Cooling MICE magnets and the Absorbers with Small Coolers?

1. Cooling MICE magnets and the Absorbers with Small Coolers? Michael A Green Oxford University Physics Oxford OX1 3RH, UK

2. The Sumitomo SDRK 415-D GM Cooler 300 K Attachment Ring Cryocooler First Stage T = 25 K to T = 80 K Cryocooler Second Stage T = 2.5 K to T = 20 K

3. 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.

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

5. 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.

6. 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.

7. 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.

8. Why is DT so important? The line labelled with a temperature are lines of Ic versus B at the MRI superconductor. The heavy lines are the magnet current versus peak B in the superconductor. The triangles and squares at low B are the 200 MeV/c case. The same symbols at high B are the 240 MeV/c case for MICE.

9. 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 thermal conductivity. DT = T3 - T0 DTc = contact resistance DTc is usually small.

10. Details of the Copper Strap Arrangement Note: For DT = 0.1 K, L = 0.15 m, and k = 600 W m-1 K-1, then A = 0.0025 m-2 and DTc = 0. In addition heat flow through 6061 Al is quite poor at 4 K (k = 6 W m-1 K-1). Note: For DT = 5 K, L = 0.3 m, and k = 1000 W m-1 K-1, then A = 0.00006 m-2 and DTc = 0.

11. Temperature Drop in the Coupling Coil with 4.3 K Cooling at One Point QR = 1 W m-2 DT = 4.085K 4.3 K

12. Cooler Connection through a Heat Pipe DTb = Boiling T Drop DTf = Condensing T Drop DTc = Contact Resistance These can be made small. DT = T3 - T0 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.

13. T = 4.3 K Temperature distribution in The Coupling Coil Cooled All Around QR = 1 W m-2 ∆T = 0.268K (4.3~4.568K) T = 4.57 K

14. 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.

15. Absorber Cooling with a Small Cooler

16. 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 DT 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 DT < 0.1 K.

17. 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.

18. 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.