Thermal Analysis of the ILC Superconducting Quadrupole

Ian RossEunJoo Thompson, John Weisend

Conventional & Experimental FacilitiesStanford Linear Accelerator Center

United States Department of Energy

Outline• Abstract

• The Magnet and Experimental Setup

• Cooling Devices and Processes

• Results

• Conclusions and Discussion

Abstract• Critical to a particle accelerator’s functioning, superconducting magnets

serve to focus and aim the particle beam. The Stanford Linear Accelerator Center (SLAC) has received a prototype superconducting quadrupole designed and built by the Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT) to be evaluated for the International Linear Collider (ILC) project. To ensure proper functioning of the magnet, the device must be maintained at cryogenic temperatures by use of a cooling system containing liquid nitrogen and liquid helium. The cool down period of a low temperature cryostat is critical to the success of an experiment, especially a prototype setup such as this one. The magnet and the dewar each contain unique heat leaks and material properties. These differences can lead to tremendous thermal stresses. The system was simulated using mathematical models, including a fairly straightforward method of energy conservation. This model lead to the ideal liquid helium and liquid nitrogen flow rates during the magnet’s cool-down to 4.2K, along with a reasonable estimate of how long this cool-down will take. With a flow rate of ten gaseous liters of liquid nitrogen per minute, the outer vacuum shield will take approximately five hours to cool down. With a gaseous helium flow rate of sixty liters per minute, the magnet will take at least nineteen hours to cool down.

The Magnet

• Magnets are used to focus accelerator beam• As beam gains energy, magnet must be

stronger• Enormous fields require larger currents• Enormous currents mean Ohmic loss

• P=I2R

• Solution - superconduction

The ILC Superconducting Quadrupole

• Designed to be used at all stages of the ILC.

• At SLAC for testing:– Measuring the magnetic center of the induced

field (to 1μm)– Measurement to be taken for a wide range of

currents, to determine if design is as versatile as hoped.

The ILC Superconducting Quadrupole

The ILC Superconducting Quadrupole

The Helium Vessel

The Helium Vessel

The Vacuum Vessel

Cooling the Magnet Down

• If it’s not superconductive, it’s useless to us.• Thermal stresses must be considered• Liquid helium

– Flows over magnet; vaporizes, heats, and leaves– Ideally, the heat it gains will all be lost by the magnet:

magnetmagnetmagnet Tcm tKhThLm HefHeHeHe He )]2.4()([

Material Property Considerations• The magnet’s specific heat is estimated using the Law of

Mixtures:

• Specific heats decrease as temperature falls, so the cooling process is broken into intervals for the calculation.

Altotal

AlFe

total

FeCu

total

Cumagnet c

V

Vc

V

Vc

V

Vc

Copper’s Specific Heat

Results

Cooling of the Magnet for Varying Helium Exit Temperature (Flow Rate of 60 gaseous liters per minute)

0

50

100

150

200

250

300

0 50 100 150

Time (hours)

Tem

per

atu

re o

f th

e M

agn

et (

K)

He leaving @ 300K

He Leaving @ 260K

He Leaving @ 220K

He Leaving @ 140K

He Leaving @ 80K

He Leaving @ 40K

ResultsCooling of the Magnet for Varying Helium Exit Temperature

(Flow Rate of 20 gaseous liters per minute)

0

50

100

150

200

250

300

0 100 200 300 400

Time (hours)

Tem

per

atu

re o

f th

e M

agn

et (

K) He leaving @ 300K

He Leaving @ 260K

He Leaving @ 220K

He Leaving @ 140K

He Leaving @ 80K

He Leaving @ 40K

ResultsCooling of the Magnet for Varying Helium Exit Temperature

(Flow Rate of 140 gaseous liters per minute)

0

50

100

150

200

250

300

0 20 40 60

Time (hours)

Tem

per

atu

re o

f th

e M

agn

et (

K) He leaving @ 300K

He Leaving @ 260K

He Leaving @ 220K

He Leaving @ 140K

He Leaving @ 80K

He Leaving @ 40K

ResultsCooling of the Magnet for Varying Helium Flow Rates (Helium

Exit Temperature of 300K)

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35

Time (hours)

Tem

per

atu

re o

f th

e M

agn

et (

K)

He Flow @ 40L/min

He Flow @ 60L/min

He Flow @ 80L/min

He Flow @ 110L/min

He Flow @ 140L/min

He Flow @ 170L/min

He Flow @ 200L/min

Results20 L/min

He Exit Temperature (K) Time to Cool Magnet to 4.2K (hours)

300 59.34

260 68.44

220 80.83

140 126.71

80 220.75

40 437.30

60 L/min

He Exit Temperature (K) Time to Cool Magnet to 4.2K (hours)

300 19.78

260 22.81

220 26.94

140 42.24

80 73.58

40 145.77

140 L/min

He Exit Temperature (K) Time to Cool Magnet to 4.2K (hours)

300 8.48

260 9.78

220 11.55

140 18.10

80 31.54

40 62.47

Cooling the Nitrogen Shield

• Same method as helium vessel

• Change in internal energy is given by the Debye model:

• At 60 gaseous liters per minute, the shield will take 4 hours to cool down

tKhKhLmum NNNNcoppercopper )]77()300([2222

T

xD

D

e

dxxTRu

/

0

3

4

4

1

81

8

9

Conclusions

• Big question: accuracy?– Test on the small scale

• If equation is accurate, then the cool down time is reasonable.

Questions?