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How does a Bitter magnet differ in its construction from a simple wound coil magnet?

A Bitter magnet is made from a stack of plates with holes in a helical arrangement separated by insulators. The idea is to get a helical flow of current so similar to a coil.

Each plate acts as roughly a single turn carrying a massive current but the current flow is apparently non-linear. So this must result in some changes to the simplified solenoid equations normally used. What are they?

Superconducting magnets do not seem to be based on the Bitter design. Why not? Couldn't the plates be made of superconductors instead of conductors? Is there a requirement for them to have some resistance? Or is it simply that plates are need to hold a massive current in a resistor and not in a superconductor, which seems like the obvious conclusion.

See https://www.ru.nl/hfml/research/levitation/diamagnetic-levitation/bitter-solenoid/

I also note (slightly off-topic) that because these are made of plates rather than windings they look much easier to construct and ripe for mass production yet the opposite seems true https://www.youtube.com/watch?v=tBz6jVC-Gg4 There is surely no shortage of demand given applications like NMR imaging. What am I missing?

There was a similar question here:

How to design a Bitter electromagnet?

It was closed as being about the design. I think this was wrong as you need to understand the physical principles involved in order to construct one.

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    $\begingroup$ This is a better picture than the Wikipedia article, which doesn't really explain how the design works. ru.nl/hfml/research/levitation/diamagnetic-levitation/… $\endgroup$
    – alephzero
    Jul 9, 2021 at 12:26
  • $\begingroup$ That is a better diagram and it looks like the answer is yes each plate is perhaps just under one turn. And at 20,000A that explains the need for a wide conductor and cooling. Its odd that neither description just says that. I guess they thought it was obvious. $\endgroup$ Jul 9, 2021 at 15:36

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The short answer is that electromagnets are limited in the total field they can create by overheating. Overheating is dealt with by cooling. You can flow water over the outside of coils to cool them, but then they get hot in the middle and melt. For traditional wire-wound electromagnets you can use hollow wire and flow chilled water at high pressure to cool the electromagnets. This has a few problems. 1) for long wires, the water may have heated up substantially by the time it reaches the end of the electromagnet so it doesn't cool as efficiently. 2) high pressure is required to flow water at high velocity for efficient cooling. 3) A blockage, which is likely in the narrow piping, bricks the entire electromagnet.

Bitter coils get around these problems. The idea with bitter coils is to have a way to flow water in a way such that it flows through all of the volume of the coils (so that there are no hot pockets), but it never has to flow a very long path before returning (so you don't have pressure problems). You want cooling water current which is massively parallel through the coils despite electric current being serial.

From https://arxiv.org/pdf/1309.5330.pdf

Image from https://arxiv.org/abs/1309.5330. We see water flows in some holes and other others and current flows in a spiral along the sheets.

Why are they designed and manufactured with these sheets? That is just the easiest way to get the appropriate pattern of conductors and insulators so that electrical and water currents flow in the right patterns. It could equivalently be made with additive manufacturing techniques such as 3D printing and sintering but this would probably be much more difficult.

Superconducting magnets: Frankly, I know very little about superconducting magnets. What I do know is that superconducting magnets are a little bit of a different beast because, so long as the magnets are cold enough to be superconducting, the current doesn't actually generate any heat because there is zero resistance. I think this changes the design tradeoffs because you don't need to worry about hot pockets appearing within the meat of the electromagnets that you can't cool. And in fact, you may not want to give up precious volume for current to flow in. That said, maybe a bitter design would make it easier to reach and maintain superconducting temperatures in the first place. There could also be an issue with finite resistance occurring at the physical interface between two separate pieces of superconducting material that ruins the design, but this is 100% speculative, I don't know if such an effect is real.

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The answer from Jagerber48 is very good, but I thought I could add a bit of extra detail.

In an electromagnet, the magnetic field is produced from a circulating electric current that is carried by some conductor. Roughly speaking, the strength of the field is proportional to the current and the number of turns in your magnet, as well as inversely related to the size of the bore, i.e. the hole in the middle which you can do your experiment or whatever it is you need the field for.

If using a conventional metal, e.g. copper, and your aim is to generate a strong field (maybe homogeneous too), then you have two options - increase the current or increase the number of turns. Both ultimately increase the power dissipation in the magnet (I^2 R). At some point, a limit will be reached where it is not possible to dissipate all the power just in the air, without some kind of active cooling.

