Helium

The launch loop doesn't need cryogenic magnets for deflection - conventional copper-and-iron magnets dissipate more heat, but they are less likely to fail catastrophically.

The launch loop may use cryogenic systems for vacuum pumping and sensors. Unlike magnets, a few pumps or sensors can fail without losing mechanical containment of the rotor, as long as other pumps and sensors keep the sheath evacuated and produce enough measurements to generate a complete real-time model.

But helium will be used, and some will be lost over time. Liquid helium and cryogenic superconducting magnets are vital for research and medical applications, and there is a very limited supply, mostly accumulated in impermeable natural gas formations below the midwestern United States. When that is inevitably used up, whether that takes tens or millions of years, the only remaining sources are Earth's atmosphere, and the cold outer planets. (there's a vast quantity in the sun, but that is gravitationally inaccessable).

A "zero loss" Siemens MRI machine uses 30 liters of LHe, 3.7 kg at 125 g/m³. Losses in real operation, with leaks and transfer losses and accidents, will be higher than zero, but let's be Really Optimistic and assume that 30 liters lasts 100 years before it escapes into the atmosphere. If an MRI machine performs 2 scans per hour, 14 hours per day, that is 1 million scans per 3.7 kilograms of LHe.

The atmosphere weighs 5e18 kg and is 5 ppm helium, so the total amount of helium, if it could be practically extracted, is 2.5e13 kilograms or 200 trillion liters. Which seems like a lot, until you realize that you would have to process the entire atmosphere with filter separation and cryogenic distillation to get to it.

Wild Ass Guess: Assume the air is enriched 10% in helium after each filter stage, with 10 atmospheres pressure drop. To get from 5 ppm to 1% helium would require 80 stages of filtering. To produce a liter of helium would require processing 25,000 cubic meters of air this way. The compression energy per stage (assuming perfect efficiency and near-isothermal compression and expansion) is the pressure times ( ln(10)-0.9 ) times the volume, or 1.4 times 25000 cubic meters times 100 kPa or 2.5e9 joules, or 2e11 joules for 80 stages. 55,000 kilowatt hours. At 6 cents per kilowatt hour, that is $3300 per liter of helium. Cryogenic fractionation, capital cost, maintenance and operations could easily push that to $10K per liter, $80K per kilogram.

For comparison, the atmosphere of Neptune is 15% helium, and cold. Direct cryogenic separation may be possible, and much more energy efficient . Escape velocity is 21 km/s, the gravity is 9 m/s², and about 30 km/s of velocity change would be needed to transport liquid helium to earth. Assuming 10% launch loop efficiencies and 51 km/s total velocity change, the energy would be "only" 1.3e10 joules per kilogram or 1.6e9 joules per liter, less than 1% of the energy cost of terrestrial gas separation. But at 20 AU distance, an SSPS power source would receive 1/400th of the sunlight, so energy near Neptune will be very expensive.

Bottom line: Don't waste helium!!!