We describe the SPIDER flight cryostat, which is designed to cool six
millimeter-wavelength telescopes during an Antarctic long-duration balloon
flight. The cryostat, one of the largest to have flown on a stratospheric
payload, uses liquid helium-4 to deliver cooling power to stages at 4.2 and 1.6
K. Stainless steel capillaries facilitate a high flow impedance connection
between the main liquid helium tank and a smaller superfluid tank, allowing the
latter to operate at 1.6 K as long as there is liquid in the 4.2 K main tank.
Each telescope houses a closed cycle helium-3 adsorption refrigerator that
further cools the focal planes down to 300 mK. Liquid helium vapor from the
main tank is routed through heat exchangers that cool radiation shields,
providing negative thermal feedback. The system performed successfully during a
17 day flight in the 2014-2015 Antarctic summer. The cryostat had a total hold
time of 16.8 days, with 15.9 days occurring during flight.