RFQ Cooling Studies.

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RFQ Cooling Studies

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?

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

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

Magnetic field Boundary mesh elements Electric field Surface heat losses

E-field vectors show good quadrupole field

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

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

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

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

Detailed Pipe Position Study

Detailed Pipe Position Study

Detailed Pipe Position Study

Detailed Pipe Position Study

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

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!