# Electromagnetics: Non-Symetrical coil with external iron

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1. Jan 6, 2016

### Karmaslap

Hello, and thanks for looking at my question. For starters, this is NOT a homework question, or a question I will receive any credit for except maybe a "hey, cool". The level of difficulty is
roughly a junior-year Electromagnetics class homework quesiton, I suppose?

My Question is rather open-ended. Because of the nature of the problem, I am asking for general answers to help me focus on what to simulate, I am not asking any members to simulate or do iterations by hand. If such open-ended questions are not allowed and this needs to be removed, then I apologize, I read the forum rules and saw nothing banning them.

Specifically, feedback I would like: Ideas for how to shape the field and external material to fit the design constraints. A crudely drawn paint image with materials labeled (I am using 600A of 18AWG copper wire, 1000 turns for coil simulation) for any ideas of coil/external iron shape would be great. I have some simulations done, and any analysis of those results would be helpful as well.

I am looking at non-symmetrical coil shapes in an attempt to "shape" the intensity inside the coil. A solenoid is generally symmetrical, so I will refer to it as a coil. Picture is the fastest way to describe what it is that I mean by non-symmetrical.

My desire in shaping the field is to form an intensity shape which is long on one side of the maximum and short on the other side. Graphs work best to show the picture here.
Typical Magnetic Field inside a normal solenoid:

The "Ideal" Shape for me (not realistic, just Ideal) Is for the Magnetic field to build up roughly exponentially, then drop to 0 at the exact point that the field is most intense. Because the inductor won't drop its current to 0 instantly, and ignoring any electrical "tricks" that can get it to drop extremely quickly, I am looking for a design to get me close to this:
Actualy, the ideal curve would have a perfectly flat or gently curved top (a constant magnetic field being just as good as no magnetic field, and a flat spot giving a good place to flip the current off) not a sharp pointy one, but it's already been uploaded.

There is more to the problem, of course, and some other constraints might help. Most importantly, the coil will have an air gap inside, and must maximize interior field strength while minimizing the length of the coil (from entrance to exit of center hole, not wire length except for lower resistance). The coil also must minimize resistance and inductance, while providing a very specific field strength at the very center of the coil (With the desired field strength corresponding to the inner diameter, overall coil length, values for inductance and resistance, and the "length" of the field from the maximum to the edge of the coil). It cannot have a ferromagnetic core, but small may have small mounts of external iron (or other magnetic material) to guide or shield the flux. Depending on the maximum value of T I will also need to carefully regulate the slope of the graph of Field Strength vs distance from coil start to its maximum value. Fortunately, I can make simulations in FEMM and use some RLC circuit simulations to help with the work once I have a good idea from the FEMM simulation. The hard part now is thinking of what to put into the simulation.

My attempt at a solution/my current work: Some brainstorming, and some FEMM simulations of what I think such a coil would look like. I have yet to do the problem by hand as I am simply looking at generalized shapes.
Coil shape:
Tried an "L" shaped coil: skinny at the top, and thick at the bottom. It caused the field to drop off more quickly and to "ramp up" more slowly:

External Material:
Looked at using pure iron (hopelessly rare but a very very good magnetic material):

You can clearly see that this causes the field to drop off more quickly! It was a rather large slab of iron, though, and length of the coil is a primary concern, so It has yet to be seen if this would be of actual benefit, but in theory it has the desired effect. (If someone wants to see what any of this looks like in FEMM I will be more than happy to share, I just don't want to upload a ton of pictures to IMGUR for the question).

Okay, that worked, so how about MORE external Iron? or Steel? (fixed Nd magnet simulation on outside did not have any relevant effect on the magnetic field). For testing purposes to see the effects, the external material was 50% of coil length (unnacceptable length) but that did help me see what worked.

Trying different configurations of external Iron and steel: The strength of the field at the center was raised considerably, and the magnetic field wanted to drop off more quickly outside of the coil, as the flux lines are being redirected. Iron helps, but not a whole lot.
Curve from Grade A carpenter's silicon steel:

placed like this

As a side note, the steel increased the magnetic field in the center by 50% compared to 8% for pure iron. The corner of the steel closest to the "Exit" (bottom in pic) of the core was magnetized to 23T in simulation (almost 100% more!). And about 19T in center. (I realize that specific numbers here are not helpful, but the general trends and % increase are).
A few other magnetic steels had the same effect. A different material called supermalloy was the best, with over a 100% increase in core field strength and a much greater field falloff curve. (Incidentally, if any physics majors need a ~30T-50T field for a few milliseconds, simulations say it is pretty dang easy to do. You could easily sustain the field too if you had liquid nitrogen cooling. All stuff available at a typical university!)

