1. RFQ Cooling Studies

2. ANSYS Multiphysics Analysis
Mesh and solve for resonant frequency of vacuum
Use surface EM results to calculate surface heat loads
Mesh and solve for temperature distribution in copper
Use temperature distribution as structural load for thermal expansion
Mesh and solve for structural displacements of copper
Morph vacuum to fit inside newly displaced copper cavity
f = 324MHz
Δf ~ 100kHZ
Δf/f ~ 1x10-4
Mesh not good enough?

3. Slater Perturbation Theorem
Electric and magnetic fields rearrange in a deformed cavity
∴ Resonant frequency of cavity varies when its boundary surfaces move
Energy change due to deformed boundary
Stored energy of entire cavity vacuum

4. Fill this copper volume with a vacuum body
Use vacuum to solve for resonant frequency
Use copper to solve for temperature and structural distributions

5. Magnetic field
Boundary mesh elements
Electric field
Surface heat losses

6. E-field vectors show good quadrupole field

7. Predictions for 200kW input RF power: Temperature rise ~1500 °C
Simulation in ANSYS
Cold Model Tests
Temperature Rise / C 15
15.6
Frequency Shift / kHZ
-78
-89
Max Temperature = 37 °C
Predictions for 200kW input RF power:
Temperature rise ~1500 °C
Frequency Shift ~ 3 MHZ
(but irrelevant for molten copper!)
Max Structural Deformation = 0.3 mm

8. Cooling Pipe Flow Requirements
For P = 200 kW and ΔT = 40 °C
Need mass flow of 1.19 kg s-1
(If split over 4 pipes, need 0.3 kg s-1 per pipe)
If we allow a flow velocity of 5 ms-1,
need pipe diameter of ~ 9 mm
For 1m long pipes,
required pressure drop ~0.3 Bar

9. Cooling Pipe Heat Transfer
Can get Heat Transfer Coefficient
of ~ W m-2 K-1

10. Proposed Pipe Positioning
Applied HTC = W m-2 K-1

11. Detailed Pipe Position Study

12. Detailed Pipe Position Study

13. Detailed Pipe Position Study

14. Detailed Pipe Position Study

15. Max x Displacement = 6 microns
Max y Displacement = 8 microns

16. Next Steps… Confirm optimum position of pipes
Put pipes into full 3D model
Predict operational temperatures and frequency shift
Work with Pete to make cooling circuit work in reality!