Tube length (3 half cell length each side)
236.03
Ltotal
Iris/Tube ID
100
kcc (cell-to-cell coupling) %
2.37
Total surface area
cm2
Tube surface area
1483.0
Cavity surface w/o beam tube
8631.4
Total volume
cm3
10/9/2018

37. Comparison of Main JLEIC Five-cell Candidate Shapes
Parameter
Unit
Value
Cavity type
JLEIC
(JG)
(FM)
Frequency
MHz
952.6
Number of cells 5
Lactive mm
770.7
786.8
R/Q = Veff2/(ω*W) Ω
574.7
569.0
R/Q/cell
114.9
113.8 G
279.6
273.0
R/Q∙G
 Ω2
160667
155355
Flat equator (each mid cell) +8
Flat equator (each end cup)
-0.043
+2.11
Eq. Diameter
276.8
272.7
Iris Diameter
100
Tube Diameter
Eq./Iris ratio
2.77
2.73
Wall angle (mid-cell)
deg.
Epeak/Eacc (mid cell)
2.42
2.16
Bpeak/Eacc (mid cell)
mT/(MV/m)
3.98
4.03
kcc %
2.81
2.37
N2/kcc
 1/%
8.90
10.57
Cutoff TE11
GHz
1.76
Cutoff TM01
2.29
3.3% deviation
10.6% deviation
1.3% deviation
15.7 % deviation
10/9/2018