Thermal model for Nb3Sn Inner Triplet quadrupoles - 140 mm aperture option

Hervé Allain, R. van Weelderen (CERN)

4th September 2012

Overview• General aspect• Cases considered – proposed features• Coil insulations• Typical to be expected T-map for a coil with cooling

at 1.9 K up to 2.05 K• Parametric study•Main observations• Proposed features

Coil cooling principle•Heat from the coil area (green) and heat from the beam pipe (purple) combine in the annular space between beam pipe and coil and escape radially through the magnet “pole” towards the cold source “pole, collar and yoke” need to be “open”

•Heat Conduction mechanism in the coil packs principally via the solids, except for dedicated helium channels deliberately machined in the midplane

•Longitudinal extraction via the annular space is in superfluid helium, with T close to Tλ and with magnets up to 7 m long not reliable “pole, collar and yoke” need to be “open”

≥ 1.5 mm annular space

Superfluid helium cooling, 140 mm aperture, 2 cases considered:3.7 mm cold bore + 7 mm W inserts3.7 mm cold bore + 2 mm beam screen + 6 mm W absorbers

Proposed features

Feature Value comments

Annular gap 1.5 mm Safest choice for cooling and pressure rise due to quench

(to be verified)collar open 2 % Can be lower in steady state

Dynamic to be verifiedYoke open 2 % Can be lower in steady state

Dynamic to be verifiedTitanium piece open 4 % More investigation needed with the

real holesAluminium collar keys 4 % More investigation needed with the

real holesMidplane open

Beam screen actively cooled by helium channels

4 x 4.5 – 4.7 mm ID or8 x ~ 3.4 mm ID

estimated for ~ 400 W total

2 heat exchangers 68 mm ID calculated for ~ 500 W total

Some Materials thermal properties need to be measured

Naked coil in He II bath assumed for calculations to evaluate the best case

• Cable: 0.15 mm G-10 insulated

• 2-3-4 have been homogenized to form one mono layer

• Lack of some material thermal properties: need to be measured

2) 50 µm kapton + 25 µm stainless steel 50 % filled3) 200 µm G-104) 0.5 mm kapton

0.5 mm G-10

Inner coil layer Outer coil layerCold bore

Collars

2 3 4

1) 1.5 mm annular space1

0.5 mm G-10

Inner coil layer Outer coil layer

21 & 2: superfluid helium

1

Coil magnet configuration assumed for calculations

• Cable: 0.15 mm G-10 insulated

Energy deposition 2D map for Q1 at peak power

Courtesy of F. Cerutti and L. Salvatore

1) 3.7 mm cold bore + 7 mm W inserts 2) 3.7 mm cold bore + 6 mm W inserts + Beam Screen

Corresponding Energy deposition used for the model on the coil

Same heat load on the coil (~16 W/m)peak at 4.6 mW/cm3

Difference between 1 and 2: heat load on the cold bore -> 55.6 W/m2 for 1 and 6.8 W/m2 for 2

Absorbed by the heat exchanger

Simulated T-distribution

coils in a He II bath at 1.9 k coils in magnet configuration - HX at 1.9 kHe II channels in midplane (4 % open)

T He II midplane

Midplane He II channels closed 1 side open 2 sides open

T max (K) coils in a He II bath at 1.9 k 2.243 2.075 2.069

T max (K) coils in magnet configuration - HX at 1.9 k

3.265 2.396 2.377

ΔT (K) 1.022 0.321 0.308

Dangerous:T max He II midplane ~ 2.06 K

Too close to TLamda

Safe: T max He II midplane ~ 1.93 K~ Maximum effective

thermal conductivity of He II

Parametric study (1/2)

• Variation of the heat exchanger temperature• Midplane 4 % open, 2 sides open• Annular space: 1.5 mm

1.88 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 2.060

0.005

0.01

0.015

0.02

0.025

0.03ΔT max annular space

no beam screen, HeII channel 2 sides openbeam screen, He II channel 2 side openno beam screen, no He II channel

T heat exchanger

ΔT (K

)

1.88 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 2.060

0.05

0.1

0.15

0.2

0.25

0.3 ΔT max midplaneno beam screen, HeII channel 2 sides openbeam screen, He II channel 2 side openTlamda-Theat exchanger

T heat exchanger

ΔT (K

)

1.88 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 2.060.4

0.450.5

0.550.6

0.650.7

0.750.8

0.850.9

ΔT max on the coil

no beam screen, HeII channel 2 sides open

beam screen, He II channel 2 side open

no beam screen, no He II channel

T heat exchanger

ΔT (K

)

Parametric study (2/2)

• Variation of the midplane % open• 2 sides open• THX = 2.05 K• Annular space: 1.5 mm

He II -> He I in themidplane -> too dangerous

BS, if ≤ 2 % openno BS , if ≤ 3 % open

Remark:

3 4 5 6 7 8 9 10 110

0.02

0.04

0.06

0.08

0.1

0.12

0.14ΔT max midplane

no beam screenbeam screenDTlamda

% midplane open

ΔT (K

)

3 4 5 6 7 8 9 10 110.4320.4340.4360.438

0.440.4420.4440.4460.448 ΔT max on the coil

no beam screenbeam screen

% midplane open

ΔT (K

)

3 4 5 6 7 8 9 10 110

0.0005

0.001

0.0015

0.002

0.0025ΔT max annular space

no beam screenbeam screen

% midplane open

ΔT (K

)

Main ObservationsMidplane opened:

• Midplane open means He II channels in the midplane which communicate with the annular space and He II in space between laminations (NEED OF A WAY FOR THE HEAT TO GO TO THE HEAT EXCHANGER)

• Temperature field : 500 mK < Tmax coil – THX

• 7 mm W insert or 6 mm W insert + beam screen: • 1 side open Tmax HeII midplane over Tlamda (except for very low HX temperatures)

• 2 sides open assures functionality up to 2.05 K

• Safest choice: midplane > 7 % open (transits from He II to He I for Midplane ≤ 4 %)

• Caution: midplane taken open to He II homogeneously, more investigations needed with the real channels and experiments must be planned to assess the efficiency of the chosen geometry and design

Proposed featuresFeature Value comments

Annular gap 1.5 mm Safest choice for cooling and pressure rise due to quench

(to be verified)collar open 2 % Can be lower in steady state

Dynamic to be verifiedYoke open 2 % Can be lower in steady state

Dynamic to be verifiedTitanium piece open 4 % More investigation needed with the

real holesAluminium collar keys 4 % More investigation needed with the

real holesMidplane open 7 %

(≈ 35 µm for a 500 µm midplane spacing)

Assures functionality up to 2.05 KBeware of slit compression, actual size needs experimental validation

Beam screen actively cooled by helium channels

4 x 4.5 – 4.7 mm ID or8 x ~ 3.4 mm ID

estimated for ~ 400 W total

2 heat exchangers 68 mm ID calculated for ~ 500 W total

Some Materials thermal properties need to be measured

References1. “Investigation of Suitability of the Method of Volume Averaging for the

Study of Heat Transfer in Superconducting Accelerator Magnet Cooled by Superfluid Helium”, H. Allain, R. van Weelderen, B. Baudouy, M. Quintard, M. Prat, C. Soulaine, Cryogenics, Available online 14 July 2012.