fusionsuperconductivity
As we know, there is several kind of high-temperature superconductors discovered. However, when I learned that current tokamaks and stellarators just mainly use Niobium-tin superconductor (which is mainly operated in 4.2K), I was surprised.
As I know(or believe), higher critical temperature allows more current density, allowing more powerful magnet, thus we can have higher confinement.
Why current scientists are not using the high-temperature superconductors for fusion reactor?
… an ideal power source capable of providing infinite current with no drop in the voltage it supplies. … Let's ignore the effects of current density on superconductors for now. …
In these phrases is the explanation for the contradictory possibilities you have computed: you have supposed an impossible circuit.
As a mathematical model, the behavior of your circuit is undefined; it is an inconsistent overdetermined system. There is no value of the current which satisfies the equations defining the ideal components as you have connected them.
As a physical system, when you close the circuit, the current will rise from zero (at a rate determined by the inductance of the system, which depends on its shape and size) and quickly reach a limit where either
or some of both effects at once. You cannot escape these limitations.
I personally doubt that the Compact Fusion Reactor as presented by Lockheed Martin last week can work, but I haven't seen enough information to be certain. And to some extent, you never know until you try. (As I understand it, they only have a very early prototype, I mean try as in a full scale prototype.)
What I think I can say with certainty, is that it won't be as small as they claim - "can fit on the back of a truck". Trucks are about the same width as standard containers, so about 2.5m wide. I've had to make quite a few guesses, but I've tried to justify them and choose the smallest size possible.
In the second image here, you can see a grey blanket around the device which absorbs 14MeV neutrons to generate tritium and protect the rest of the plant. The internal coils will also need such a blanket to protect them (it's unclear if the orange skin is this blanket, or just the cryostat). It's also unclear if the outer coils are superconducting or not, but I'll assume they are otherwise the ohmic losses use too much of the power you're supposed to be generating. Superconducting coils need to be cooled with liquid helium and insulated inside a cryostat.
Blankets for a tokamak reactor are estimated at 1m thick. I'm not sure if this is dictated by the tritium breeding or the protection. If it's protection, you might be able to reduce their thickness if you're operating at 100MW instead of 1GW, so let's be optimistic and assume 0.2m thick. I'll assume the same width for the coils and the cryostat (probably optimistic again). I'll neglect any structural elements. So going from the outside of the machine to the centre we have
They don't give any figures for the size of the plasma, but I think it just looks silly if the plasma diameter is less than a third of the coil diameter, so I'll put 0.5m in both of those plasma columns. (Note that this is a very small distance between where the fusion happens at 10^8Kelvin and the wall at 10^3K, and would be extremely good magnetic confinement.)
Totalling up gives 2.6m from the outside to the centre, so the machine is about two trucks wide already. You might give them the benefit of the doubt at this stage, even though all those values were optimistic. But then you need to add peripherals:
heating system (the neutral beam injectors shown in the Lockheed diagram are usually about the size of a truck by themselves)
cryogenic plant for liquid helium (at least half a truck)
power supplies for the coils
vacuum pumping system
steam turbine
bioshield. Even the 1m blanket on a tokamak doesn't block all of the 14MeV neutrons. Safety regulations will require a few metres of concrete shielding in all directions (multiple trucks)
So even if it would work, I don't think anyone will be putting it on a plane.
Best Answer
Using High-Temperature Superconductors (HTS) appears to be a natural choice for magnetic confinement. Their usage in fusion reactors was proposed in the early 2000s but the major problem has been with the production scale. For example, REBCO. But now with new advances, we have capabilities to rely on HTS like REBCO which produce stronger magnetic fields than conventional $Nb_3Sn$. In fact, the SPARC collaboration aims at using these new advancements in HTS to build future fusion technologies with more gain $Q>1$ (or to break the $Q\sim1$ limit). For a recent review, please see "Overview of the SPARC tokamak", J. Plasma Phys. (2020), vol. 86, 865860502.
We need a large confinement time to have high fusion which implies we need large magnetic fields. You can also find information on one of the chapters of Superconducting Magnets in Fusion Reactors, R.G. Sharma, Springer Series in Materials Science, vol 214 (2021).
So usage of superconducting coils has been an active area of research, both on the material science aspects, their applications in a fusion reactor, and also engineering aspects.