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

56 MHz SRF Cavity Thermal Analysis

and Vacuum Chamber Strength

C. Pai1-19-2011

Thermal Analysis of Transition adaptor

Purpose of the calculation1. 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.

Thermal Transition of 56 MHz cryomodule

Thermal Transition

SRF Cavity

Cryostat

Tuning plate Connecting yoke

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

Note: The Tuner yoke has liquid Helium channel embedded (Cold anchor)

Tuner Yoke with Helium flow Channel

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 Temperature4.5 K

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 headQ: -.298 W

Tuner RF body , cooling channel Q: -.005 W

Yoke anchorQ: -.010 W

TotalQ: +.313 WQ: -.313 W

4.5 K

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

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

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

300 K




Tuner RF body , cooling channel Q: -.815 W


Radiation heatQ: +.85 W

TotalQ: +1.163 WQ: -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

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

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

300 K




Tuner RF body , cooling channel Q: -7.494 W


Radiation heatQ: +.85 W

TotalQ: +7.862 WQ: -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

4.5K

7.73K

6.5 KAssumed 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

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

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

Model, 56 MHz SRF Cavity Vacuum chamber

Thickness:Cylinder: 5/16”Head: .375”Material: SS304Yield strength: 30,000 psi

Displacement, in cylindrical coordinate, radialUnder Vacuum P=14.7 psi

Cylindrical Coordinate

Max : .0216”

Equivalent Stress, cylinder shell

Max. Equivalent stress”S=4,600 psi

Yield Strength: 30,000 psiAllowable:Membrane: 20,000 psiBending: 30,000 psi

Equivalent Stress, cylinder shell

Max. Equivalent stress”S=3,971 psi


Equivalent Stress, 3 port Head

Max. Equivalent stress”S=7,680, psi


Equivalent Stress, 4 port Head Max. Equivalent stress”S=5,345 psi


Buckling Multiplier in cylinder, M=12.39,> 2.5 (Cylinder)

P=14.7 psi

ASME Viii-2Required Multiplier for Cylinder: 2.5

Buckling Multiplier in Head, M=91.5,>16.13 (head)

ASME Viii-2Required Multiplier for head: 16.13

Cost Estimate of Cryomodule AssemblyMach.

Mat. Cost Estimate Hr Mach. Costhr

1 Vacuum chamber $78,650 730 $80,3002 Thermal transition $5,284 136 $14,9603 Outer Magnetic shield $19,669 100 $11,0004 Space frame $19,698 76 $8,3605 Outer Super insulation $2,5805 Thermal heat shield $1,735 104 $11,4406 Middle Super insulation $2,7207 Inner Magnetic shield $12,176 160 $17,6008 Inner super insulation $1,8759 Radial Nitrionic Rod 8 sets $960 48 $5,280

10 Axial Nitronic Rod, 8 sets $960 48 $5,28011 Nuts, and bolts, etc $6,800 56 $6,16012 Welding, cryo and vacuum 120 $13,20013 RF-Shielded Gate Valves (2) $78,00014 Misc. Components $18,530

$249,637 1578 $173,580$ hr $

Total Mat. Mach.

Documents

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