So, it seems clear that an external end cap can help "cut off" the field more quickly.

Combining the "L" shape with Grade A carpenter's silicon steel:
Shape for simulation:

Simulation results through center of core:

Simulation results through the innermost edge of the coil and steel external piece:

This seems pretty close to what I want (The picture two above! the one directly above is just a "cool" pic) I am thinking about trying ramps rather than the "L", trying an extremely thin piece of silicon steel (coil you see is 40 mm tall, by thin I mean 1/2 -1 mm) along the inside of the coil. Do you guys think that would be a good idea? Are there any problems with these sims, that FEMM doesn't realize or that I am doing wrong? (will the external material "steal" the energy that would go to a ferromagnetic object in the core?) I'm asking this before I spend more time doing simulations. I think that I am on to something here with the combinations, I just won't know until I can build models in the lab: one of a normal solenoid, and one that I design, both with the same calculated inductance and resistance. Obviously, I would like to run simulations and think a lot before I purchase wire and high grade steel and spend a long time winding the cores.

Note: All simulations graphs show field strength from about twice the distance of coil length, through center of coil, to same distance away. 0 is the "top" shown in simulation pictures, and the maximum is the "bottom". The top is the coil "entrance" and the bottom (Where the external material is) is the "Exit"

Any feedback or help is appreciated! Part 2 of the question will be regarding the electrical components: specifically how to quickly switch off the current without damaging components. I meant to type up a brief question with a few simulation results. Woops.

Last edited: Jan 6, 2016
2. Jan 6, 2016

### Alfred Cann

I'm not sure I understand your question. I think you want to generate a field with a sawtooth-shaped intensity plot. I think that is not even approximately possible because every turn of the coil generates a field that drops off gently on each side, sort of like your second figure. To find the field generated by a coil of any shape, use superposition, i.e. add up the contributions of all the turns.
Do this mentally and on paper to see what is going on. Do not use simulation at the conceptual stage because it hides what is going on and may mislead you. Use simulation only to get an exact solution for a particular design and to refine the design.
When you talk about current dropping to zero instantly (about par. 5) it seems you are confusing current vs. time with field intensity vs. distance.

3. Jan 6, 2016

### Karmaslap

Hi, thanks for looking at it.
I should edit out the sawtooth looking image and replace it for one with a flat top, which i would prefer. I wrote that above it... But huge wall of text means notes get skipped over.

The second figure is exactly how a normally-shaped field would be. Thinking of these with superposition is how I got the figures I ended up trying to simulate (The "L" and where to put the external material" but actually doing those problems on paper is much harder than running a simulation which takes ~2 minutes, and gives a nice graph of field strength through the center to confirm the initial concepts.

What I meant was that current can't instantly drop to 0 in an inductor, therefore the magnetic field causes by an inductor can't drop instantly to 0 (magnetic field and current vs time being linked). The problem involves material passing through the center of the solenoid and is an optimization of field vs distance. I should have clarified that, as a reader wouldn't know.

4. Jan 7, 2016

### Alfred Cann

Please tell me why you want an axial field whose plot of intensity vs distance drops off sharply at some point. What do you want to use it for, a railgun?

Does it have to be an axial field? I think you could make a transverse field with a fairly sharp edge more easily, using iron pole pieces. But I don't know if that would suit your purpose.

Your last paragraph looks as if you are still mixing up amps vs time with ampere-turns vs distance; are you? Note that magnetic field is not proportional to current vs time; it is just proportional to current.

5. Jan 7, 2016

### Karmaslap

I'll draw up a diagram to help explain why I am interested. (Also, a solenoid-based accelerator would be a coilgun, not a railgun. This is a linear motor: This would use the same principle as a coilgun, except that I don't need a huge discharge from a capacitor into the coil for rapid acceleration like they do. And yes, I know that this is not an efficient way to accomplish this, there are easier and simpler methods, etc.)

Links in "front" of the coil will be more affected than links which have already moved through the coil, if the current is briefly shut off right as the link reaches the peak until it is carried away. with a few coils
The field needs to be axial, yes.
I'm not, I understand it. I should have labeled time and distance better. the graph of magnetic field vs time in an inductor will never drop to 0 instantaneously is what I mean, not magnetic field vs distance.