Superconductor general concept questions

Question

I was thinking about building an electric motor using superconductors and I have some general concept questions in regards to how the behavior might be different from ordinary wires.

1. The Meissner effect, expulsion of magnetic fields from the superconductor. If you construct a solenoid out of superconducting wire does this Meissner effect significantly change the field pattern compared to a regular wire solenoid?

2. If a solenoid is created out of superconducting wire is the current limited to the magnitude of the magnetic field it creates because if the magnetic field strength is too large it will return the superconductor to a non superconducting state?

3. If you have a superconducting wire with a current flowing through it and you expose it to a magnetic field does it still experience a force (obeying the same rules as a regular wire with current flow) or because of the Meissner effect the magnetic field never reaches the current carriers and so no force is experienced? Or is there only a fraction of the expected force experienced because the magnetic field does not penetrate through all the current carriers?

4. If you have two or more strips of superconducting tape stacked on top of each other with current flowing in the same direction through them and then you have a magnetic field strength probe and you probe the space above the stack, would the field be just the sum from each strip or would the Meissner effect in the strips closer to the top surface cause magnetic shielding of the lower strips and so the real magnetic field strength near the surface of the top strip would be less than the sum of the magnetic fields from each current carrying strip?

5. Is current flow in a superconductor only a surface effect? (i thought it was) Why did I see one company selling 3D wires? is that really isolated 2D stacks?

6. Is the only way to make a loop of superconductor run a continuous current is by induction?

Thanks for reading and thanks in advance for any responses.

Answer 1

For question number five, the answer is it depends on the type of superconductor. For type I superconductors, the superconducting carriers are ideally only running along the surface of the material in a layer called the London penetration depth. For type II superconductors, the carriers start on the surface, but can ultimately use the entire volume. There's a mathematically accurate model of this called Bean's model. Basically as each layer of the superconductor hits reaches its critical field, (or critical current), the next layer begins carrying current. The diagram1 below describes the model briefly.

References 1. Bean, C., "Magnetization of High-Field Superconductors", Rev. Mod. Phys., 36, (1964), 31

Answer 2

Axawire, I can answer a few of these question, though not all of them (I don't know the answers to 4 and 6), I just took a course on this subject ^^

1. The field will not change significantly outside the solenoid; the solution of Maxwell's laws will be the same if you use a superconductor or any other material. However, the field will be very different inside the wires. Also, take into acount that the magnetization in a superconductor follows a hyteresis loop if you are planning to use tunable magnetic fields.

2. Yes, it is limited to this maximum current, which is usually called "critical current". In order to have a good estimate of this quantity, consider that the solenoid you are going to build is not infinitely large, so you have to carefully calculate the resulting magnetic field on the surface of the solenoid, which could be significantly bigger than in the center.

3. The solenoid will experience a force. Since superconducting wires can carry a lot more current than regular ones, they produce magnetic fields which are much stronger, and thus the resulting force experienced by the solenoid will be huge; if you don't take enough previsions, your solenoid can break even with the self-induced force.

4. The current will be concentrated in a thin layer on the superconducting surface, though generally it presents a finite depth depending on the particular material. With some materials you can construct cylindrical wires, and with other materials you have to make strips. I don't know the difference between different comercialised wires, but it might be related to this.

I hope this is useful advice!

Answer 3

To answer question six, it is very common to use what is often refered to as a "switch heater" or "persistent switch" in order to produce a persistent current in superconducting magnets.

The superconducting coil is connected at each end to leads that run to a current supply so that you can drive a current through the coil. Additionally, each end of the coil is connected together via a small portion of superconductor that is kept in the normal-state via a heater. You drive a current through the coil with the heater turned on until you have produced a magnetic field of desired strength. By turning off the heater, you short-circuit the leads to the current source and create an isolated superconduting loop through which the current will continue to persist. The power supply can then be turned off. I've never seen a superconducting magnet that has not been fitted with a switch of this type.

I should probably add that, in practice, the field will not last forever and is subject to the usual inductive time constant. There is a resistance due to flux motion that I can elaborate upon if you wish.