1. Magnet and Absorber Heat Loads and Cooling with Various Small Coolers
Michael A. Green
University of Oxford Department of Physics Oxford OX1 3RH, UK
18 June 2004

2. The Small Coolers Studied for MICE
4.0 to 4.5 K two stage coolers studied:
Sumitomo RDK-415 GM cooler, K, 6.5 kW* input power
Cryomech PT-410 pulse tube cooler, K, 8.0 kW^ input power
Cryomech is developing pulse tube coolers at 1.2 W and 1.5 K
6.0 to 20 K two stage coolers studied:
Sumitomo RDK-408S GM cooler, 8 11 K, 6.5 kW* input power
Cryomech PT-810 pulse tube cooler, K, 8.0 kW^ input power
30 K to 80 K single stage coolers studied:
Cryomech AL-330 GM cooler, K, 7.5 kW^ input power
Cryomech PT-60 pulse tube cooler, K, 3.3 kW^ input power
*The Sumitomo compressor power is given for 50 Hz; for 60 Hz the power goes up to 7.5 kW.
^Cryomech does not say what the input power is for 50 Hz. The power is assumed to be for 60 Hz.
The compressors run on three phase power and are water cooled with flows up to 8 L/min.
The input power for all of the MICE coolers is from 101 kW to 136 kW depending on the scenario used.
From 108 to 136 L per minute water flow is needed to cool the cooler compressors.

3. Pulse Tube Coolers Versus GM Coolers
Both types of coolers can be used on MICE at the heat loads that are assumed for magnets and absorbers.
Pulse tube coolers have a maintenance interval of hr. No maintenance is needed during the life of MICE. The pulse tube cooler cold head requires no maintenance. The GM cooler cold head maintenance is every 6000 hr.
The unit size for the 4.2 K coolers is larger for the GM coolers (1.5 W versus 1.0 W at 4.2 K). The pulse tube cooler unit size has been going up. By Cryomech expects to have a K pulse tube cooler.
The GM coolers may be a little more efficient in terms of power consumption. However, recent changes in pulse tube cooler refrigeration at 4 K have occurred without increasing input power to the compressor.

4. Load Map for a Sumitomo RDK-415D Cooler
Cost per Machine = 45 k$

5. Load Map for a Cryomech PT-410 Cooler
Typical PT-410 Load Map with 50 Hz Power
PT-410 Two Stage Cooler
Cost per Machine = 36 k$

6. Coupling Magnet Cooling with 1 RDK-415 Cooler
  First Stage of Cooler
1 RDK-415
MLI Radiation Heat Leak (W)
5.2
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
1.0
Current & Instrumentation Lead Heat Load (W)
21.3
Total Heat Load to 1st Stage per Cooler (W)
30.5
First Stage Temperature (K)
~45
Second Stage of Cooler
0.40
Cold Mass Support Heat Leak (W)
0.10
0.20
~0.25
Total Heat Load to 2nd Stage (W)
~0.95
2nd Stage Temperature (K)
~ 3.8
A liquid helium cold pipe is needed to keep the coupling magnet uniformly cold.

7. Coupling Magnet Cooling with 1 PT-410 Cooler
  First Stage of Cooler
1 PT-410
MLI Radiation Heat Leak (W)
5.2
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
1.0
Current & Instrumentation Lead Heat Load (W)
21.3
Total Heat Load to 1st Stage per Cooler (W)
30.5
First Stage Temperature (K)
~40
Second Stage of Cooler
0.40
Cold Mass Support Heat Leak (W)
0.09
0.18
~0.22
Total Heat Load to 2nd Stage (W)
~0.89
2nd Stage Temperature (K)
~ 4.1
A liquid helium cold pipe is needed to keep the coupling magnet uniformly cold.

