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Cooling MICE magnets and the Absorbers with Small Coolers?

Michael A Green

Oxford University Physics

Oxford OX1 3RH, UK

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The Sumitomo SDRK 415-D GM Cooler

300 K Attachment Ring

Cryocooler First StageT = 25 K to T = 80 K

Cryocooler Second StageT = 2.5 K to T = 20 K

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Characteristics of the 415D GM Cooler

• 1.5 W is delivered at 4.2 K at the second stage.

• 18 W is delivered at 15 K at the second stage.

• With 50 Hz power, the cooler delivers 38 W at 50 K at the first stage.

• Cooling delivered at both stages concurrently.

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Sumitomo SDRK 415-D Two-Stage GM 4.2 K Cooler Characteristics

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What is required to use a cooler to cool a magnet?

• The magnet heat load at must be less than the cooler capacity at 4.2 K.

• The lower magnet current leads must be high temperature superconductor (HTS), in order to get the 4.2 K heat load down to a reasonable level.

• The first stage heat leak is dominated by the upper magnet current leads.

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Cooler Requirements for MICE Magnets

• The coupling coils have a single pair of 300 A leads. Use a single 1.5 W cooler. 1 cooler T = 3.9 K

• The focusing coils have two pairs of 300 A leads. Use two coolers. 1 cooler T = 4.7 K; 2 coolers T = 3.6 K

• The detector magnet has five coils. Each magnet coil has a pair of 300 A leads. Three coolers are needed. 2 coolers T = 5.1 K; 3 coolers T = 4.2 K

• As many as fourteen coolers may be needed to cool the MICE magnets.

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Connection of the Cooler to the Load

• If one wants to cool a magnet down with a cooler, the cooler second stage must be connected directly to the magnet with a flexible OFHC copper strap. The first stage can be connected to the shields using a copper strap.

• The temperature drop between the magnet high field point and the cooler cold head has a negative effect on magnet operation. Even a 0.4 K temperature drop will affect the performance of the MICE coupling and focusing coils.

• A gravity separated heat pipe can connect the cooler 2nd stage cold head to the load with a very low temperature drop (0.1 to 0.2 K) between the magnet hot spot and the cold head.

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Why is T so important?

9.08.58.07.57.06.56.0150

175

200

225

250

275

300

T = 4.2 KT = 5.0 KCouplingFocusing

Magnetic Induction in the Wire (T)

Con

du

ctor

Cu

rren

t (A

)

4.4 K

4.6 K

4.8 K5.2 K

5.4 K5.6 K

5.0 K

4.2 K

The line labelled with a temperature are lines of Ic versus B at the MRI superconductor. The heavy lines are the magnetcurrent versus peak B inthe superconductor.

The triangles and squaresat low B are the 200 MeV/c case. The same symbols at high B are the 240 MeV/ccase for MICE.

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Cooler Connection through a Flexible Strap

The temperature drop from the load to the cold head is proportional to the strap length and inversely proportional to the strap area and the strap thermalconductivity.

T L

kATc

Tc = contact resistance

Tc is usually small.

P

Q

T3T2

T1

T0

Cryocooler Cold Head

Cryostat Boundary

Cooling Cryogen

Cooled Load

Liquid Fill Valve (if needed)

Relief Valve

Flexible Cu Strap

T = T3 - T0

10Details of the Copper Strap Arrangement

Note: For T = 0.1 K, L = 0.15 m, andk = 600 W m-1 K-1, then A = 0.0025 m-2

and Tc = 0.

Note: For T = 5 K, L = 0.3 m, andk = 1000 W m-1 K-1, then A = 0.00006 m-2

and Tc = 0.

In addition heat flow through 6061 Alis quite poor at 4 K (k = 6 W m-1 K-1).

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T = 4.085K

4.3 K

QR = 1 W m-2

Temperature Drop in the Coupling Coil with 4.3 K Cooling at One Point

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Cooler Connection through a Heat Pipe

The temperature drop from the load to the cold head is independent of the distance between the load and the cooler cold head.

Liquid He distributes the cold around the coil.

T Tb Tf TcP

Q

T3T2

T1

T0H

h = head for circulating the liquid cryogen

Cryocooler Cold Head

Condensation Plate

Cryostat Boundary

Liquid Tube (any length)

Gas Tube (any length)

Cooling Cryogen

Cooled Load

Gas Charge Valve (if needed)

Relief ValveTb = Boiling T DropTf = Condensing T DropTc = Contact ResistanceThese can be made small.

T = T3 - T0

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Temperature distribution inThe Coupling Coil CooledAll Around QR = 1 W m-2

∆T = 0.268K (4.3~4.568K)

T = 4.57 K

T = 4.3 K

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Cooler Requirements for the Absorbers

• The absorber total heat leak should be 10 W or less. Beam heating and dark are not a factor in MICE.

• A single cooler should be capable of holding the intrinsic heat load into a MICE liquid hydrogen absorber. Direct cool down of a MICE liquid hydrogen absorber using a cooler may be difficult. The cooler first stage plays almost no role in cooling the absorber.

• If one cools the absorbers with small coolers, a total of three such coolers will be needed. A liquid helium absorber can not be cooled.

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Cool Down Circuit

304 St. St, Can ~ 4 liters

304 St. St, Neck Tube, 30 mm ID

Cu Pipe 15 mm ID

St. St. to Cu Braize Joint

St. St. to Al Transition

St. St. to Al Transition

St. St. to Cu Braize Joint

Cu Pipe 6.4 mm ID

H2 Condensing Surface

Neck Part of Absorber Vacuum Vessel

Absorber Vacuum Vessel below Neck

LH2 Absorber Vessel ~20 liters

LH2 Level Gauge

< 20 K Cooler Cold Head

Optional Cu Cool Down Strap

Heat Exchanger

Absorber Cooling with a Small Cooler

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Concluding Comments

• It appears that a coupling magnet can be cooled with a single cooler. The use of a heat pipe is advised to keep the T between the far side of the magnet and the cold head down to 0.1 K.

• The focusing magnets may require two coolers to cool the magnet and its leads. The leads are the dominant reason for needing a second cooler. The coolers may be connected to the magnet directly and through a heat pipe so that T < 0.1 K.

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Concluding Comments continued

• The detector magnet requires three coolers to cool the magnet. The dominant heat load is the leads on both stages of the coolers. Direct conduction cooling is precluded by the INFN magnet design.

• It is unlikely that small coolers will be used to cool down the magnets to 80 K. Using coolers to cool down some of the magnets from 80 K to 4 K is possible, but it is probable that liquid cryogens will be used to cool down the magnets over the entire range of temperature.

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Concluding Comments continued

• It appears that the liquid hydrogen absorber can be cooled using a small cooler. The total heat leak into the absorber must be less than 10 W. A heat pipe connection between the 2nd stage cold head and the absorber is probably mandatory

• Direct cool down of the absorbers may be possible, but the cooling strap length is long and the cross-section area must be kept small. Liquid cryogen cooling using the absorber heat exchanger will be the most likely absorber cool down scenario.