# Magnetic flux conduit for flux concentration?

1. ## Magnetic flux conduit for flux concentration?

I came across a patent for a thick wall copper tube with an electrical gap in its side so there won't be current flow. Does this type of design actually work for concentrating flux? Like this: https://patents.google.com/patent/US6720855B2/en

If this flux conduit doesn't work, how do people usually create an area of more concentrated flux inside a coil?

If it does work, how does it work when no current flows in the thick copper tube?

Thanks, George

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2. ## Re: Magnetic flux conduit for flux concentration?

I suspect the author hopes that some method of wireless power transfer can derive from his idea of a 'flux conduit' made from a copper tube. Or possibly a directional energy beam?

Some aspects of the theory could work, however there is the opposing effect of eddy currents which are generated within the copper. These eddy currents result in a physical force which resists moving magnetic fields, including the very magnetic field which created them. Of course there are gaps in my knowledge.

I'm reminded what happens when I drop a neodymium magnet inside a thick-walled copper pipe. The magnet creates eddy currents which oppose the magnet's motion. Like magic the magnet defies gravity, taking a few seconds to drop through the pipe. As soon as it emerges, it falls freely as gravity dictates.

Videos on Youtube show how a moving magnet slows down just before it impacts a slab of copper. Or in another experiment, a magnet levitates on a string held above a spinning slab of copper.

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how do people usually create an area of more concentrated flux inside a coil?
A ferromagnetic substance normally is the core of inductors. Usually you want to minimize eddy currents because they waste power by generating heat. Thus transformers are built up from many thin iron plates, or else formed from slurry which contains ferromagnetic particles separated by non-conductive material.

3. ## Re: Magnetic flux conduit for flux concentration?

The slot stops -eddy- currents from an AC magnetic field.
It's not confining magnetic flux.

4. ## Re: Magnetic flux conduit for flux concentration?

This will not work with a DC magnetic field; a constant magnetic field will penetrate the copper tube.

If the coil (as seen in the picture) is fed with AC the magnetic flux will penetrate the copper sheet only to a small extent (the skin effect): the copper will effectively repel the magnetic field.

If the copper is replaced with a superconductor, the magnetic field will not penetrate the superconductor and will follow the conduit. This is the famous Meissner effect. See, e.g., https://en.wikipedia.org/wiki/Meissner_effect

A constant magnetic field can be shaped only with a superconductor.

The slot in the copper tube must be very thin: just sufficient to stop current but much smaller than the skin thickness (else flux will leak happily)

I do not know any practical application of this device.

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These eddy currents result in a physical force which resists moving magnetic fields, including the very magnetic field which created them. Of course there are gaps in my knowledge.
The magnetic field is parallel to the axis of the solenoid; the induced eddy currents will be antiparallel to the current flow in the solenoid. But due to the presence of the slot, the eddy currents will not complete the circuit.

Same case applies for a common power transformer: the eddy currents will be antiparallel to the current flow in the coils and the laminations will prevent that.

However, for some part of the current flow, the laminations will be parallel to the direction of the current and we shall need (i) thin laminations and (ii) high resistance steel sheets.

Eddy losses can be significant even with a laminated core; you may use an insulated iron wire shaped like a core (something like a toroidal core).

5. ## Re: Magnetic flux conduit for flux concentration?

Later yesterday, after posting my questions, I came across what people are calling a "Lenz lens" which is utilized to concentrate flux. It uses a similar gap but they are usually flat or wire frame and not conduit shaped.

Also later yesterday I heard back from the patent's listed inventor. She confirms that they have built these in their university lab and they really work.

But I'm still trying to understand them better when conduit shaped.

George

6. ## Re: Magnetic flux conduit for flux concentration?

A point to consider is that the flux conduits other than a magnetic core are not reducing reluctance but increasing it. Means you need many ampere turns to achieve a certain flux at specific point of the conduit. I would say, the flux "conduit" is only able to displace flux but not concentrate it. It's no method to make the flux density in any spatial point considerably higher that without the conduit.

I do not know any practical application of this device.
I agree with c_mitra.

I know applications of similar slotted metal screens used in transformers to reduce leakage inductance.

