The exceptionally slender aspect ratio comes from 1) need to reach around two coils with >10K ampere turns each. That's the minimum to get 1 tesla in 1 inch of air, for any pole diameter. Plus roughly 6% to magnetize about 1 lineal meter of steel to similar B value, same as in MCM. And 2) keeping the pole area down to facilitate DIY steel fabrication and handling, since no minimum diameter was required. I still believe this would be hunky dory if not for the leakage flux challenge.

**Thanks for all the hints**. After some reading, thinking, and just a little computing, my grasp of leakage flux is much better than it was a few days ago. The Internet teaches that all electromagnets and transformers have leakage flux percentages. It helps to keep air gaps narrow (duh!). And if wide, to place the coils as close as possible to the gap.

Some simulations, and multi-point flux measurements (with various gap lengths), are in the planning stage.

**I bet they will support the view that in**Permeability is second, and nonlinearity (saturation) is last.

*this*application, aspect ratios are what matter most.Let's assume the core's top half is a mirror image of the bottom. Take the magnet's nominal size (pole diameter) as the unit of length. I claim that the dimensions which matter most are air gap length, pole length, and radial distance between pole and "side bar". The last two are driven by coil length and diameter. The numbers for MCM appear to be in the mainstream -- about (0.24, 1, 1). For BTI they are (0.33, 2.33, 1.5).

For simplicity, keep B enough below saturation that the steel B-H curve is still sort of linear. Then we can look at the B/2 field generated by bottom coil only. Later superimpose a mirror image to get the total field.

Consider the flux impelled upward by the lower coil, when it reaches the bottom pole surface. If there's no air gap, the least reluctant return path is to carry on into the upper pole piece, and come back around the yoke. Nothing but steel! Total reluctance is low, and so is the total MMF for a design amount of flux. The "magnetic potential" is distributed around the whole circuit, so a small fraction of the flux will take a short cut through air from the pole pieces to the yoke.

It doesn't take much of an air gap to greatly raise the magnetic potential difference between the two pole surfaces, and demand lots more ampere turns. Now as the flux emerges from lower pole, the upper pole surface isn't so inviting. The yoke bars are still on the far side of some air, but their broadside view presents plenty of area.

I think simulations (and measurements) will show that when the air gap reaches 1 inch, between 3 inch diameter poles, the total reluctance of sideways leakage paths is less than that of the air gap itself. Both are much larger than the reluctance of the intended flux path through steel. Yoke bars could all be twice as thick, or twice as permeable, without greatly reducing the leak percentage. If 3D simulation were available, we might see if it helps to place my side plates with narrow edges instead of broad faces oriented toward the pole axis.

And that's one man's novice opinion.