8. Cryogen Free Operation OK
Focus Magnet Cooling with 1 or 2 RDK-415 Coolers
  First Stage of Cooler
1 RDK-415
2 RDK-415 
MLI Radiation Heat Leak (W)
4.8
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
1.0
Current & Instrumentation Lead Heat Load (W)
42.6
Total Heat Load to 1st Stage per Cooler (W)
51.4
First Stage Temperature (K)
~63
~40
Second Stage of Cooler
0.45
0.36
Cold Mass Support Heat Leak (W)
0.15
0.07
0.25
0.12
~1.0
~0.6
Total Heat Load to 2nd Stage (W)
~1.85
~1.15
2nd Stage Temperature (K)
> 4.6
> 3.4
Cryogen Free Operation OK
With two coolers, the 1st and 2nd stage temperatures are lower along with the 2nd stage heat load.

9. Focus Magnet Cooling with 2 RDK-415 Coolers or 2 PT-410 Coolers
  First Stage of Cooler
2 RDK-415
2 PT-410 
MLI Radiation Heat Leak (W)
4.8
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
1.0
Current & Instrumentation Lead Heat Load (W)
42.6
Total Heat Load to 1st Stage per Cooler (W)
51.4
First Stage Temperature (K)
~40
~38
Second Stage of Cooler
0.36
Cold Mass Support Heat Leak (W)
0.07
0.12
0.11
~1.6
~0.55
Total Heat Load to 2nd Stage (W)
~1.15
~1.09
2nd Stage Temperature (K)
> 3.4
> 3.7
Cryogen Free Operation OK
Two coolers PT-410 coolers may be used in place of 2 RDK-415 coolers.

10. Load Map for a Cryomech PT-60 Cooler
PT-60 Single Stage Pulse Tube Cooler
Cost per Machine = 45 k$

11. Focus Magnet Cooling with Two RDK-415 Coolers or with a PT-60 Cooler plus a RDK-415 Cooler
  First Stage of Cooler
2 RDK-415
RDK PT-60 
MLI Radiation Heat Leak (W)
4.8
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
1.0
Current & Instrumentation Lead Heat Load (W)
42.6
Total Heat Load to 1st Stage per Cooler (W)
51.4
First Stage Temperature (K)
~40
~44
Second Stage of Cooler
0.36
0.38
Cold Mass Support Heat Leak (W)
0.07
0.08
0.12
0.13
~0.6
~0.63
Total Heat Load to 2nd Stage (W)
~1.15
~1.22
2nd Stage Temperature (K)
> 3.4
~ 4.0
Boosting the 1st stage cooling with a PT-60 allows one RDK-415 to be used.

12. Focus Magnet Cooling with Two RDK-415 Coolers or with a PT-60 Cooler plus a PT-410 Cooler
  First Stage of Cooler
RDK PT-60
PT PT-60 
MLI Radiation Heat Leak (W)
4.8
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
1.0
Current & Instrumentation Lead Heat Load (W)
42.6
Total Heat Load to 1st Stage per Cooler (W)
51.4
First Stage Temperature (K)
~44
~42
Second Stage of Cooler
0.38
0.37
Cold Mass Support Heat Leak (W)
0.08
0.13
~0.63
~0.61*
Total Heat Load to 2nd Stage (W)
~1.22
~1.19
2nd Stage Temperature (K)
~4.0
~ 4.4*
*If the HTS lead heat leak is improved by 0.2 W, the PT PT-60 is OK.
*If the PT-410 is improved to a PT-412 or a PT-415, it is OK with a PT-60.

13. Can current lead heat leaks be reduced?
The HTS lead heat leak at 4 K assumed is 1 W per kA lead pair with the top end of the HTS leads at 60 K. The actual performance of the ASC leads is better (<1 W per kA lead pair with top at 80 K). The lead heat leak is proportional to the top end temperature squared.
The heat leak into the first stage through the copper leads is about 70 W per kA lead pair. A liquid nitrogen to intercept will reduce the heat flow to the first stage by a factor of two. The cost of liquid nitrogen cooling and its control system may be more than the cost of an extra cooler.
The lead heat leak can be reduced by reducing the number of leads and the lead current. One should be able to reduce the lead heat leak in the detector 30 percent by doing this.

