Development of the SRF Cavity Design for the

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

ERL Baseline Conceptual Design Parameters from Haipeng Wang’s slides, Nov/2015 MEIC-ERL 1 for Electron Cooler, 952. 6 MHz Five-cell, Iris diameter = 100 mm, Low Loss (LL) shape cavity design JLab High Current (HC) for FEL-ERL Five-cell, Iris diameter = 70/140 mm (1497/748. 5 MHz) 11/6/2020 2 F. Marhauser

ERL Baseline Conceptual Design Parameters from Haipeng Wang’s slides, Nov/2015 On Crest Full Energy Gain 50 Me. V Full energy 55 Me. V Acceleration phase (0 on crest) -20 deg. Deceleration phase (0 on crest) 159 deg. Dechirper/rechirper RF peak voltage 1. 8 MV Dechirper/rechirper beam phase (0 on crest) -90/90 deg. Linac beam pass 2 Injector CW beam current 200, 2… m. A Bunch charge 420 p. C 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 11/6/2020 3 MV/m F. Marhauser

ERL Baseline Conceptual Design Parameters from Haipeng Wang’s slides, Nov/2015 On Crest Full Energy Gain 50 Me. V Full energy 55 Me. V Acceleration phase (0 on crest) -20 deg. Deceleration phase (0 on crest) 159 deg. Dechirper/rechirper RF peak voltage 1. 8 MV Dechirper/rechirper beam phase (0 on crest) -90/90 deg. Linac beam pass 2 Injector CW beam current 200, 2… m. A Bunch charge 420 p. C 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 11/6/2020 4 F. Marhauser

Comparison of Different Cavity Shapes on ERL Projects from Haipeng Wang’s slides, Nov/2015 r/l BERLin. Pro-ERL uses Cornell-ERL cavity shape 50 mm radius for 952. 6 MHz 0 0 z/(bl) 0. 5 11/6/2020 5 F. Marhauser

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 ~ N 2/kcc* δfcell, error) • N 2/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 11/6/2020 6 F. Marhauser

What are the Main Operational Constraints? • Given: Eacc = 10. 6 MV/m (CW) comparably low 19. 2 MV/m CW, spec’d for CEBAF upgrade (with contingency) 16 MV/m CW spec’d for LCLS-II 23. 2 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 11/6/2020 7 F. Marhauser

Field Emission 11/6/2020 8 F. Marhauser

Epk = 30 MV/m Field Emission C 100/R 100: Epk/Eacc = 2. 17 11/6/2020 9 F. Marhauser

What are the Main Operational Constraints? • Given: Eacc = 10. 6 MV/m (CW) comparably low 19. 2 MV/m CW, spec’d for CEBAF upgrade (with contingency) 16 MV/m CW spec’d for LCLS-II 23. 2 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 11/6/2020 10 F. Marhauser

How to make sure that one has obtained an optimum cell shape given all the trade-offs to make ? 11/6/2020 11 F. Marhauser

JLEIC Design Optimization All cells scaled to 952. 6 MHz and iris ID = 100 mm > 400 cell shapes Epk/Eacc = 2. 17 11/6/2020 12 F. Marhauser

JLEIC Design Optimization All cells scaled to 952. 6 MHz and iris ID = 100 mm > 400 cell shapes Epk/Eacc = 2. 17 11/6/2020 13 F. Marhauser

JLEIC Design Optimization Epk = 30 MV/m All cells scaled to 952. 6 MHz and iris ID = 100 mm Bpk < 60 m. T Epk < 30 MV/m Eacc = 10. 6 MV/m + 30% = 13. 8 MV/m 11/6/2020 14 F. Marhauser

JLEIC Design Optimization All cells scaled to 952. 6 MHz and iris ID = 100 mm Eacc = 10. 6 MV/m + 30% = 13. 8 MV/m Parameter Unit Value Value LCLS-II JLEIC cavity type LHe. C study CEBAF HC CEBAF OC CEBAF LL (TESLA) (JG) kcc % 2. 14 3. 12 1. 89 3. 15 1. 49 2. 81 2 N /kcc 11. 71 8. 01 42. 97 7. 94 32. 89 8. 90 11/6/2020 15 F. Marhauser Value JLEIC (FM) 2. 37 10. 57

New JLEIC Cavity Cell Multipacting Barrier 11/6/2020 16 F. Marhauser

Elliptical Cavity Cell Multipacting Barriers 11/6/2020 17 F. Marhauser

HOM Excitation 476. 3 MHz 1. 9052 GHz 952. 6 MHz Excitation lines from Haipeng Wang’s slides, Nov/2015 476. 3 MHz rep. rate 200 m. A injection current 11/6/2020 18 F. Marhauser

