1. Thermal Analysis of the ILC Superconducting Quadrupole Ian Ross EunJoo Thompson, John Weisend Conventional & Experimental Facilities Stanford Linear Accelerator Center United States Department of Energy

2. Outline Abstract The Magnet and Experimental Setup Cooling Devices and Processes Results Conclusions and Discussion

3. 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.

4. 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=I 2 R Solution - superconduction

5. 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.

6. The ILC Superconducting Quadrupole

8. The Helium Vessel

10. The Vacuum Vessel

11. 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:

12. 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.

13. Copper’s Specific Heat

14. Results

18. 20 L/min He Exit Temperature (K)Time to Cool Magnet to 4.2K (hours) 30059.34 26068.44 22080.83 140126.71 80220.75 40437.30 60 L/min He Exit Temperature (K)Time to Cool Magnet to 4.2K (hours) 30019.78 26022.81 22026.94 14042.24 8073.58 40145.77 140 L/min He Exit Temperature (K)Time to Cool Magnet to 4.2K (hours) 3008.48 2609.78 22011.55 14018.10 8031.54 4062.47

19. 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

20. Conclusions Big question: accuracy? –Test on the small scale If equation is accurate, then the cool down time is reasonable.

21. Questions?