14. Detector Magnet Cooling with 2 or 3 RDK-415 Coolers
  First Stage of Cooler
2 RDK-415
3 RDK-415 
MLI Radiation Heat Leak (W)
15.0
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
2.0
Current & Instrumentation Lead Heat Load (W)
106.0
Total Heat Load to 1st Stage per Cooler (W)
126.0
First Stage Temperature (K)
~75
~53
Second Stage of Cooler
1.30
1.05
Cold Mass Support Heat Leak (W)
0.16
0.12
0.36
0.30
2.80
2.04
Total Heat Load to 2nd Stage (W)
4.62
~3.51
2nd Stage Temperature (K)
> 5.1
~ 4.0
Three RDK-415 coolers instead of two are needed to cool each detector solenoid.

15. Detector Magnet Cooling with 3 RDK-415 Coolers or 2 RDK-415 Coolers plus a PT-60 Cooler
  First Stage of Cooler
3 RDK-415
2 RDK PT-60 
MLI Radiation Heat Leak (W)
15.0
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
2.0
Current & Instrumentation Lead Heat Load (W)
106.0
Total Heat Load to 1st Stage per Cooler (W)
126.0
First Stage Temperature (K)
~53
~56
Second Stage of Cooler
1.05
Cold Mass Support Heat Leak (W)
0.12
0.13
0.30
0.32
2.04
2.15*
Total Heat Load to 2nd Stage (W)
~ 3.51
~3.65
2nd Stage Temperature (K)
~ 4.0
~ 4.4*
*The lead heat leak must be reduced about 25 percent to get the second stage T down to 4.2 K.

16. Load Map for a Cryomech AL-330 GM Cooler
AL-330 Single Stage GM Cooler
Cost per Machine = 35.1 k$ (water cooled) to 37.2 k$ (air cooled)

17. Detector Magnet Cooling with 3 RDK-415 Coolers or 2 RDK-415 Coolers plus a AL-330 Cooler
  First Stage of Cooler
3 RDK-415
2 RDK AL-330 
MLI Radiation Heat Leak (W)
15.0
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
2.0
Current & Instrumentation Lead Heat Load (W)
106.0
Total Heat Load to 1st Stage per Cooler (W)
126.0
First Stage Temperature (K)
~53
~33
Second Stage of Cooler
1.05
0.60
Cold Mass Support Heat Leak (W)
0.12
0.07
0.30
0.19
2.04
1.02
Total Heat Load to 2nd Stage (W)
~ 3.51
~1.88
2nd Stage Temperature (K)
~ 4.0
~ 3.8
The AL-330 reduces the 1st stage temperature to allow it and two RDK-415 to be used.

18. Detector Magnet Cooling with 3 RDK-415 Coolers or 2 PT-410 Coolers plus a AL-330 Cooler
  First Stage of Cooler
3 RDK-415
2 PT AL-330 
MLI Radiation Heat Leak (W)
15.0
Cold Mass Support Heat Leak (W)
3.0
Plumbing Heat Leak (W)
2.0
Current & Instrumentation Lead Heat Load (W)
106.0
Total Heat Load to 1st Stage per Cooler (W)
126.0
First Stage Temperature (K)
~53
~33
Second Stage of Cooler
1.05
0.60
Cold Mass Support Heat Leak (W)
0.12
0.07
0.30
0.19
2.04
1.02
Total Heat Load to 2nd Stage (W)
~ 3.51
~1.88
2nd Stage Temperature (K)
~ 4.0
~ 4.2
With AL-330 cooling on the first stage, even two PT-410 coolers can be used at 4.2 K.