Higher Order Mode (HOM) Studies • Including 3 waveguide dampers (plus coaxial coupler) 11/6/2020 19 F. Marhauser

Higher Order Mode (HOM) Studies • Including 3 waveguide dampers (plus coaxial coupler) 11/6/2020 20 F. Marhauser

Higher Order Mode (HOM) Studies • Including 3 waveguide dampers (plus coaxial coupler) tube = 100 mm Ql~5 e 7 11/6/2020 21 F. Marhauser

Higher Order Mode (HOM) Studies • Trapped dipole mode pair close to beam tube cutoff 1794. 659 MHz, TM 111 /5 -mode Ql~4. 9 e 7 1794. 661 MHz, TM 111 /5 -mode Electrical field (logarithmic scale) Ql~5. 1 e 7 Electrical field (logarithmic scale) 11/6/2020 22 F. Marhauser

Tuning Sensitivity & Stiffness (Frederic Fors) • • 3 D FE models have been created 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. C 100 helium vessel end discs and end cell stiffener rings added 11/6/2020 23 F. Marhauser

Tuning Sensitivity & Stiffness (Frederic Fors) 5 -cell cavity with 3 mm wall thickness with end cell stiffeners Stiffening radius (mm) df/d. L Tuning Force c f 1 (MHz) f 2 (MHz) Δf (Hz) (k. Hz/mm) (N) Tuning Stiffness (lbf/in) 72. 5 949. 38 949. 67 295785. 57 295. 79 2861. 9 16342 80 949. 37 949. 68 307258. 43 307. 26 4601. 9 26278 85 949. 38 949. 69 315427. 43 315. 43 6410. 2 36603 90 949. 38 949. 70 324370. 57 324. 37 8672. 5 49521 100 949. 38 949. 71 332152. 59 332. 15 12868. 7 73482 df/d. L Tuning Force 5 -cell cavity with 4 mm wall thickness Stiffening radius (mm) c f 1 (MHz) f 2 (MHz) Δf (Hz) (k. Hz/mm) (N) Tuning Stiffness (lbf/in) 0 949. 37 949. 64 266472. 43 266. 47 2565. 0 14647 72. 5 949. 37 949. 66 298100. 6 298. 10 4748. 3 27114 80 949. 37 949. 67 307225. 24 307. 23 6386. 1 36465 90 949. 37 949. 68 317978. 44 317. 98 9147. 1 52231 100 949. 37 949. 69 322999. 23 323. 00 11703. 4 66828 110 120 949. 37 949. 69 949. 68 320539. 2 315097 320. 54 315. 10 13325. 4 14175. 1 76090 80942 130 949. 37 949. 68 311547. 06 311. 55 14777. 4 84381 11/6/2020 24 F. Marhauser

Tuning Sensitivity (Frederic Fors) 5 -cell Cavity Final 3 mm, w/ end rings 5 -cell Cavity Final 4 mm df/d. L (k. Hz/mm) 340 330 320 310 300 290 280 270 260 70 80 90 100 110 Stiffening radius (mm) 11/6/2020 25 120 F. Marhauser 130

Tuning Stiffness (Frederic Fors) 5 -cell Cavity Final 3 mm, w/ end rings 5 -cell Cavity Final 4 mm Tuning Stiffness (lbf/in) 90000 80000 70000 60000 50000 40000 30000 20000 10000 0 Horizontal lines indicate levels without stiffener rings 70 90 110 130 Stiffening radius (mm) 11/6/2020 26 F. Marhauser

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 = 530. 8 k. N/mm (3031000 lbf/in)) 11/6/2020 27 F. Marhauser

Pressure Sensitivity (Frederic Fors) 5 -cell cavity with 3 mm wall thickness with end cell stiffeners Stiffening radius (mm) df/d. P 72. 5 f 1 (MHz) 949. 33 f 2 (MHz) 949. 32 Δf (Hz) -8281. 34 (Hz/torr) -11. 04 (Hz/mbar) -8. 28 Smax (excl. cav ends) (MPa) 13. 87 80 949. 32 949. 31 -10332. 01 -13. 77 -10. 33 14. 41 85 949. 33 949. 32 -11330. 84 -15. 11 -11. 33 14. 89 90 949. 34 949. 32 -11847. 68 -15. 8 -11. 85 15. 19 100 949. 32 949. 31 -11766. 15 -15. 69 -11. 77 23. 59 df/d. P c 5 -cell cavity with 4 mm wall thickness Stiffening radius (mm) 0 f 1 (MHz) 949. 3 f 2 (MHz) 949. 26 Δf (Hz) -42713. 16 (Hz/torr) -56. 95 (Hz/mbar) -42. 71 Smax (excl. cav ends) (MPa) 8. 52 72. 5 949. 31 949. 27 -41158. 04 -54. 87 -41. 16 14. 46 80 949. 31 949. 27 -37462. 08 -49. 95 -37. 46 16. 73 90 949. 31 949. 28 -31000. 93 -41. 33 -31. 00 16. 55 100 949. 31 949. 28 -25288. 47 -33. 72 -25. 29 19. 71 110 120 130 949. 31 949. 29 -21392. 26 -19144 -18148. 58 -28. 52 -25. 52 -24. 2 -21. 39 -19. 14 -18. 15 12. 65 8. 802 8. 827 c 11/6/2020 28 F. Marhauser

