Magnetic Field Lookup Tables

It may be difficult to separate "theory" from "application," but let''s see if this helps facilitate the discussion.
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JamesC
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Magnetic Field Lookup Tables

Post by JamesC »

So I have begun my journey into magnetic fields, and want to plug these into my simulation tool which is a real-time interactive environment so I want a fast way to resolve basic magentic fields. In particular I am interested right now in round air core solonoids which are much wider than they are long, ie small number of turns.

Most math I have seen for calculating the magnetic field at an arbitary location is tractable for a single loop eg.

http://www.netdenizen.com/emagnet/offax ... ffaxis.htm

But to take it to multiple loops and the way more than one solonoid interacts with the other I suppose what I really want is the CPO package from Simion, and this discusses several techniques
http://simion.com/docs/solenoid.html

BUT! - and finally I come to my question

Magnetic fields seem to be scaleable? I mean if you double the current in a torroid can you just use the same magnetic vector field multipled by the additional scalor of the new current.

So the crux of where I am going is can I have a couple of base case magnetic fields for say a Torroid, two torroids at distance N etc and keep the results as a (large) lookup tables for all points in space. Thence when I want a new case I can just transform the lookup table with the appropriate operators, stretching it, increasing it's strength etc, or doesn't work this way.

And finally and perhaps most importantly do lookup tables of standard magnetic fields like this exist somewhere or could I 'encourage' someone with CPO to generate one for me

If they do work this way I had the idea of configuring my little desktop CNC machine I built recently to map out a magnetic field - probably would interfere with it during measurement though but would make a neat experiment.

Thanks!
Wilfried Heil
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Re: Magnetic Field Lookup Tables

Post by Wilfried Heil »

The magnetic field vector at an arbitrary point can be calculated with the law of Biot-Savart. There are analytical solutions for a number of simple cases (long coil, short coil, single loop, parallel wires) check e.g. Wikipedia.

For anything with a more complicated geometry, you're on your own. If you're writing a program for this, then you can use numerical integration over short lengths of wire.
JamesC
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Re: Magnetic Field Lookup Tables

Post by JamesC »

THanks, I have seen the Biot-Savart calcuations and can probably handle that for the simple cases.

The main issue for me is how this holds up as two fields are bought close together, ie how to they squash. For example two opposing mag fields lines won't cross, they compress each other but what is a good model for this, maybe something like bubbles pushing up against each other.

In any case, I think I have decided to not do the math but instead rig up a couple of test cases in the real world scan in the magnetic field using a CNC machine and a hall-effect sensor or similar. I will have to research if there is a sensor that can give the vector direction of the field also or derive it, and go from there.
Brett
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Re: Magnetic Field Lookup Tables

Post by Brett »

Magnetic fields don't interact in a vacuum. They can only do so through the intermediation of charged particles. You bring two coils together, you just apply Biot-Savart to both of them at the same time, and the result is field lines that don't cross. Comes out of the math, but the two fields aren't interacting with each other, though they WILL interact with the current in each other's coils.

Now, if there's enough plasma around to carry a significant current, it becomes hideously complex. But that's not the case in fusors, generally.
JamesC
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Re: Magnetic Field Lookup Tables

Post by JamesC »

>Comes out of the math, but the two fields aren't interacting with each other

OK so already my understanding is improving. A numerical approach might be the go after all

Found this : http://www.ripplon.com/BiotSavart/
DaveC
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Re: Magnetic Field Lookup Tables

Post by DaveC »

James -

The task of determining the magnetic field at a point in space can be very complicated if the field is time varying and there are materials involved with non-linear permeabilities. For DC fields and non-magnetic materials, linear superposition holds, and the effort is largely a "bookeeping" process for the computer, adding the field contributions (with their respective vector components) of all current carrying conductors.

As soon as one has time varying fields, life gets very involved. Current density distributions in any form of conductor, metallic or gaseous are, at best rather complicated involving all the math we would like to avoid. And in the case of plasmas, even the structure of the conductor is affected. Almost always, the computational effort requires successive approximations - ("numerical methods"), or statistical simulations.

It is probably worthwhile to make some attempts of your own to thrash through some simple cases with DC fields and convenient geometries. Setting up some computer code of your own design and strategy, will develop the general approach and provide some basic insight. For there you will soon see how to make useful approximations for the shapes and arrangements that get to be beastly.

I'd be very interested to hear how your work goes.


Dave Cooper
JamesC
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Re: Magnetic Field Lookup Tables

Post by JamesC »

Thanks for the encouragement.

Interestingly, and it shows how quickly and easily one can get the wrong idea, I didn't realise magnetic fields superimposed rather I thought they were conserved (like energy) and pushed up against each other in some sort of energy minimisation thing which would be much harder to calculate.

Superposition on the other hand should be easier to deal with and fortunately for what I have in mind at least for now should hold for something approximating the DC conditions described.

James Caska
JamesC
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Re: Magnetic Field Lookup Tables

Post by JamesC »

Just to report I have made some progress ( I think ) in calculating the magnetic fields I am interested in.

Actually it was not all that difficult which mean I probably don't understand something! I think I spent more time trying to figure out how to visualise the results.

I still have to validate the results and more difficulty improve the visualisation but here is a pretty pic. This is a pic of the magnetic field of a small solonoid 5 coils, it is calculated using the Biot-Savart algorithm with 100 segment per coil and 200x200 pixels. Takes only a few seconds to compute, gotta love modern day computers compared to what you would have to do in the past.. I will expand on this to import some DXF or something and include 3D visualisation but this is first step.

Anyhow, in the end this will all end up in the fusor sourceforge tools collection
http://sourceforge.net/projects/fusortools/

Thanks Pascal Dennerly for setting that up.

Cheers,
James Caska
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nathematics
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Re: Magnetic Field Lookup Tables

Post by nathematics »

I'd be interested in seeing the source code.
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Chris Bradley
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Re: Magnetic Field Lookup Tables

Post by Chris Bradley »

It's a great effort and well worth the learning experience. Though you could also just download Maxwell SV (2D) from their website for free! (That's not to take anything away from your work - good effort!!)
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