Pavel has pointed out that I overlooked a remarkable paper on experimental physics in Nature:
45.5-tesla direct-current magnetic field generated with a high-temperature superconducting magnet (by Hahn, Kim, 9 more)Magnets are cool. When we were 10 or so, our class would work in nearby gardens. Some of the greenhouses were covered by plastic films that were attached by... wonderful square magnets, 10 x 10 x 2 cm or so. I was facing a dilemma: on one hand, the founder of Czechoslovakia Prof Thomas Garrigue Masaryk taught us "don't be afraid and don't steal". On the other hand, the magnets were wonderful and I was a curious kid.
A few times, my curiosity prevailed over Masaryk. By taking a few magnets, I was helping to disassembly the communist regime – some four years before I became a full-time dissident.
The world's strongest man-made magnetic field was created in a Japanese lab last autumn: a whopping 1200 tesla. Unless we're overlooking something remarkable, this device isn't feasible for the construction of colliders.
We need simpler magnets that are easily scaled. Something that resembles the cool things we were stealing in the Gardens National Corporation. And when it comes to these fields, there is quite a general "scale" of the magnetic field that is reproduced by pretty much any realistic material. This claim is similar to the claim that atoms have similar heat capacities and metals have similar densities.
So far, for two decades, the strongest direct-current (D.C.) magnetic field that was produced in the world was 45 tesla. Hahn and pals have finally broken this record. Because their new magnetic field is just 45.5 tesla, it's clear that the previous 45-tesla threshold was an important psychological benchmark that they simply needed to beat.
But what they did was more than an improvement from 45 to 45.5. The 45-tesla magnet was a very strong, 33.6-tesla resistive magnet inside 11.4 low-temperature superconducting magnet. Instead, their new magnet uses a high-temperature superconductor with 14.4 tesla inside a 31.1-tesla resistive magnet. So the resistive magnet was moved from outside to the inside of the magnet; and the superconducting magnet switched from a low-temperature one to a high-temperature one.
High-temperature superconductors used to be considered a holy grail of material science. It's too bad that almost no one is hyping this sport these days. I think it's a wonderful sport. The paper seems like an important advance in ambitious claims about high-temperature superconductors.
When I look at it again, the change doesn't look so deep. I have no idea how much it costs, whether such magnets are usable for the accelerators. But Pavel's simple calculation is surely unbelievably attractive. If the LHC/FCC dipole magnets could be increased to 45 tesla, the LHC tunnel could be upgraded to a 75 TeV center-of-mass energy collider while the improved FCC could boast something like 300 TeV total energy of the two beams. Note that the center-of-mass collision energy is basically proportional to the magnetic field. For proton beams, the beam energy in TeV is about 0.81 times the magnetic field in tesla (for the LHC design). For every tesla, you get almost 1 TeV per beam and almost 2 TeV from both beams.
I think that it's great when psychological patients are allowed to leave the mental asylums, if they can walk in the forests, and so on. It may be relaxing and the fresh air is pleasant etc. But this tolerant approach must have some limits, in order to protect their health and the society. The people who wouldn't agree to build a 300 TeV collider for $30 billion should definitely be held in a psychiatric asylum for 24 hours a day. I can even tell you the ID of the optimum pavilion for such patients – it's the most hardcore pavilions for men and women, respectively.
It's possible that one can't really afford the resistive magnets at all (power consumption?) – so what is usable is the high-temperature superconducting magnets approaching 15 tesla. Well, if the LHC energy could be doubled, it would still be the best next step to do with the LHC tunnel. This page lists the price of the LHC bending dipole magnets as CHF 0.5 million – times 1232 is some CHF 616 million. The Swiss franc is almost precisely one dollar. If one could update the dipoles for $1 billion and double the LHC energy, I could find a way to fund it myself.
For some $9 billion, the LHC managed to increase the total energy from 2 TeV – the Tevatron – to 13 TeV which is almost three doublings. The price of the doubling of the center-of-mass energy was about $3 billion, if you accept this optimistic "constant cost of a multiplicative factor". So if the "dipoles that double the LHC energy" were cheaper than $3 billion, I think it would be a no-brainer. The FCC should still be built on top of that.
Note that the current FCC assumes the increase of the center-of-mass energy from 13 TeV to 100 TeV which is again 3 doublings – but the cost is almost $30 billion i.e. $10 billion per energy doubling. In this counting, just the upgrade of the LHC magnets looks like a cheaper move, relatively speaking.