Liquid oxygen is paramagnetic. Those coils in the article are from an electromagnet that sucks the oxygen into the compressor once it has been pre-cooled by expansion (Joule-Thomson-effect). And it wouldn't cost them that much of electric energy if they use superconducting coils (it's f***ing cold in there anyways). And for the freezing moisture: Use hydrophobic surfaces like graphite or nanostructured surfaces with a lotus-effect.

The incoming air has to be cooled from 1000 degrees celsius down to 200 below or so in less than a hundredth of a second. Expansion cooling may also be a part of it, but as mentioned, the biggest problem is icing in the precooler. Sounds like graphite would be the way to do it - you need a substance that resists water condensing or freezing onto it, but that can also resist the 1000 degree temperatures of hypersonic flight.

Liquid Helium has a boiling-point of 4K. -150°C=123K
This means, that you would get massive amounts of Helium-vapor (=gas) you would have to store somewhere. (Helium is way too expensive to just blow it out.)
On top of this, the proper insulation for liquid Helium is also quite big and technically challenging: about 0.5 meters thick all around + a liquid-nitrogen-cryostat to pre-cool the insulator. And even then the cryostat has to be refilled every day. (A former colleague of mine invented a liquid-Helium-cryostat that can last for a week, but that's high-end-engineering and so far only about a dozen have been built and sold world-wide.)

Also, using fine tubes to spread the cold increases the risk of damages and leaking (e.g. by shaking, bumping...).

You could use liquid Nitrogen: It has a boiling-point of 70K and is piss-cheap, so you could just vent the excess gas. But that still leaves the problem with the tubes.

All in all, I doubt liquid gas is used for cooling. The machinery and insulation to handle it eats up way too much volume and is too prone for accidents/damages/malfunctions.

The thing is that you can't use expansion to cool the incoming air - you have to compress the air to make it suitable for running the rockets, but the problem is that when you compress air, it heats up, and could melt the rocket engine components, hence the need to cool it to -150 degrees C.

I'm betting that it is a graphite coating on the precooler tubes, combined with careful aerodynamic design work to ensure the air flows over the tubes cleanly and fast - if eddies cause air to slow down in a particular point on the intercooler, that could be where frost begins to form - the idea is to keep the air flowing so fast that frost can't form and the air remains supercooled.

I would imagine that the SABRE would have to use a closed loop, keep the liquid helium or gaseous helium from escaping. Since the Skylon is designed to be reusable, that would hopefully keep the liquid helium expense down.

The insulation is a major problem:
Let's start with pipe that leads to a coil and back.
1. The innermost layer is a metal-pipe. Next comes vacuum (mere air at room-temperature already means a massive heat-source) with some thin wires as supporting beams, connecting the pipe to the next layer: A liquid-nitrogen-cryostat. (Mere infra-red-radiation from metal at room-temperature is also a heat-source.) Next up, again vacuum with thin beams (connected to first vacuum for sake of simplicity). And then finally the rest of the spaceship.
MAYBE you can forgo the LN-cryostat, but it's extremely risky: If something unforeseen happens, there is simply way too much heat you can handle and your engines drop dead.
2. The pipe leads inside a volume, turns into a coil, and leaves the volume again. This means, the pipe has be attached airtight to the cooling chamber, which again means a massive heat-source.



I worked with a liquid-Helium-cryostat. One mistake and only fast action by somebody with knowledge how the cryo is built and who has direct manual access to the vents and pipes can prevent the worst. And even then it leads to downtime until the pressures (several minutes) and temperatures (several hours) have stabilized. The worst-cases are an accidental helium-blowout or an intentional helium-blowout to start a repair. And that's only if you can REACH the cryo and the pipes.
(EDIT: When following the proper procedures, a liquid-helium-cryostat isn't dangerous at all to use or maintain. But if you slip up or there's a malfunction, then you are in deep shit, because repair is always tricky and can be very time-consuming. If the cryo has an uncontrolled blow-out, that's the worst-case-scenario, you simply die of suffocation and that's it.)

I don't want to know what happens to a cryo that's shaken with the force of a rocket-launch. Or that somehow has to keep the heat of reentry out of its system.

Since liquid hydrogen is the Skylon's fuel, and it boils at 14K, maybe that would make it easier to store the liquid helium - not as much insulation required.

In other words, use the fuel tank in place of the LN2 cryostat layer.

And you've got LH2 fuel pipes running out to the engines already, so you might as well use them to encapsulate the LHe lines and help keep them cold.

The precooler doesn't use liquid helium. Gaseous helium. So it doesn't have to be cooled down to 4K. It is cooled by the liquid hydrogen down to 14K or so, which is what enables it to bring the temperature of the incoming air from 100C to -150C.

Also, apparently, the precooler does not liquefy the incoming air - just chills it so the rest of the engine doesn't get toasted when the spacecraft is hurtling through the atmosphere at Mach 5+, and it doesn't separate the oxygen out of the air - the rest of the air is sent through the combustion chamber and is useful as reaction mass, boosting efficiency during the air-breathing phase of Skylon's flight.