Can you avoid the costs of cooling superconductors for magnetic shields by separating them from the spacecraft and using shades?

Question

As the answer to this thread states, cooling superconductors in spacecraft is necessary because of waste heat from secondary systems and thermal radiation of the sun. The application in which superconductors are the most interesting to me is magnetically shielding spaceships from solar wind and galactic cosmis rays to reduce the radiation risks for manned spaceflight.

What I'm thinking about is getting rid of anything superfluous, making the system as simple as possible and just shooting it away from the ship with a conductive tether connected to the superconductive coil, which is itself connected to a large and thin reflective film that blocks heat from the sun. After positioning the solar shade, the coil should slowly radiate away energy and eventually become superconductive (at 10 Kelvin for conventional niobium-titanium alloy), right? You could then gradually add current to the coil until the magnetic field is strong enough to block harmful radiation.

Problems I see with this approach:

1) Orienting the solar shade

You can never let the coil heat beyond its critical temperature, so the solar shade has to stay in front of the coil at all times. This probably requires thrusters and a computer, which makes the solar shade a kind of mini satellite in itself.

2) Tethers, secondary systems and waste heat

The electrical energy comes from the conductive tether which is not a superconductor itself, so there'll be waste heat. Deflecting charged particles will also take energy, you constantly have to add new current to the coil. On top of that you probably also need a computer and something to monitor and regulate the coil, producing even more waste heat.

3) Magnetic field strength

The farther the magnetic shield is from the spacecraft the smaller is the amount of protection you'll get. If you get too close to the ship, thermal radiation from it might heat up your superconductor and the magnetic field will affect metal inside of it. Does the required distance from the craft give you enough protection to make this worthwhile?

4) Shutting the coil off

You can let it heat beyond the critical temperature, but the superconducting material will quench and release a lot of heat, which might damage it.

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All in all, is this actually a feasible idea compared to just using active cooling?

Answer 1

A lot depends on the temperature requirements for your superconductors. That in turn depends on how much magnetic field you need, your mass budget for the coils, and how exotic a material you can afford.

There's a nice summary of (mostly active) space cryogenics here. Passive cooling to 50K has already flown on Planck (they were planning 60K, but did better), and the JWST is planning 40K.

The environment matters a lot. "Cooling" comes from radiating to space at ~5k (averaging over star flux in the local area of the Galaxy); heating comes from any local object. The more and larger shields you need for Sun, Earth, Moon, etc, the less solid angle you have to radiate to the rest of the sky.

JWST's 5-layer shield was designed to meet the requirement of no more than 2W passed flux, which in turn could be radiated to space for a telescope instrument temperature of 40K. Because flux goes like $T^4$, keeping all things the same, you'd need to drop the flux by a factor of $4^4 = 256$ to get to 10K. If everything was perfect, this would just require 2 (maybe 3) more layers.

But it's hard to keep such a shield perfect, and even a defect at the 0.1% level could let through enough heat flux to overwhelm the passive cooling by radiation. At some point, the requirement for perfection becomes too expensive.

Answer 2

Deflecting charged particles will also take energy, you constantly have to add new current to the coil.

No, magnets do not change the energy of the particle, just their momentum. Otherwise permanent magnets wouldn't work constantly. But the momentum is transferred to the magnet, so you need active station keeping for it as well.

After positioning the solar shade, the coil should slowly radiate away energy and eventually become superconductive at 10 Kelvin

Yes, it will cool down, but likely not as much: There are crates close to the poles of the Moon that never receive sunlight. They have a temperature of about 100 Kelvin.

But, a solar shield doesn't protect you from all the heat the Sun delivers: Your solar shield will heat up and due to thermal conduction its backside will get warm as well. You can add more insulation in the shield, but this will not prevent the heat transfer, just making it slower. Once the shield is warm, it will radiate heat by itself and thus heat up the magnet coil. You will need some active cooling to keep the backside cold enough.

Also note that the distance of the shield doesn't matter: The closer it is, the smaller it can be. The amount of radiation the coil receives depends on the angular size (coverage of the hemisphere) of the shield, not its distance nor size.

Without doing the calculations: To reach such low temperatures, I assume you need, besides active cooling, a shield to protect the coil from radiation coming from Earth and possibly even the Moon.