FWIW, the physical reason underlying it, is achievable flux density.
We can achieve quite high flux density with or without core, if we deliver enough current. But dropping 10kA through even very cold silver, will make it not-cool very quickly. That is, we need a metric shitload of ampere-turns to do any work at high flux density.
So we are mostly confined to work within the limits of core materials -- having a saturation flux density around 1.8T or less.
The most thrust we can get, is to distribute that 1.8T over as large an area as possible. Flux density is also energy density in air (namely, in the air gap between rotor and stator), and energy density is also pressure. Anywhere we have a difference in pressure, we have net force.
1.8T is equivalent to (1.8T)^2 / (2 * 1.257e-6 H/m) = 1.28MPa, or about 13 atm. Which is higher than, say, a blowgun powered by your average air compressor (~6 atm), but much, much less than a gun (~1000 atm).
Which, speaking of guns, this is why gauss guns are so unimpressive.
Now, the neat thing about the electromagnetic force is, it's not a scalar pressure -- it's a vector. Which means we can have this pressure applied tangentially as well as radially -- we aren't limited to pushing pistons in cylinders, we can spin them on axis, too! You can imagine if we have 1.8T in the 0° position (in the air gap of a radial flux machine, with cylindrical rotor and stator) and none at 90°, and the rotor has the opposite, then the rotor will be torqued so as to balance the fluxes. And the torque is proportional to the area of the rotor's cylindrical face, and the flux density.
We can also subdivide the rotor and stator into smaller magnetic domains -- multiple poles. A single winding each gives two poles (N and S). A pair of windings, placed in quadrature and wired sequentially opposing, gives four poles (and divides the electrical frequency by half, hence 60Hz machines run synchronous at 1800 RPM -- this is the most common configuration). The field alternates more frequently around the circle, but it's the same flux density, and if anything there are more chances to waste it (flux leakage) because the distance between poles is smaller.
(When the distance between poles is comparable to the air gap, the flux density drops off extremely quickly across that gap; very small gaps are required in that case, and even then, the available power may not be much. This isn't so much a problem with motors (because no one uses motors with this many poles), as it is for alternators, which have been used to generate higher frequencies for induction heating and even radio transmission purposes! Simply using more poles is feasible up to the low kHz, but they used a different strategy to push to
over 100kHz.)
I'm... pretty sure, but I can't quite convince myself that: torque depends on area period. It's tempting to think of multiple poles as teeth on a gear, but gear teeth are limited by the physical strength of materials and the the engagement width and depth; here, the magnetic "teeth" are weaker simply by the fact that they are smaller, i.e. they have less area each, at the same flux density. (But flux density will also decrease with more poles, due to leakage.)
So, you can imagine constructing a machine, around the air gap where work is done. We use steel and copper, reaching 1.8T in the air gap. It is rotationally symmetric (so, a disc, cylinder, or other surface of revolution). We need as much steel going away from the gap, as the width of the poles -- that is, we must maintain core cross-section as the core wraps around the copper windings. We can potentially save on core material if we use more poles (the core can have less height above/below the air gap), so long as leakage doesn't compromise performance.
The resistivity of copper, available cooling, and desired efficiency, sets how much copper is needed, and thus how much space the core must wrap around. (This doesn't much depend on number of poles, as we normally divide the core into many slots anyway, distributing the windings between them to get a smooth magnetic field that minimizes harmonics and torque pulsation.) We can pack copper more efficiently using square wire (or even more specialized shapes, I suppose), and we can dissipate more power (at lower efficiency) if we have liquid cooling, or less power (higher efficiency) if we cool it a lot (copper's resistance has a strong tempco; the core does too, so that we can potentially run a little higher flux density at very low temperatures).
Though the power we'll spend on
that much cooling, won't actually win us efficiency overall, plus the cryocooler takes up a lot of space, ruining our overall power density (though maybe that's still a win in some very special applications).
Of course if we're going to that trouble, we might as well use superconductors. We can get nearly zero losses in the windings, but we still have to deal with core losses, which will be very expensive indeed to keep that cool. (It's probably not feasible to keep the windings that cold, separate from the core.) At least we can use much less wire, so the core can be somewhat smaller. We might even use a lower-loss material, even at the expense of flux density or permeability. But then again, what do we really need core for, at all? If we have almost no loss in the windings, let's just use all windings, and dump kiloamperes through it because we can! This has some consequences: we still need some structure to support the rotor and stator, and we don't have air gap so much, because it's
all leakage -- there's no core to confine flux, we need to get the windings in just the right places. Even then, we'll necessarily have poorer performance (less torque) because of that leakage. So we'll need to run it a bit higher to compensate. (Fortunately, 2-10T flux density is quite reasonable even for high-temperature superconductors!)
This doesn't give much technical detail, but it seems they are indeed pursuing it:
https://www.engineering.com/AdvancedManufacturing/ArticleID/19454/Fully-Superconducting-Motor-Prepares-for-Testing.aspxTim
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