RFQ Cooling Studies

ANSYS Multiphysics Analysis

f = 324MHzΔf ~ 100kHZΔf/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

dVHE

dVHE

f

f

V

V

)(

)(

20

20

20

20

Stored energy of entire cavity vacuum

Energy change due to deformed boundary

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

Electric field

Boundary mesh elements

Surface heat losses

E-field vectors show good quadrupole field

Max Temperature = 37 °C

60W input RF power

Simulation in ANSYS

Cold Model Tests

Temperature Rise / C

15 15.6

Frequency Shift / kHZ

-78 -89

Max Structural Deformation = 0.3 mm

Predictions for 200kW input RF power:

Temperature rise ~1500 °C

Frequency Shift ~ 3 MHZ(but irrelevant for molten copper!)

Cooling Pipe Flow RequirementsTcmP p 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)

v

mDAAvlAm

2

4If we allow a flow velocity of 5 ms-1,need pipe diameter of ~ 9 mm

25.1

75.15105D

vlxp For 1m long pipes,

required pressure drop ~0.3 Bar

Cooling Pipe Heat Transfer

D

kNhtc u

4.08.0023.0 Reu PRN

k

cP pR

2.0

8.0

1977D

vhtc

Can get Heat Transfer Coefficientof ~ 14000 W m-2 K-1

vD

Re

Proposed Pipe Positioning

Applied HTC = 10000 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!