19. Absorber Cooling with 1 RDK-415 Cooler
  First Stage of Cooler (up in the neck)
1 RDK-415
MLI Radiation Heat Leak (W)
1.0
Cold Mass Support Heat Leak (W)
0.5
Plumbing Heat Leak (W)
2.0
Instrumentation Lead Heat Load (W)
Total Heat Load to 1st Stage per Cooler (W)
4.0
First Stage Temperature (K)
~30
Second Stage of Cooler (the Absorber and LH2 System)
MLI Radiation Heat 2 W m-2 (W)
Cold Mass Support Heat Leak, buttons plus longitudinal (W)
~5.0
Plumbing Heat Leak and Instrumentation Lead Heat Leak (W)
Radiation Heat Leak on Window (2 layers of MLI)
~0.8
Total Heat Load to 2nd Stage (W)
~7.8
2nd Stage Temperature (K)
~ 11*
* Extra Heat (about 4 W) is required to keep cooler cold head above 15 K.

20. Load Map for a Sumitomo RDK-408S Cooler
The 50 Hz performance is 90 percent of below.
RDK-408S 2 Stage Cooler
Cost per Machine = 42 k$

21. Absorber Cooling with 1 RDK-408S Cooler
  First Stage of Cooler (up in the neck)
1 RDK-408
MLI Radiation Heat Leak (W)
1.0
Cold Mass Support Heat Leak (W)
0.5
Plumbing Heat Leak (W)
2.0
Instrumentation Lead Heat Load (W)
Total Heat Load to 1st Stage per Cooler (W)
4.0
First Stage Temperature (K)
~30
Second Stage of Cooler (the Absorber and LH2 System)
MLI Radiation Heat 2 W m-2 (W)
Cold Mass Support Heat Leak, buttons plus longitudinal (W)
~5.0
Plumbing Heat Leak and Instrumentation Lead Heat Leak (W)
Radiation Heat Leak on Window (2 layers of MLI)
~0.8
Total Heat Load to 2nd Stage (W)
~7.8
2nd Stage Temperature (K)
~ 10.8*
* Extra Heat (about 7 W) is required to keep cooler cold head above 15 K.

22. Load Map for a Cryomech PT-810 Cooler
About the same for 50 and 60 Hz power
PT-810 Two Stage Pulse Tube Cooler
Cost per Machine = 33 k$

23. Absorber Cooling with 1 PT-810 Cooler
  First Stage of Cooler (up in the neck)
1 PT-810
MLI Radiation Heat Leak (W)
1.0
Cold Mass Support Heat Leak (W)
0.5
Plumbing Heat Leak (W)
2.0
Instrumentation Lead Heat Load (W)
Total Heat Load to 1st Stage per Cooler (W)
4.0
First Stage Temperature (K)
~38
Second Stage of Cooler (the Absorber and LH2 System)
MLI Radiation Heat 2 W m-2 (W)
Cold Mass Support Heat Leak, buttons plus longitudinal (W)
~5.0
Plumbing Heat Leak and Instrumentation Lead Heat Leak (W)
Radiation Heat Leak on Window (2 layers of MLI)
~0.8
Total Heat Load to 2nd Stage (W)
~7.8
2nd Stage Temperature (K)
~ 10.6*
* Extra heat (about 5 W) is required to keep cooler cold head above 15 K.

24. Some Concluding Comments
Using a straight forward approach one can cool all the MICE magnets with fourteen RDK-415 Coolers
Extra cooling on the first stage of the focusing and detector magnets reduces the number of RDK-415 coolers to nine.
Cryomech PT-410 coolers can be used for the coupling and focusing magnets. When Cryomech extends their product line to include a PT-412 cooler or a PT-415 cooler, pulse tube coolers can be used on all magnets.
One RDK-415, RDK-408, PT-410, or PT-810 cooler can cool each liquid hydrogen absorber. Added heat is needed.
The magnets and the absorbers are assumed to be cooled down using liquid nitrogen and liquid helium.
The DT from magnet coil hot spot to the cooler cold head can be <0.2 K using a liquid interface.