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2D toroidal solenoid simulation

Posted Apr 10, 2021, 10:39 p.m. EDT Electromagnetics, Low-Frequency Electromagnetics, General 3 Replies

John Hughes
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Is it possible to simulate the inductance of a toroidal solenoid in 2D--say, a single copper wire with 100 windings?

I am looking for instructions on how to do this, and cannot find out whether it is possible to simulate this with a 2D axisymmetric model. Will a 2D model allow me to simulate a toroidal solenoid that is helically wound? Can it model the windings with a slight pitch, as would be the case in 3 dimensions?

I'm trying to cut down on the size of my current 3D model and would love to work with a 2d cross-section along the XY plane. See the photo attached for an example.

Please let me know whether this is possible. It's important that it is a single copper wire with multiple windings.

3 Replies Last Post Apr 12, 2021, 4:16 p.m. EDT
Jeff Hiller COMSOL Employee

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Posted: 3 years ago Apr 12, 2021, 9:36 a.m. EDT

Hi John,

Axisymmetry means that everything in the 3D problem definition is invariant by rotation about a straight line. I don't see how that applies to your problem.

Best,

Jeff

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Jeff Hiller
Hi John, Axisymmetry means that everything in the 3D problem definition is invariant by rotation about a straight line. I don't see how that applies to your problem. Best, Jeff
Robert Koslover Certified Consultant
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Posted: 3 years ago Apr 12, 2021, 10:38 a.m. EDT
Updated: 3 years ago Apr 12, 2021, 10:52 a.m. EDT

I suspect that you might be able to accomplish your objectives by creating a 3D structure that includes only (and exactly) 1 turn, and (for the case of 100 turns) a pie wedge worth of the subject torus (with a pie wedge of the surrounding space, too) consisting of 360/100 (aka, 3.6) degrees in azimuth, and then applying periodic boundary conditions. If you do take that approach, you'll want to set up the model very carefully and make sure you fully understand the details. If accounting for the (likely-modest) perturbation to the inductance due to the slight pitch to the windings is actually important to you, then it could be worth the effort. You could even check it, in part, by preparing a two-turn model (a 7.2 deg pie wedge) and then see if you obtain the same result. Added: For an example of using periodic boundary conditions in cases of section-wise rotational symmetry, see the "sector_generator_3d.mph" model provided in the Comsol Application Library.

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Scientific Applications & Research Associates (SARA) Inc.
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I suspect that you *might* be able to accomplish your objectives by creating a 3D structure that includes only (and exactly) 1 turn, and (for the case of 100 turns) a pie wedge worth of the subject torus (with a pie wedge of the surrounding space, too) consisting of 360/100 (aka, 3.6) degrees in azimuth, and then applying periodic boundary conditions. If you do take that approach, you'll want to set up the model *very carefully* and make sure you fully understand the details. *If* accounting for the (likely-modest) perturbation to the inductance due to the slight pitch to the windings is actually important to you, then it could be worth the effort. You could even check it, in part, by preparing a two-turn model (a 7.2 deg pie wedge) and then see if you obtain the same result. Added: For an example of using periodic boundary conditions in cases of section-wise rotational symmetry, see the "sector_generator_3d.mph" model provided in the Comsol Application Library.
Walter Frei COMSOL Employee

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Posted: 3 years ago Apr 12, 2021, 4:16 p.m. EDT

As Robert says, a good approach here is to consider a "pie-slice" of just one turn. You can actually take that a bit futher, and cut that pie slice in half via the PMC symmetry condition (parallel to direction of current flow) and in half again, via the Magentic Insulation symmetry condition (in the plane of the toroid, and you'll then be left with a very simple model to solve in 3D. Regarding symmetry, see also: https://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/ and note that you could also consider the finite precession if you wanted to, as Robet says, using the Periodic condition.

As Robert says, a good approach here is to consider a "pie-slice" of just one turn. You can actually take that a bit futher, and cut that pie slice in half via the PMC symmetry condition (parallel to direction of current flow) and in half again, via the Magentic Insulation symmetry condition (in the plane of the toroid, and you'll then be left with a very simple model to solve in 3D. Regarding symmetry, see also: https://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/ and note that you could also consider the finite precession if you wanted to, as Robet says, using the Periodic condition.

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