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RFQ Cooling Studies

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**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?

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**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

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**Fill this copper volume with a vacuum body**

Use vacuum to solve for resonant frequency Use copper to solve for temperature and structural distributions

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Magnetic field Boundary mesh elements Electric field Surface heat losses

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**E-field vectors show good quadrupole field**

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**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

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**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

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**Cooling Pipe Heat Transfer**

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

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**Proposed Pipe Positioning**

Applied HTC = W m-2 K-1

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**Detailed Pipe Position Study**

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**Detailed Pipe Position Study**

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**Detailed Pipe Position Study**

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**Detailed Pipe Position Study**

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**Max x Displacement = 6 microns**

Max y Displacement = 8 microns

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**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!

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