a few kW of resistive loss
Is this already accounting for the energy penalty of cooling at cryogenic temperatures? 20K to room temperature is more than a factor of 10. You pay the energy cost once in resistive losses and 10 times in pumping the generated entropy out of the cold bath. I guess the electricity bill is not a huge constraint on these things, but it could mean a higher cost for cooling equipment?
Is this already accounting for the energy penalty of cooling at cryogenic temperatures?
post:
- cryocooler energy usage comparable to current MRI energy use
A lot of MRI machines use >70 kW.
If you care about the heat coming out on the hot side rather than the heat going in on the cold side (i.e. the application is heat pump rather than refrigerator), then the theoretical limit is always greater than 1, since the work done gets added onto the heat absorbed:
Cooling performance can absolutely be less than 1, and often is for very cold temperatures.
Right. But I was using net efficiency values from papers on cryocoolers, not Carnot efficiency values.
That's another issue with liquid hydrogen fuel:
- combustion to gas: 119.93 kJ/g
- vaporization: 446 J/g
- ortho-para conversion: 670 J/g
Burning liquid hydrogen in a car engine would probably make less energy than it takes to liquify the hydrogen.
1
cold aluminum
Very pure aluminum at the boiling point of hydrogen is a very cool material. At 20K, 99.999% pure aluminum has 1000x the electrical conductivity it has at 0 C. At 4K, it has maybe 4000x.
At such low temperatures, electron free paths in aluminum become macroscopic, which is why even small amounts of impurities greatly increase resistance. Even wire diameter has a noticeable effect. Magnetic fields can also increase resistance, but this is also a purity-dependent effect: 99.999% aluminum might have 3x the resistance at 15T, but even purer aluminum is much less affected.
Yes, aluminum purification costs some money, but it's not particularly expensive. It might cost 3x as much as standard aluminum, but it's far cheaper than superconductors. Another point to note is that superconductors only have 0 resistance for constant current. Cryogenic aluminum isn't affected by current changes like superconductors are.
It seems like that sort of interesting effect that massively increases a figure of merit should have some sort of application, don't you think? Yet, while there are superconducting electric motors for ships, I'm not aware of cryogenic aluminum conductors being used for any commercial applications. What could it be used for?
power lines
An obvious application for low-resistance conductors is long-distance power transmission. My estimations indicated that using cryogenic aluminum for that is somewhat too expensive, because the (cryocooler cost)*(insulation cost) product is too high for reasonable line currents. Connecting it to ambient-temperature lines is also an issue, because cold pure aluminum also has high thermal conductivity.
As temperatures decrease, resistance decreases, but cryocoolers become more expensive and less efficient. In general, liquid hydrogen seems better than liquid helium or liquid nitrogen for cryogenic aluminum conductors.
At such temperatures, it's worth using multilayer vacuum insulation. That's far more effective than typical insulation like fiberglass or polyester, but it still doesn't seem good enough to make insulation + cryocoolers sufficiently cheap for large underground power lines.
While the economics don't work out, it is possible to use cryogenic aluminum for high-power electricity transmission. It's merely expensive, not unfeasible. Feel free to use that for flavor in hard SF stories.
What are some attributes of applications that make cryogenic aluminum more suitable?
One application that's been proposed is electric motors with cryogenic aluminum conductors in aircraft fueled by liquid hydrogen, which would provide free cooling for the aluminum. Obviously, such aircraft don't currently exist, and I don't think they're very practical, but that's beyond the scope of this post.
MRI
— some blog
You've probably heard that MRI scans are expensive because the machines are expensive, but they're ~5x more expensive in the USA than in Mexico. You might then think they're expensive because of labor requirements, but the Netherlands has among the lowest prices for MRI scans.
In any case, yes, the machines are somewhat expensive. Here are some approximate machine prices. Supposing a $400k machine is used for 10 people a day with 5 year amortization, that's $22/use. Considering typical price multipliers for US healthcare, you can see how that could become expensive...?
Some of that cost is for superconducting magnetic coils. Is there some way to potentially reduce that expense by using cold aluminum instead, or perhaps improve MRI performance somehow?
gradient coils
A typical approach in MRI machines is to have 2 superconducting coils (with constant current) to make an approximately homogeneous field, and use copper coils to create a (much smaller) magnetic field gradient that changes at perhaps 2 kHz. NMR precession frequency depends on field strength, so this field gradient can be used to localize emissions to a particular slice.
With aluminum, the same coils could theoretically be used for both purposes. How expensive would replacing superconductors with aluminum be? I'm estimating that would involve:
So, cold aluminum is usable for MRI machines, but not strictly better than superconductors. How about high-temperature superconductors? People have of course considered that, but they're really not as good a choice as many people seem to think.
Cold aluminum could also be used together with superconductors for gradients. Is that better than using copper?
A larger field gradient allows better localization between slices. This can improve resolution (with higher field strength) or scan speed (with higher repetition rate). Both those things also obviously add to other costs. The slew rate (field change / time) is limited by induced current triggering longer nerves, but only the most expensive MRI machines are close to that limit.
The cost of cryocoolers and pure aluminum for making the highest gradients seen in MRI machines today actually seems very reasonable. Using cold aluminum instead of copper could potentially reduce their size, weight, and even cost. It could allow larger maximum field gradients in a given volume; alternatively, it could allow having some open space between coils, which could make scans less unpleasant.
There's a reason I think very high field gradients could become more important for MRI machines in the future: simultaneous multi-slice imaging. In the past, higher repetition frequency was favored over that because of the higher computational requirements for MRI reconstruction, but today that's not a problem; that calculation is less demanding for a GPU than running Starfield or Cities Skylines 2. High-gradient multi-slice imaging could potentially make scans several times faster at the same quality. That not only increases machine throughput and reduces labor costs, it also improves patient experiences and makes real-time performance better.
Using cryogenic high-purity aluminum to make large field gradients in MRI machines using simultaneous multi-slice imaging not only seems to give better cost-performance — it's also, finally, a real application for cryogenic high-purity aluminum.