# Question about Superconductor Flux Pinning

1. Mar 10, 2006

### snip

As I understand it, flux pinning is when a material becomes a superconductor in the presence of a magnetic field, say from a permanent magnet, and the lines of flux from the permanent magnet are trapped inside the superconductor causing the superconductor to be held ("pinned") at a fixed distance from the magnet. Ok. My question is this:

Let's say I have a cube of superconducting material and 6 cube-shaped permanent magnets. I set up the permanent magnets on a rigid structure in such a way that the cube of superconducting material is in the center and each side of the superconductor has a permanent magnet next to it, with a small gap (let's say 1 mm). So, once I set this up (the superconducting material isn't a superconductor yet), I hold the superconducting cube in the very center with tweezers (at a fixed distance of 1 mm from each magnet), then I cool down the whole thing and the cube becomes a superconductor. Now for the real question: am I correct in assuming that the magnetic field of the permanent magnets surrounding the superconductor will become pinned in such a way that, when I remove the tweezers, the superconducting cube in the center will stay 1 mm from all of the magnets, effectively holding the superconductor in the center no matter how I tilt or otherwise move the entire device. In other words, will the superconductor become locked in the center of the magnets?

2. Mar 10, 2006

### ZapperZ

Staff Emeritus
You are missing an important factor here - the CAUSE or origin of such flux pinning.

In many instances the flux is pinned to a defect, or grain boundary, etc. So if the material is anisotropic (such as in a high-Tc superconductor), it would not create a pinned flux in all direction equally. Furthermore, with magnetic fields in all different directions as in your example, the flux lines will have to snake through the material and this is not conducive to creating a pinned flux line.

Zz.

3. Mar 10, 2006

### snip

Well it doesn't have to be perfectly symmetrical just to hold the cube in place does it? I'm really just curious about question of whether or not a superconductor can be fixed in place somehow without touching anything.

4. Mar 10, 2006

### Gokul43201

Staff Emeritus
Can you draw (for simplicity) a 2D picture of the field lines caused by 4 such magnets (in a square arrangement) ?

5. Mar 10, 2006

### ZapperZ

Staff Emeritus
Er... you haven't seen the ridiculously popular demonstration of a levitated superconductor on a magnet that almost every high school and college students have seen?

Zz.

6. Mar 10, 2006

### snip

Of course I have, and you aren't listening to me. I made it clear in my post I'm not talking about just levitation. In those demonstrations the superconductor can still move and spin around, it just can't move up and down. I'm talking about when the superconductor can't move in any direction relative to the magnets. Like if I attached the device to the end of a rod like a torch, I could throw it up in the air and spin it around and do whatever I want and the superconductor would stay exactly in the center of the magnets without moving relative to them. Is it possible or not?

7. Mar 11, 2006

### ZapperZ

Staff Emeritus
But the spinning around is just a "bonus". It DOESN'T HAVE TO be spinning around if no spin is imparted. It also totally depends on how strong of a magnet one uses.

The magnetic levitation trains make use of such flux pinning. If you have a magnet that is strong enough that can make many penetration through a superconductor, then what you have a many of these flux lines being penetrated. When this occurs, the levitation becomes very stable because these flux lines do not like to be twisted. That is why such technology is used. A spinning, levitated train is not a good thing.

Zz.

8. Mar 11, 2006

### Gokul43201

Staff Emeritus
Not with the set-up you've described. If you drew the picture I asked you to, you'd see that there is no stable equilibrium in any of the possible configurations - unless the 6 magnets are connected to each other rigidly. And even then, the only configuration that will permit reasonable flux entry is one where 3 of the magnets have S-poles facing the SC cube. This, however, means that flux "lines" through the SC must enter and leave through adjacent, rather than opposite, faces of the cube. I'm not sure how energetically feasible that would be.

Last edited: Mar 11, 2006
9. Mar 11, 2006

### snip

Ok, so I just made a diagram of a better way to do it. How about instead of one superconductor in the center we have 6 superconductors, each next to one of the permanent magnets, and attached to a cube in the center. You really have to see the attachment. Anyways, since the magnets are sufficiently spread out we don't have all these magnetic fields crossing each other, so the superconductor will basically lock in the flux of the magnet next to it. It's like the classic flux pinning experiment, but one on each side of a cube. I can't think of a way this one wouldn't work.

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10. Mar 11, 2006

### Intuitive

You could also drill holes into each face of the Super Conductor Cube to where it looks like a Die or Dice, instead of dimples, it would have holes, each hole exits out each opposite side so that the Meissner effect can penetrate the Super Conductor Cube from 6 sides, This could help control the flux pinning of the Super Conductor between multiple Magnets by controlling the Meissner effect over and through the Super Conductor.

11. Mar 13, 2006

### Gokul43201

Staff Emeritus
Depends on what you mean by "work". If you plan on spinning this around, or chucking it in the air, it might not stay suspended any longer. If you subject the device to larger than critical accelerations, you will exceed the critical field that will drive the SC normal.