7. ## Magnetic flux conduit

I stumbled on an earlier thread entitled "Magnetic flux conduit for flux concentration?"

From the opening posting :-

I came across a patent for a thick wall copper tube with an electrical gap in its side so there won't be current flow. Does this type of design actually work for concentrating flux? Like this: https://patents.google.com/patent/US6720855B2/en

If it does work, how does it work when no current flows in the thick copper tube?
I am an electronic and magnetic designer that works in the field of physics research, and this device really pricked my interest, firstly because I had not seen this idea before so it took me a while to figure out if and exactly how it works, and secondly because I wondered what application it might have in my field of physics research, where I spend much time designing coils and devices to generate all manner of magnetic fields.

Others on the original thread did make a lot of relevant points, but maybe I can add a little more.

I conclude that the device does more-or-less work as claimed, but that the closer you look, the less magical and useful it becomes.

The hand waving explanation for how it works is in terms of eddy-current magnetic field screening. An AC magnetic field cannot penetrate a thick, highly conductive metal sheet. To be more precise, it will only penetrate to the "skin depth" which becomes more shallow at higher frequencies, and for higher conductivity of the material. The mechanism by which this works is induced eddy currents, which set up a magnetic field which opposes the original magnetic field.

So to the question "how does it work when no current flows in the thick copper tube?", the answer is that eddy currents most certainly do flow in the copper tube, and it is the opposing magnetic field from these eddy current that prevents flux from "escaping" from the tube. And as (virtually) no flux can escape from the tube, then it is true that whatever flux (eg from a coil) enters the tube at one end, must be directed along the tube without leakage, to the far end of the tube, where the flux spreads out in the normal way and completes the magnetic circuit by returning (outside of the tube) back to the other end of the tube where the flux was created with the coil.

The longitudinal slot along the tube is crucial for this to work. Without it, the open end of the tube will act like a shorted turn of a single-turn secondary winding, and the large eddy current that thus flows unimpeded around the circumference of the tube will do it's very best to prevent flux entering the tube at all. To be more precise, the "shorted turn" open end of the tube will try hard to prevent any net transfer of flux into the coil, which is the very opposite of what you want if you are trying to create a "conduit".

So far, so good, but there is a question that begs to be asked. If the induced eddy currents are prevented from completing a loop around the circumference due to the longitudinal cut, then just what the heck does the distribution of eddy currents in the tube look like??

After considerable thought I think I know the answer, and the answer sheds light on exactly what this device does and what it does not do, and how useful it actually is.

So at this stage, what do others think about the shape of the eddy current loops in the copper tube, given the presence of the longitudinal cut?

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8. ## Re: Magnetic flux conduit

Originally Posted by Precision99
So far, so good, but there is a question that begs to be asked. If the induced eddy currents are prevented from completing a loop around the circumference due to the longitudinal cut, then just what the heck does the distribution of eddy currents in the tube look like??

After considerable thought I think I know the answer, and the answer sheds light on exactly what this device does and what it does not do, and how useful it actually is.

So at this stage, what do others think about the shape of the eddy current loops in the copper tube, given the presence of the longitudinal cut?
Is no one else interested in what the shape of the eddy currents look like? Or is no one game to guess or estimate what they look like? Hard to know. Plenty of people looking at the thread, but no one posting ....

Well here is what I think the eddy currents do. Firstly, from circular symmetry considerations, the eddy currents must flow in circumferential loops. Ampere-turns, if you like. But how is this possible, given the longitudinal slit?

But it is possible, and here is how. Grab yourself a cylinder and a pen, and mark the slit, running from one end to another. Now, place your pencil at end of the cylinder, on the outside surface, very close to the slit. Now draw a current loop, going around the circumference, and ending back at the other side of the slit. So far, no current can flow, because the loop is broken by the slit. But now continue your line, parallel to the slit, ending up at the opposite end of the tube. Now do another full turn around the circumference, ending up at the other side of the slit, then follow parallel to the slit until you end up exactly where you started, tracing out a continuous loop or, more precisely, two complete loops, one at each end of the cylinder. If the slit is sufficiently narrow, then these 2 loops are effectively continuous, and the two current paths along the edge of the slit cancel, because the current in these straight sections flows in opposite directions.

