After winding several coils by hand, I wished to eliminate the guesswork and model the coils using Finite Element Analysis with the freeware program FEMM.
After talking to design engineers at Buckley Systems and Wellington Drive, I realised that they are striving for focused flux lines with the absolute minimum of stray magnetic flux, which is the opposite of what I am trying to achieve. The advice from both companies was to model the magnets myself, as the electromagnets can be resolved as a linear equation at any given point in time. Additionally, this would give me the ability to investigate the different geometries and materials that I wanted to test.
Using FEMM and some online calculators I manage to create a base former/coil to use as a control and worked from there. In order to have enough ‘pixels’ in my grid the maximum coil diameter (coil + former) was 8mm and 40mm high. Thus the control coil was:
Outer Diameter 8mm
Wire Diameter 0.5mm
Coil Windings 320x
Current 1 Ampere
Coil Former Pure Iron
Finite Element Method Magnetics models coils axisymmetrically, and shows the output in Tesla with the pink regions being the strongest at round 0.001T: