1. 56 MHz SRF Cavity Thermal Analysis and Vacuum Chamber Strength C. Pai 1-19-2011

2. Thermal Analysis of Transition adaptor

3. Purpose of the calculation 1. Verify the function of the thermal transition. The thermal transition is a bridge to connect the superconducting cavity to the room temperature cryostat. It should minimize the heat load into SRF cavity. This thermal transition has no cooling tube attached. 2. Calculate the total heat load input from room temperature to the superconducting Cavity from 3 sources. 2.1 Conduction from cryostat to the cavity. 2.2 Radiation heat from room temperature beam pipe into cavity space. This heat is conservatively assumed that half of the radiation heat is deposited in the neck of the tuner plate. 2.3 Heat generated by field emission current in the cavity gap. The field emission heat is when gap temperature is kept at 6.5 K. 3. Calculate the maximum temperature in the tuner plate. 4. Calculate the heat load in the Helium bath and Cooling channel.

4. Thermal Transition of 56 MHz cryomodule Thermal Transition SRF Cavity Cryostat Tuning plate Connecting yoke

5. ANSYS Model of Thermal transition with tuner plate for heat transfer analysis Tuning Plate Nb Formed Head Double welded bellow Formed bellow End flange Welded to vacuum chamber Tuner yoke with Helium channel embedded Beam pipe Flange Cooling Channel

6. Note: The Tuner yoke has liquid Helium channel embedded (Cold anchor) Tuner Yoke with Helium flow Channel

7. Case 1, Heat leak from cryostat only, No radiation and field emission heat in the gap Helium channel, at 4.5 K Brass threaded rod Room temperature Helium Temperature 4.5 K

8. Result of case 1, Overall Temperature distribution Heat input from cryostat only, No radiation and field emission heat in the gap 300 K Vacuum chamber: Q= +.294 W Pipe flange: Q: +.0191 W Helium head Q: -.298 W Tuner RF body, cooling channel Q: -.005 W Yoke anchor Q: -.010 W Total Q: +.313 W Q: -.313 W 4.5 K

9. 4.537 K 4.5 K Result of case 1, Tuner Neck temperature Heat input from cryostat only, No radiation and no field emission heat in the gap

10. 4.5 K 4.87 K Result of case 1, Yoke and tuner neck Temperature, Heat input from cryostat only, No radiation and field emission heat in the gap

11. Case 2, Heat input from cryostat plus radiation heat. No field emission heat in the gap Radiation heat: half of 3.38 watt (in half model) deposited in the neck of tuner plate Room temperature

12. 300 K Vacuum chamber: Q= +.294 W Pipe flange: Q: +.0192 W Helium head Q: -.299 W Tuner RF body, cooling channel Q: -.815 W Yoke anchor Q: -.0489 W Radiation heat Q: +.85 W Total Q: +1.163 W Q: -1.163 W 4.5K Result of case 2, Overall Temperature distribution Heat input from cryostat plus radiation. No field emission heat in the gap

13. 4.5K 6.84K Result of case 2, Tuner Yoke and neck temperature, Heat input from cryostat plus radiation. No filament current heat in the gap 6.30K

14. From Field emission heat, T= 6.5 K Case 3, Heat input from cryostat, plus radiation and Field emission heat in the gap Radiation heat: half of 3.38 watt (in half model) deposited in the neck of tuner plate Room temperature

15. 300 K Vacuum chamber: Q= +.293 W Pipe flange: Q: +.0192 W Helium head Q: -.299 W Tuner RF body, cooling channel Q: -7.494 W Yoke anchor Q: -.0696 W Radiation heat Q: +.85 W Total Q: +7.862 W Q: -7.764 W 4.5K Field emission heat: Q: +6.7 W Result of case 3, Overall Temperature distribution Heat input from cryostat plus radiation and field emission heat in the gap

