1. RFQ Thermal Analysis Scott Lawrie

2. Vacuum Pump Flange Vacuum Flange Coolant Manifold Cooling Pockets Milled Into Vanes Potentially Bolted Together Tuner & Coupler Ports Vanes

3. Vane Cut-Back Vane End Cooling Pocket Shaped to Follow Vane Cut-Back Tuner & Coupler Ports O-Ring Joint to Mount to End Wall

4. RFQs normally use cooling channels Indian SNS: Six per quadrant American SNS: Four per quadrant Chinese SNS: Five per quadrant HINS (FNAL): Three per quadrant

5. Replace distributed channels with one cooling pocket Set of cooling channels drilled along length of vane

6. Replace distributed channels with one cooling pocket

7. Pocket milled into vane from air side Plate bolted on to cover the pocket and allow water in/out Baffle attached to cover plate; shaped to leave 2-3mm gap Water flow directed along gap between pocket and baffle Replace distributed channels with one cooling pocket

8. Cooling Pocket DisadvantagesAdvantages New, untested design Complicated water flow Unknown cooling efficiency Lots of material removed Novel Allows for 3D heat distribution Simple to manufacture No vacuum to water interfaces Flow can be directed where needed Highly configurable Easily adjusted & maintained Gap can be replaced with channels Could be the new standard!

9. ANSYS Coupled solver process Resonant frequency: High-frequency electromagnetic eigenmode solver Surface heat flux: Use macro to convert magnetic fields to thermal element loads Temperature distribution: Thermal solver Vane and wall displacement: Structural solver Frequency shift: Export results to MATLAB Slater perturbation algorithm

10. Model geometry (from Autodesk Inventor)

11. Simplified model with applied boundary conditions Vacuum body inside cavity Vacuum port pumping-slot cooling channels Tuner & coupler ports with integrated cooling Cooling pocket and baffle Vane end cut-back

12. Eigenmode Solver Surface H-Field Results Highest magnetic field intensity at vane end cut-back Magnetic field strongest at corners e.g. at tuners 2m

13. Eigenmode Solver Magnetic Field Vector Results H-Field flowing around vane cut-backs H-Field flowing past tuner port and vacuum pump slots

14. Eigenmode Solver Surface E-Field Results

15. Eigenmode Solver Electric Field Vector Results Quadrupole Mode 333.56 MHz (should be 324 MHz) Dipole Modes 330.02 MHz

16. Frequency varies with RFQ length Mode Frequency / MHz Resonant Frequency:

17. Total Surface Power Loss Heat Flux Per Element P solver = Calculated total surface power (W) ρ = Surface resistance (Ω) H = Tangential magnetic field at surface (T) dA = Area of surface mesh element (m 2 ) f = Cavity resonant frequency (Hz) µ 0 = permeability of free space (H m -1 ) σ = Conductivity of cavity walls (S m -1 ) F = Heat flux due to surface losses (W m -2 ) P real = Expected total surface power (W) where:

18. Surface heat flux Large power losses at vane end cut-back Relatively high heat loads at coupler, tuner and vacuum pump ports Heat flux / Wm -2 800 kW total peak RF power in 4 m RFQ  2.5 kW average power in this 1/32 model

19. Thermal solver solution Water-bath HTC = 3000 W m -2 K -1 Ports are well cooled Cooling pockets are able to remove bulk body heat Vane ends are not sufficiently cooled Copper Temperature / °C

20. Structural solver solution Walls move outward Vanes move inward Net 25 µm transverse expansion of vanes is within machining tolerances Longitudinal expansion of vane ends is unacceptably large Y-displacement Z-displacement Vane ends grow toward end wall by 70 µm

21. Frequency shift vs. RF power Frequency Decrease / kHz Maximum Temperature / °C Cooling Pocket HTC = 1000 Wm -2 K -1 Cooling Pocket HTC = 3000 Wm -2 K -1 Vane end temperature Cavity frequency shift

22. Max Temperature = 37 °C 60W input RF power ANSYS Simulation Cold Model Tests Temperature Rise 15 °C15.6 °C Frequency Shift -78 kHz-89 kHz Max Structural Deformation = 0.3 mm RFQ cold model with 60 W DC input RF power and no cooling applied.

23. Conclusions FETS RFQ will have a novel cooling system ANSYS used to assess performance Full 4m RFQ will have a higher frequency Cooling pockets successfully remove RF power Vane end not sufficiently cooled Vane displacements should not affect beam CFD simulations needed to predict HTCs Overall, cooling strategy seems to work!