Bingo! Circumferential loops, AKA ampere-turns, are possible, despite the longitudinal slit. The particular example that I asked you to trace is of course only one of an infinite number of possibilities, where the 2 loops can be anywhere along the length of the cylinder or, and this is more likely in practice, one or both loops are distributed along the length of the cylinder.

But here is the crucially interesting part. No matter how you distribute these 2 loops along the length of the cylinder, the net number of ampere turns that you produce is always zero. That is really significant, because it means that on average, the eddy current loops do not assist with pushing the flux along the interior of the cylinder, they merely redistribute the flux lines so they are parallel to the cylinder. The only thing available to push the flux along the cylinder is the ampere-turns that you supplied in the first place, at or near one end of the cylinder.

So this is not a "flux conduit" in any normal or useful sense. Every time you double the length of the conduit, you halve the flux density within the conduit, and leaving at the far end of the conduit. This fairly useless behaviour happens because regardless of the length of conduit, you still only have the same number of ampere turns pushing the flux along the conduit, and the magnetic reluctance (resistance to the flow of flux) scales as the length of the conduit. This is not at all like a useful structure such as a transmission line, where (to a good approximation) one can double the length of the line without significantly reducing the amplitude of what comes out.

Finally, I will take a very specific example, and describe exactly how the flux distribution IMO must look for this particular example. Imagine that the driving coil is a single turn of thin wire, or it can be multiple turns of very thin wire, either will do. And this zero-length coil has the same diameter as the thin-walled, long cylinder, and is placed against the end of the cylinder. What must the eddy current distribution in the copper tune look like, in order to produce a uniform field along the length of the cylinder. And, as stated, the net ampere turns of the eddy current loops must be zero because of the slit.

IMO. the eddy currents will be like this. One of the two eddy current loops will be an exact mirror of the applied current loop, located right up against it, so that it exactly cancels the applied current loop. But, as stated previously, there must in addition be an equal and opposite number of ampere turns so that the net number of ampere turns is zero. OK, no problems. The other current loop, which will be assisting the applied current loop, will be uniformly distributed along the length of the conduit. Those familiar with the field of a "long solenoid", which what we are talking about here, will know that the result is a uniform field where the flux lines are parallel and not diverging, exactly what is required for the tube to behave as a "conduit".

The distribution of eddy currents in the cylinder when the driving coil has significant length, or is not placed right up against the cylinder, etc, will be rather more complex and difficult to exactly predict, but the general flavour of the result will be the same. The net number of ampere turns of the eddy currents will be zero, so giving no assistance in pushing the flux along the cylinder, and the precise distribution of these eddy current loops will be such as to produce a uniform field inside the cylinder.

Have I obviously cocked up or missed something in my interpretation of how it all works? Anyone agree, or disagree with the above?

As c-mitra put it, I can think of no useful application of such a device.

9. ## Re: Magnetic flux conduit for flux concentration?

It's surely interesting to know how the current distribution looks like.

Skin effect requires that at higher frequencies the current flows only near the surface. Respectively I expect that it's circulating under the surface, e.g. outside forward, inside backward.

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10. ## Re: Magnetic flux conduit for flux concentration?

Originally Posted by FvM
It's surely interesting to know how the current distribution looks like.

Skin effect requires that at higher frequencies the current flows only near the surface. Respectively I expect that it's circulating under the surface, e.g. outside forward, inside backward.
Interesting theory. As far as I know, the magnitude of the eddy currents simply decreases at greater depths, but the direction of the current loops remains the same. If what you say is true, then I would expect it to be well documented, for eddy current screening, eddy current brakes, etc etc is a very well known phenomenon for many, many situations other than the copper tube. Can you find any evidence for your expectation? You will need to convince me.

11. ## Re: Magnetic flux conduit for flux concentration?

You can use a 3D solver to verify it.

12. ## Re: Magnetic flux conduit for flux concentration?

Originally Posted by FvM

Attachment 155953

You can use a 3D solver to verify it.
OK. Now I understand. Sorry about that.