16. 4.5K 7.73K 6.5 K Assumed by filed emission heat Result of case 3, Tuner Yoke and neck temperature, Heat input from cryostat plus radiation and filed emission heat in the gap 7.0K

17. Summary of results (Note number is for whole model) Case 1: Heat leak: From cryostat only, No radiation or field emission heat in the gap Heat load in the system: Total:.626 W From: Cryostat, +.626 W To: Helium Bath, -.616 W Tuner plate and cooling channel, -.01 W Maximum temperature: (Helium at 4.5 K) At end tip of Tuner plate : 4.537 K At Tuner Yoke: 4.87 K Case 2: Heat input: From cryostat plus Radiation. No field emission heat in the gap Heat load in the system: Total: 2.326 W From: Cryostat,+.626 W Radiation, +1.70W (Conservatively, in the neck of tuner plate) To: Helium Bath: -.695 W Tuner plate and cooling channel: -1.63 W Maximum temperature: (Helium at 4.5 K) At end tip of Tuner plate : 6.84 K, most of the neck is below 6.3 K At Tuner Yoke: 6.84 K

18. Summary of results (Continue) Case 3: Heat input: Heat input from cryostat plus radiation and field emission heat in the gap Heat load in the system: Total: 15.724 W From: Cryostat, +.624 W Radiation: +1.7 W Field emission heat : + 13.4 W (when Gap Max. T at 6.5 K) To: Helium Bath, -.737 W Tuner plate and cooling channel, -14.988 W Maximum temperature: (Helium at 4.5 K) At end tip of Tuner plate : 7.73K, At Cavity Gap: 6.50 K At Tuner Yoke: 7.73K

19. Model, 56 MHz SRF Cavity Vacuum chamber Thickness: Cylinder: 5/16” Head:.375” Material: SS304 Yield strength: 30,000 psi

20. Displacement, in cylindrical coordinate, radial Under Vacuum P=14.7 psi Cylindrical Coordinate Max :.0216”

21. Equivalent Stress, cylinder shell Max. Equivalent stress” S=4,600 psi Yield Strength: 30,000 psi Allowable: Membrane: 20,000 psi Bending: 30,000 psi

22. Equivalent Stress, cylinder shell Max. Equivalent stress” S=3,971 psi Yield Strength: 30,000 psi Allowable: Membrane: 20,000 psi Bending: 30,000 psi

23. Equivalent Stress, 3 port Head Max. Equivalent stress” S=7,680, psi Yield Strength: 30,000 psi Allowable: Membrane: 20,000 psi Bending: 30,000 psi

24. Equivalent Stress, 4 port Head Max. Equivalent stress” S=5,345 psi Yield Strength: 30,000 psi Allowable: Membrane: 20,000 psi Bending: 30,000 psi

25. Buckling Multiplier in cylinder, M=12.39,> 2.5 (Cylinder) P=14.7 psi ASME Viii-2 Required Multiplier for Cylinder: 2.5

26. Buckling Multiplier in Head, M=91.5,>16.13 (head) ASME Viii-2 Required Multiplier for head: 16.13

27. Cost Estimate of Cryomodule Assembly Mach. Mat. CostEstimate HrMach. Cost hr 1Vacuum chamber$78,650730$80,300 2Thermal transition$5,284136$14,960 3Outer Magnetic shield$19,669100$11,000 4Space frame$19,69876$8,360 5Outer Super insulation$2,580 5Thermal heat shield$1,735104$11,440 6Middle Super insulation$2,720 7Inner Magnetic shield$12,176160$17,600 8Inner super insulation$1,875 9Radial Nitrionic Rod 8 sets$96048$5,280 10Axial Nitronic Rod, 8 sets$96048$5,280 11Nuts, and bolts, etc$6,80056$6,160 12Welding, cryo and vacuum120$13,200 13RF-Shielded Gate Valves (2)$78,000 14Misc. Components$18,530 $249,6371578$173,580 $hr$ Total Mat.Mach.