1. RFQ End Flange Dipole Tuner Finger Cooling

2. Basis of Study Need multi-purpose end flange –Adjustable dipole mode suppression fingers –Beam current transformer toroid mount –Potentially high heat loads Not much room between LEBT and RFQ Want simple, compact cooling scheme Need estimates of cooling performance

3. First design from Pete 2cm 1cm 3cm 5cm 6mm 4cm 5cm

4. First Estimate of Heat Load FETS RFQ: 62 Wcm -2 at vane cut-back Assume less than half this on fingers? So 25 Wcm -2 is reasonable. IPHI RFQ end flange: 26 Wcm -2 on fingers (CW RFQ, though, so ours will have much less than this in reality, but 25 Wcm -2 will allow large safety margin)

5. Bulk copper in end flange is ~ 40 °C Finger gets pretty warm (100 °C) but that shouldn’t matter at all

6. As a Rough Example Simulation: 160W of heat per finger removed ok Indirect cooling means finger gets hot …but not enough to worry about Overall, this cooling strategy should be fine Assumes 25 Wcm -2 heat load (OVERESTIMATE!) Commence RF simulation to get better estimate of heat load on fingers

9. RF Simulation of Heat Load Internal vacuum of RFQ for solution of eigenmodes. Finger intrudes into vacuum. Parameterised to vary length and position. High resolution vacuum around finger.

10. End-on Views of RF Fields Around Finger Quadrupole magnetic field Dipole magnetic field 10mm diameter, 80mm long finger 15mm in x and y from beam axis 15mm 21.2mm

11. End-on Views of RF Fields Around Finger Quadrupole electric field Dipole electric field 10mm diameter, 80mm long finger 15mm in x and y from beam axis

12. Overall Body Surface Heat Flux (non-linear scale) Quadrupole heat flux Dipole heat flux 10mm diameter, 80mm long finger 15mm in x and y from beam axis

13. Cut-back and Finger Heat Flux (non-linear scale) Quadrupole heat flux Dipole heat flux > 50 Wcm -2 at vane cut-backs 10mm diameter, 80mm long finger 15mm in x and y from beam axis

14. Quadrupole heat flux Dipole heat flux Finger Surface Heat Flux 16 Wcm -2 on finger from dipole mode 3 Wcm -2 on finger from quadrupole mode 10mm diameter, 80mm long finger 15mm in x and y from beam axis 10mm 80mm

15. Variation of Finger Length 10mm diameter fingers of varying length 15mm in x and y from beam axis

16. Variation of Finger Position 10mm diameter, 80mm long fingers Vary finger distance from beam axis

17. Fingers allow very fine tuning of RFQ For optimal tunability, need: –Variable length (2 to 10cm) fingers –Close (< 5cm) to beam axis –Cooling close as possible to entrance hole Max. heat assumes resonating on the dipole mode which won’t be the case Overall, finger heat won’t be a problem Conclusion

18. Spare slides

19. 15°C Water in at 1 ms -1 flow rate Water out with temperature raised and at 0 Bar relative pressure 25 Wcm -2 heat flux load on finger High mesh density in region between finger and pipe Copper starting temperature = 22°C

20. Flow Estimates Total power, P, to be removed from each finger ≈ 160 W Water mass flow rate,, per pipe = 0.028 kgs -1 (assuming flow speed = 1 ms -1 = 1.7 l min -1 ) Estimated temperature rise, ΔT, of cooling water = 1.35 °C Pipe length, L, within copper = 10 cm Average water flow rate v av = 1 ms -1 Pipe diameter, D H = 6 mm Estimated pressure drop, Δp = 0.003 Bar Nusselt number, N u, of water flow = 55.03 Thermal conductivity of water, k = 0.6 Wm -1 K -1 Estimated heat transfer coefficient = 5500 Wm -2 K -1

21. Intersection of drilled pipes slightly disrupts smooth flow

22. Faster, disrupted flow round corner increases local HTC Average HTC ~ 6000 Wm -2 K -1 which agrees with estimate

23. Temperature rise of water ~ 2 °C which agrees with estimate

24. Pressure drop is slightly higher than estimate because the pipe doesn’t have a smooth bend at corner, but it’s still nice and low