Yes, I agree that such eddy currents most certainly will exist. But they will exist whether or not the field along the tube is diverging, and their magnitude will increase with the thickness of the tube, even as the tube thickness becomes much greater than the skin depth. For these reasons I suspect that eddy currents of this type are not major players in the operation of the "conduit", but am willing to be convinced otherwise. If a 3D solver shows otherwise, then I will of course be convinced. My own 3D FEA solver that I wrote 35 years ago, long before such software was generally available, is for magnetostatic problems only. If you have a suitable solver then feel very free to do a simulation and tell us the results.

13. ## Re: Magnetic flux conduit for flux concentration?

With sufficient conduit conductance and field frequency, the field is completely displaced from the metal. It can only exist in the conduit opening. The sketched eddy currents must exist at the inner surface to compensate the field. Continuity demands that the current flows back along the the gap and at the outside.

Of course this is pure conclusion. But unless you show me an alternative solution, I'll stay with it for the time being.

14. ## Re: Magnetic flux conduit for flux concentration?

Originally Posted by FvM
With sufficient conduit conductance and field frequency, the field is completely displaced from the metal ...
Agreed that the field will not penetrate beyond the skin depth, which is small for high conductivity and frequency. AFAIK we all agreed on that from the outset, and in a hand waving way, we can use that fact to predict that the flux that enters the conduit cannot escape except at the far end, and that therefore the flux density within the conduit is (very nearly) constant. But none of that tells us what the shape and distribution of the eddy currents in the copper tube looks like.

It (the magnetic flux) can only exist in the conduit opening.
That depends on the size and placement of the exciting coil. If there is an axial gap between the exciting coil and the end of the conduit, then I'm very certain that not all of the flux will enter or exist in the conduit opening. Likewise if the exciting coil diameter is greater than that of the conduit.

The sketched eddy currents must exist at the inner surface to compensate the field. Continuity demands that the current flows back along the the gap and at the outside.
There is no argument that the eddy currents that you have sketched will exist. But I don't believe that these eddy currents are major players in the operation of the "conduit". And, as a fact, it is not true that continuity demands that the eddy loops that you sketched are the only possibility. I carefully described another loop structure that I suspect (but did not prove) is the main player in the operation of the conduit.

Of course this is pure conclusion. But unless you show me an alternative solution, I'll stay with it for the time being.
But hang on, I specifically did show you an alternative solution, an alternative loop geometry. Not only that, I went on to describe exactly how my proposed loop structure could give rise to correct operation of the conduit, for the specific geometry of a thin coil placed right against the entrance of a long conduit tube. If and when your loop structure can similarly predict the correct behaviour of the conduit, then I'll believe it.

I do not have a 3D solver that can solve for (predict) the shape and magnitude of the eddy currents. However, for any proposed distribution of eddy currents, my magnetostatic solver can show the resultant flux density at all points in space, from which we know if the proposed distribution of eddy currents is correct. I predict that your proposed eddy currents cannot correctly predict the known behaviour of this "conduit", where no flux escapes from the tube. I can model the field produced by your proposed eddy currents if you like.

15. ## Re: Magnetic flux conduit for flux concentration?

Originally Posted by Precision99
I do not have a 3D solver that can solve for (predict) the shape and magnitude of the eddy currents. However, for any proposed distribution of eddy currents, my magnetostatic solver can show the resultant flux density at all points in space, from which we know if the proposed distribution of eddy currents is correct. I predict that your proposed eddy currents cannot correctly predict the known behaviour of this "conduit", where no flux escapes from the tube. I can model the field produced by your proposed eddy currents if you like.
But before I can do the modelling, you need to tell us how the magnitude of the eddy currents that you have sketched varies along the length of the conduit.

If we assume that the magnitude of your sketched eddy currents is the same along the length of the conduit, then I have already modelled it, and can tell you the result.

16. ## Re: Magnetic flux conduit for flux concentration?

Originally Posted by FvM

You can use a 3D solver to verify it.
We agree that eddy currents of this type will in general definitely exist, though for many reasons I don't believe that they are a significant player in making the split tube act as a "flux conduit".

I asked how the magnitude of such eddy currents would vary along the length of the split conduit tube, but received no answer, so I'll try to answer it instead.