Bitter magnets are a possible solution to this problem, and work by flowing cooling water through the magnet, parallel to the direction of field and perpendicular to the conductor plates (https://www.ru.nl/hfml/research/bitter-solenoid-magnet-explained/). The magnets at the High Field Magnet Laboratory (HFML, The Netherlands) can produce some of the strongest static magnetic fields in the world, and are used for all manner of physics and science research. The downside is that ultimately quite a lot of power is consumed due to the heating in the magnet, and also in the cooling of the cooling water. Generally speaking, this kind of installation is not easy to implement outside of a research setting, e.g. MRI in hospitals, due to the infrastructure required.

If you observe the holes in the Bitter plates, you'll see that they are not uniform, but concentrated towards the centre of the plate. This is because, as you say, the current flows in a non-uniform distribution through the plate. The path around the inside edge is shorter and that bit of copper will have less resistance, thus more current will flow, compared to the copper on the outside edge. However, the flowing current causes heating, which affects the conductivity of the copper in that region (generally, hot metals are worse conductors than cold metals). This will heat the central portion more than the outer portion, and will cause a redistribution of the current through the plate that depends on the heat and temperature distribution. This is not trivial to solve and will depend on a number of material and geometric parameters, and probably is best attempted using a finite-element calculation (e.g. COMSOL). The pattern of holes in the plate therefore give you an idea of where the heat and current are concentrated (generally towards the centre).

If you make an electromagnet using superconductors, you now have a different set of problems to deal with. Superconductors must be cooled below their transition temperature (Tc) before they become superconducting. Most elemental and binary alloy superconductors have a Tc < 20 K, usually < 10 K. For instance, lead has a Tc of about 7.2 K and aluminimium a Tc of 1.7 K, while Nb3Sn is about 18 K and NbTi is about 10 K. (High temperature superconductors, such as YBa2Cu3O7-x, can have Tc's of the order of 100 K, but these have not been widely adapted for this purpose, compared to decades of conventional superconductor technology). So, to begin with, cryogenics are required and typically this will be liquid helium (boiling point around 4.2 K). The major advantage of superconductors is that, when superconducting, they can carry large amounts of current without dissipating any heat, at least, to the first approximation. This is actually only true up to a particular magnitude of current, above which the superconductor stops being superconducting and reverts to the normal state (for our purposes, a metal). This current is called the critical current, Ic, and is a material specific property but is usually really very large. (Really, it is the critical current density Jc = Ic / A). That is problem number 1.

Problem number 2 is that superconductors also stop superconducting if subjected to a strong enough magnetic field - the critical field (side note - either Hc or Hc2 depending on whether it is a type 1 or type 2 superconductor). So the magnetic field the electromagnet creates could in principle kill off the superconductivity and prevent it from carrying the large current you need for your field. This is problem 2.

So, when designing your superconducting magnet, it is necessary to consider both of these factors to ensure the superconductor will remain superconducting during its intended use. If not, it can result in permanent and irreversible damage to the magnet.

The reason that superconducting magnets not being made in the Bitter design is, I think, for three main reasons.

The first is, as Jagerber48 said, you want to maximise your current density and not sacrifice volume to empty space that doesn't contribute to your overall field.

Reason 2 is that is not necessary - there is no need to flow any kind of coolant through the magnet. Provided the current and field are kept within specification, the magnet should remain superconducting and thus dissipates no heat itself (it must remain below Tc and not be allowed to heat above due to environmental heat leaks).

Reason 3 is that, at least for conventional superconducting wires (the most popular being Nb3Sn and NbTi) it is easy enough to extrude these materials into wires of all kinds of diameter and length. A typical lab superconducting magnet can contain hundreds or thousands of meters of wire. As an addition, I think it is also generally easier to design and fabricate typical wire-wound solenoids, and in particular it easier to vary the overall design by just changing where your wires go, compared machining out whole new plates for Bitter magnets.

Regarding superconducting-superconducting interfaces, this can certainly be achieved. For normal-metallic (e.g. elemental, alloy) superconductors, this is quite easy to achieve. For other materials, e.g. ceramics, this is much harder and is the top of current on-going research by numerous academics and industry players. The key is to get the resistance of the joint below a sufficiently low value such that the heat generated from the large current (hundreds of amps, maybe a thousand) is sufficiently small not to cause any problems.

There are a number of other idiosyncrasies of superconducting magnets (e.g. quenching, flux creep, trapped field), but that might be a bit beyond the scope of the question. Hope that helps!

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