RFQ End Flange Dipole Tuner Finger Cooling. Basis of Study Need multi-purpose end flange –Adjustable dipole mode suppression fingers –Beam current transformer.

RFQ End FlangeDipole Tuner Finger Cooling

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

First design from Pete

2cm

1cm

1cm3cm

5cm

6mm

4cm

5cm

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)

Bulk copper in end flange is ~ 40 °C

Finger gets pretty warm (100 °C) but that shouldn’t matter at all

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

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.

End-on Views of RF Fields Around Finger

Quadrupole magnetic field Dipole magnetic field

10mm diameter, 80mm long finger15mm in x and y from beam axis

15mm

15mm21.2mm

End-on Views of RF Fields Around Finger

Quadrupole electric field Dipole electric field


Overall Body Surface Heat Flux(non-linear scale)

Quadrupole heat flux Dipole heat flux


Cut-back and Finger Heat Flux(non-linear scale)


> 50 Wcm-2 at vane cut-backs



Finger Surface Heat Flux

16 Wcm-2 on finger from dipole mode3 Wcm-2 on finger from quadrupole mode


10mm

80mm

Variation of Finger Length

10mm diameter fingers of varying length15mm in x and y from beam axis

Variation of Finger Position

10mm diameter, 80mm long fingersVary finger distance from beam axis

• 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

Spare slides

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

Flow Estimates

pcm

PT

2504.1

7513.1

1419.5H

av

D

vLp

H

u

D

kNHTC

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 cmAverage water flow rate vav = 1 ms-1

Pipe diameter, DH = 6 mmEstimated pressure drop, Δp = 0.003 Bar

m

Nusselt number, Nu, of water flow = 55.03Thermal conductivity of water, k = 0.6 Wm-1K-1

Estimated heat transfer coefficient = 5500 Wm-2K-1

Intersection of drilled pipes slightly disrupts smooth flow

Faster, disrupted flow round corner increases local HTC

Average HTC ~ 6000 Wm-2K-1 which agrees with estimate

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

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

RFQ End Flange Dipole Tuner Finger Cooling. Basis of Study Need multi-purpose end flange –Adjustable dipole mode suppression fingers –Beam current transformer.

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