The answer depends somewhat on the geometry and placement of the exciting coil, but let's assume that the OD of the exciting coil is the same as the OD of the tube. The exciting coil is of course on axis with the tube, and let's assume a smallish axial gap between the two.

If the split conduit tube was non conductive (and of course non magnetic) then the flux from the coil would penetrate the annular, planar end of the copper tube. From Faraday's law, the eddy current loop sketched by FvM would have a voltage induced around the loop, and as a result, with a conductive tube you would get a loop of eddy current just as per the sketch. And as per Lenz's Law, this eddy current loop would set up a field opposing the applied field, with the result that the said eddy current loops would drop off rapidly along the length of the split copper tube.

Not only that, but it is easily shown that the constant flux density along the conduit does not induce eddy currents of the type sketched. To induce such eddy currents, you need flux travelling axially, and passing through the sketched loop, ie, passing through the annular region between the tube OD and ID. Clearly the flux travelling along the inside of the conduit does not, by definition, run through this annular region of copper, so this flux cannot give rise to the the sketched eddy currents. So from this angle also, we conclude that the sketched eddy current do not extend far beyond the end of the tube where the exciting coil is placed.

Anyone disagree with that?

17. ## Re: Magnetic flux conduit for flux concentration?

Instead of lengthy explanations, can you simply sketch which form of eddy currents you expect?

I presume you agree that there must be eddy currents at the metal surface if a field is passing along the conduit.

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18. ## Re: Magnetic flux conduit for flux concentration?

Originally Posted by FvM
Instead of lengthy explanations, can you simply sketch which form of eddy currents you expect?

I presume you agree that there must be eddy currents at the metal surface if a field is passing along the conduit.
Yes, agreed that there must be eddy currents at the inner metal surface. But broadly speaking, not at the outer metal surface.

The shape of the current loops is IMO easier to describe verbally than to sketch, and I thought that I explained it clearly in a much earlier posting.

I'll try sketching a typical current loop, with a black texta pen, on the surface of a cylindrical glass jar, and then take a photo, so that hopefully you can see the entire current loop at once. Your current loops are easy to sketch, but my current loops are not. And I'll repeat me previous verbal description as well.

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As promised, I have sketched an example of what I think the eddy current loops look like, on a cylindrical glass jar. Neat idea, eh?

Now the following text, quoted from my previous post, may make more sense.

Well here is what I think the eddy currents do. Firstly, from circular symmetry considerations, the eddy currents must flow in circumferential loops. Ampere-turns, if you like. But how is this possible, given the longitudinal slit?

But it is possible, and here is how. Grab yourself a cylinder and a pen, and mark the slit, running from one end to another. Now, place your pencil at end of the cylinder, on the outside surface, very close to the slit. Now draw a current loop, going around the circumference, and ending back at the other side of the slit. So far, no current can flow, because the loop is broken by the slit. But now continue your line, parallel to the slit, ending up at the opposite end of the tube. Now do another full turn around the circumference, ending up at the other side of the slit, then follow parallel to the slit until you end up exactly where you started, tracing out a continuous loop or, more precisely, two complete loops, one at each end of the cylinder. If the slit is sufficiently narrow, then these 2 loops are effectively continuous, and the two current paths along the edge of the slit cancel, because the current in these straight sections flows in opposite directions.

Bingo! Circumferential loops, AKA ampere-turns, are possible, despite the longitudinal slit. The particular example that I asked you to trace is of course only one of an infinite number of possibilities, where the 2 loops can be anywhere along the length of the cylinder or, and this is more likely in practice, one or both loops are distributed along the length of the cylinder.

But here is the crucially interesting part. No matter how you distribute these 2 loops along the length of the cylinder, the net number of ampere turns that you produce is always zero. That is really significant, because it means that on average, the eddy current loops do not assist with pushing the flux along the interior of the cylinder, they merely redistribute the flux lines so they are parallel to the cylinder. The only thing available to push the flux along the cylinder is the ampere-turns that you supplied in the first place, at or near one end of the cylinder.