If you are reasonably gentle with the device, the inner structure will stay suspended.

Also, I imagine your "air gap" is really a cryogen.

12. Mar 13, 2006

### ZapperZ

Staff Emeritus
There is something I don't quite get in all of this. Based on your scheme, what is the real reason of requiring (i) that there has to be magnetic field penetration forming fluxes in the superconductor and (ii) that there has to be pinned flux?

Why isn't this done with purely a Type I superconductor with magnetic field below the Hc? What is the physics requiring flux formation in the superconductor and that they be pinned? Is it purely stability issue? But I haven't seen you even use such arguments. Your scenario so far has been purely geometrical.

Zz.

13. Mar 14, 2006

### snip

Well, I don't know about other ways without flux pinning, but pinning seemed like the way to accomplish what I wanted. The reason I'm curious about all of this is simply that I wondered if there was a way to create an object inside another object in a natural stable configuration where the two objects don't touch. You then seal both objects and create a vacuum between them, in the "air gap", and now the inner object is not touching ANYTHING. I don't know about you guys, but I just think that's kinda cool.

Last edited: Mar 14, 2006
14. Mar 14, 2006

### ZapperZ

Staff Emeritus
So you have no clue why, for example, you can't use a Type I superconductor?

Zz.

15. Mar 14, 2006

### snip

I don't see what your getting at. I was merely wondering if it would work at all, I don't remember saying there couldn't be other ways to do it. Are you talking about using the Meissner effect instead of flux pinning? Would that be stable?

16. Mar 14, 2006

### ZapperZ

Staff Emeritus
No, I'm just trying to understand the purpose of (i) having flux lines and (ii) having them pinned. I asked this previously, but you never answered. I thought maybe you had a particular reason for wanting to use these two effects, but based on your sketch, there's nothing there that would require these two. It's all geometrical.

That's why I asked the need for having them in case there's something I missed. Remember, you specifically and explicitly mentioned about fluxes in a superconductor, and that they're pinned, before leading into your scenario. This leads me to believe that somehow they are part of your setup. But when I look at it, there's nothing there that requires those two things. What did I miss?

Zz.

17. Mar 15, 2006

### Intuitive

I think Zapper was just trying to tell you about Type (I) Superconductors.

In http://www.americanmagnetics.com/tutorial/supercon.html" [Broken], magnetic fields are kept out of the sample until they reach a certain critical strength, after which magnetic fields pass freely into the material and it becomes non-superconducting (normal).

Last edited by a moderator: May 2, 2017
18. Mar 15, 2006

### Creator

I agree with Gokul; the inner structure will stay in place (as in your picture) provided the weight of the inner structure doesn't exceed the combined diamagnetic repulsion of the bottom SC and the flux pinning of the other five.

2ndly, from a practical point, you would need to exchange the location of the magnets vs. the superconductors, (moving the superconductors to the outside frame), so they can be more easily kept in the cryogen without adding additional weight to the inner structure, (a feat which in itself will require the patience of Job).

Weight is the critical issue, the vector of which changes with rotation, further complicating the levitaton force requirements.

Increasing the diamagnetic repulsion (and pinning) by higher field strength has practical limitations, namely, the magnitude of the B field neccesary to sustain the weight may exceed the critical B and ruin SC.

Creator

--Consciousness: That annoying time between naps.--

Last edited: Mar 15, 2006
19. Mar 16, 2006

### snip

How does one find out the amount of weight a superconductor can support? Is there a formula?

20. Mar 18, 2006

### Creator

Hmm..The easy anwer is: Trial and error.:yuck:
There is no general formula for all situations.
Diamagnetic repulsion will vary with each type of SC. Generally the type II (high temp.) have higher magnetic susceptibilities. You could check out the magnetization curves for various SC's to find which have have the greatest (negative) magnetic susceptibilities, (i.e, the ratio of magnetization to the field producing it).
For the diamagnetic part alone you would need to balance the weight (mg) against the diamagnetic repulsion force, which I think will be given by the magnetic field B, times the diamagnetic constant, times the B field gradient, dB/dz, (the change in B with height). I think that's right. (A gradient in the field is necessary for a force to develope). I could be wrong; you may need the magnetic energy per unit volume, and include the volume of the SC.

When you throw in the complications of flux pinning, (number of pinning centers, flux creep, pinning center force density), there's no easy answer.

Try designing with some cheap YBCO and get a feel for the forces involved.
You may end up wanting to forgo the cryogenic complication of SC's and redesign using bismuth or pyrolytic carbon, both of which are highly diamagnetic and easily obtainable, and the fields of which are stable against a permanent magnetic field.

Creator

-Always go to other people's funerals, or they won't go to yours.-

Last edited: Mar 18, 2006