Thermal Analysis of the ILC Superconductin Quadrupole

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 Energ{acute e}ticas, Medioambientales y Tecnol{acute o}gicas (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 analyzed mathematically, leading to ideal liquid helium and liquid nitrogen flow rates during the magnet's cool-down to 4.2 K, 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 nitrogen shield will take approximately five hours to cool down to 77 K. With a gaseous helium flow rate of sixty liters per minute, the magnet will take at least nineteen hours to cool down to a temperature of 4.2 K