Pressure Sensitivity (Frederic Fors) df/d. P (Hz/torr) 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 -110 5 -cell 3 mm Final, w/ End Rings 5 -cell 4 mm Final 70 80 90 100 110 Stiffening radius (mm) 11/6/2020 29 120 130 F. Marhauser

Modal Analyses (Frederic Fors) • Comparison between the first 6 modes of the unstiffened 4 mm cavity and the 3 mm cavity with 6 x 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 4 mm wall thickness, no stiffeners 5 -cell cavity with 3 mm wall thickness with end cell stiffeners (6 x 85 mm rings) Mode No. 1 2 3 4 5 6 f (Hz) 30. 8 104. 9 137. 6 187. 5 249. 7 269. 4 Description 1 st order bending 2 nd order bending 1 st order axial 3 rd order bending 4 th order bending 2 nd order axial f [Hz] 71. 075 236. 01 240. 39 433. 54 467. 96 742. 5 Description 1 st order bending Axial 2 nd order bending 3 rd order bending 2 nd order axial 4 th 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 40000 lbf/in • However, the smaller 85 mm rings makes the cavity weak in bending, and the modal performance is therefore worse than for the 3 mm cavity with 4 x 110 mm rings F. Marhauser

F. Marhauser

Backup Slides 11/6/2020 32 F. Marhauser

Comparison of Cavity Parameters for Existing Designs Parameter cavity type frequency number of cells Lactive R/Q = Veff 2/(ω*W) R/Q/cell G R/Q∙G/cell Eq. Diameter Iris Diameter Tube Diameter Eq. /Iris ratio Wall angle (mid-cell) Epeak/Eacc (mid cell) Bpeak/Eacc (mid cell) kcc N 2/kcc cutoff TE 11 cutoff TM 01 Unit MHz mm Ω Ω 2 mm mm mm deg. m. T/(MV/m) % GHz Value LHe. C study CEBAF HC 802 5 922. 14 583. 4 116. 7 273. 2 31877 323. 12 115 2. 81 0 2. 07 4. 00 2. 14 11. 71 1. 53 1. 996 748. 5 5 1000 518. 8 103. 8 278. 3 28876 352. 73 140 2. 52 0 2. 44 4. 24 3. 12 8. 01 1. 25 1. 64 11/6/2020 33 Value LCLS-II (TESLA) 1300 9 1036. 02 1036. 0 115. 1 270. 0 31080 206. 60 70 78 2. 95 13. 31 1. 98 4. 17 1. 89 42. 97 2. 25 2. 94 Value CEBAF OC CEBAF LL 1497 5 500 482. 5 96. 5 274. 0 26441 187. 03 70 70 2. 67 2. 56 4. 56 3. 15 7. 94 2. 51 3. 28 1497 7 700 868. 9 124. 1 280. 3 34793 173. 99 53 70 3. 28 8. 10 2. 17 3. 74 1. 49 32. 89 2. 51 3. 28 F. Marhauser

Comparison of Cavity Parameters for Existing Designs Parameter cavity type frequency number of cells Lactive R/Q = Veff 2/(ω*W) R/Q/cell G R/Q∙G/cell Eq. Diameter Iris Diameter Tube Diameter Eq. /Iris ratio Wall angle (mid-cell) Epeak/Eacc (mid cell) Bpeak/Eacc (mid cell) kcc N 2/kcc cutoff TE 11 cutoff TM 01 Unit Value CEBAF HC MHz mm Ω Ω 2 mm mm mm deg. m. T/(MV/m) % GHz 748. 5 5 1000 518. 8 103. 8 278. 3 28876 352. 73 140 2. 52 0 2. 44 4. 24 3. 12 8. 01 1. 25 1. 64 Ranking 1 TESLA (e. g. LCLS-II) 1300 9 1036. 02 1036. 0 115. 1 270. 0 31080 206. 60 70 78 2. 95 13. 31 1. 98 4. 17 1. 89 42. 97 2. 25 2. 94 2 11/6/2020 34 Value CEBAF OC CEBAF LL 1497 5 500 482. 5 96. 5 274. 0 26441 187. 03 70 70 2. 67 2. 56 4. 56 3. 15 7. 94 2. 51 3. 28 1497 7 700 868. 9 124. 1 280. 3 34793 173. 99 53 70 3. 28 8. 10 2. 17 3. 74 1. 49 32. 89 2. 51 3. 28 3 4 LHe. C study (FM) 802 5 922. 14 583. 4 116. 7 273. 2 31877 323. 12 115 2. 81 0 2. 07 4. 00 2. 14 11. 71 1. 53 1. 996 5 F. Marhauser