So this is not a "flux conduit" in any normal or useful sense. Every time you double the length of the conduit, you halve the flux density within the conduit, and leaving at the far end of the conduit. This fairly useless behaviour happens because regardless of the length of conduit, you still only have the same number of ampere turns pushing the flux along the conduit, and the magnetic reluctance (resistance to the flow of flux) scales as the length of the conduit. This is not at all like a useful structure such as a transmission line, where (to a good approximation) one can double the length of the line without significantly reducing the amplitude of what comes out.

Finally, I will take a very specific example, and describe exactly how the flux distribution IMO must look for this particular example. Imagine that the driving coil is a single turn of thin wire, or it can be multiple turns of very thin wire, either will do. And this zero-length coil has the same diameter as the thin-walled, long cylinder, and is placed against the end of the cylinder. What must the eddy current distribution in the copper tune look like, in order to produce a uniform field along the length of the cylinder. And, as stated, the net ampere turns of the eddy current loops must be zero because of the slit.

IMO. the eddy currents will be like this. One of the two eddy current loops will be an exact mirror of the applied current loop, located right up against it, so that it exactly cancels the applied current loop. But, as stated previously, there must in addition be an equal and opposite number of ampere turns so that the net number of ampere turns is zero. OK, no problems. The other current loop, which will be assisting the applied current loop, will be uniformly distributed along the length of the conduit. Those familiar with the field of a "long solenoid", which what we are talking about here, will know that the result is a uniform field where the flux lines are parallel and not diverging, exactly what is required for the tube to behave as a "conduit".

The distribution of eddy currents in the cylinder when the driving coil has significant length, or is not placed right up against the cylinder, etc, will be rather more complex and difficult to exactly predict, but the general flavour of the result will be the same. The net number of ampere turns of the eddy currents will be zero, so giving no assistance in pushing the flux along the cylinder, and the precise distribution of these eddy current loops will be such as to produce a uniform field inside the cylinder.

19. ## Re: Magnetic flux conduit for flux concentration?

The silence is deafening. This is a really odd forum. There are hundreds, or thousands, of people that read these postings, and yet almost no one writes anything. I am asked to provide a sketch of how the eddy currents look, and go to some trouble to do so, and again there is a deafening silence. Weird.

I can provide further evidence and reasoning as to why the eddy currents look broadly the way I have sketched and described them, but have little idea if the information that I am providing is of interest to others. Personally I think it is very interesting to ask the question as to how the eddy currents in the split copper conduit tube look, and then go ahead and answer the question. In my view that question is now answered fairly convincingly, but if anyone is interested I can provide further evidence by looking at the problem from a completely different angle, and reaching exactly the same conclusion. That is what I love about science and engineering. If a proposed solution is correct, then you should be able to look at it from many different angles, and always come to the same conclusion.

Anyway, here is a related thought that some may find interesting. What happens if we make a tapered conduit tube, tapering down to a small diameter at the far end? We know that flux can't escape from the tapered tube, so the same amount of magnetic flux that enters at the big end must be leaving at the small end, and thus the flux density must be increasing along the length of the tube. So we now apparently have a true flux concentrator, and the concentration of flux (AKA increase in field strength) could be very large indeed by making the exit diameter small enough. What do others think about this? Do we finally have a flux conduit that might actually be useful?

20. ## Re: Magnetic flux conduit for flux concentration?

This topic is interesting however eddy currents are invisible and tend to do the unexpected. I'm still trying to get my mind around the way a neodymium magnet defies gravity, slowing down as it falls through a copper pipe. I tried it and it really works.
And it also works with an inclined copper slab.
And there's the trick where a spinning copper plate causes a magnet to levitate as a string holds it over the plate. These tricks are demonstrated in Youtube videos. They speak of forces which are profound, and full of possibilities if only we could understand the relationships between electricity and magnetism and gravity. Probably also zero-temperature superconduction.

I suppose a slotted tube is similar to the copper slab or copper plate. We can expect eddy currents to be generated as the magnet passes close. Are you saying that a lone magnet is able to cause eddy currents (or one large eddy current) in the entire mass of copper? Is that what's meant by a flux conduit?

The webpage below is a thought-experiment which seems to explore a similar idea. A plain transformer is extended (via one diagram after another), so that it seems to convey magnetic force in a novel manner.

www.amasci.com/elect/mcoils.html

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