Comparison of Cavity Parameters for Existing Designs Parameter cavity type frequency number of cells Lactive R/Q = Veff 2/(ω*W) R/Q/cell G R/Q∙G/cell Eq. Diameter Iris Diameter Tube Diameter Eq. /Iris ratio Wall angle (mid-cell) Epeak/Eacc (mid cell) Bpeak/Eacc (mid cell) kcc N 2/kcc cutoff TE 11 cutoff TM 01 Unit MHz mm Ω Ω 2 mm mm mm deg. m. T/(MV/m) % GHz Value CEBAF HC 748. 5 5 1000 518. 8 103. 8 278. 3 28876 352. 73 140 2. 52 0 2. 44 4. 24 3. 12 8. 01 1. 25 1. 64 Value TESLA (e. g. LCLS-II) 1300 9 1036. 02 1036. 0 115. 1 270. 0 31080 206. 60 70 78 2. 95 13. 31 1. 98 4. 17 1. 89 42. 97 2. 25 2. 94 11/6/2020 35 Value CEBAF OC CEBAF LL 1497 5 500 482. 5 96. 5 274. 0 26441 187. 03 70 70 2. 67 2. 56 4. 56 3. 15 7. 94 2. 51 3. 28 1497 7 700 868. 9 124. 1 280. 3 34793 173. 99 53 70 3. 28 8. 10 2. 17 3. 74 1. 49 32. 89 2. 51 3. 28 Value JLEIC LHe. C study (FM) 802 5 922. 14 583. 4 116. 7 273. 2 31877 323. 12 115 2. 81 0 2. 07 4. 00 2. 14 11. 71 1. 53 1. 996 F. Marhauser 952. 6 5 786. 8 569 113. 8 273 31071 272. 66 100 2. 73 0 2. 16 4. 03 2. 37 10. 57 1. 76 2. 29

Five-Cell Cavity Parameters Parameter Unit frequency MHz frequency R/Q (β = 1) G R/Q *G Transit Time Factor Epeak/Eacc MHz Ω Ω Ω 2 Bpeak/Eacc m. T/(MV/m) 4. 03 Lactive κ=Sqrt(R/Q)/L Tube length (3 half cell length each side) Ltotal Iris/Tube ID kcc (cell-to-cell coupling) mm √Ω/m mm mm mm % 786. 77 30. 32 236. 03 1258. 83 100 2. 37 Total surface area cm 2 10114. 5 Tube surface area cm 2 1483. 0 Cavity surface w/o beam tube cm 2 8631. 4 Total volume cm 3 63405. 9 11/6/2020 36 Value 952. 6 (cold, vacuum with tuner) 952. 3 (cold, vacuum VTA) 949. 433 (warm, vacuum before chemistry) 569. 04 273. 01 155355 0. 720 2. 16 F. Marhauser

Comparison of Main JLEIC Five-cell Candidate Shapes Parameter Cavity type Frequency Number of cells Lactive R/Q = Veff 2/(ω*W) R/Q/cell G R/Q∙G Flat equator (each mid cell) Flat equator (each end cup) Eq. Diameter Iris Diameter Tube Diameter Eq. /Iris ratio Wall angle (mid-cell) Epeak/Eacc (mid cell) Bpeak/Eacc (mid cell) kcc N 2/kcc Cutoff TE 11 Cutoff TM 01 Unit MHz mm Ω Ω 2 mm mm mm deg. m. T/(MV/m) % 1/% GHz Value JLEIC (JG) 770. 7 574. 7 114. 9 279. 6 160667 -0. 043 276. 8 2. 77 2. 42 3. 98 2. 81 8. 90 11/6/2020 37 Value JLEIC (FM) 952. 6 5 +8 100 0 1. 76 2. 29 786. 8 569. 0 113. 8 273. 0 155355 3. 3% deviation +2. 11 272. 73 2. 16 4. 03 2. 37 10. 57 10. 6% deviation 1. 3% deviation 15. 7 % deviation F. Marhauser