Ronv:
In the three scenarios in my previous post the ampere turns of each coil is the same, about 3300. So I am expecting the same force from each coil.
The capacitor provides the power for the discharge. This is most visible in scenario #1 where a 12 volt battery charges the 100uf capacitor to 160 volts through a boost SMPS converter. The discharge of the capacitor provides 1.28 joules of energy. The battery cannot provide this amount of energy for a 2 millisecond period, so the capacitor stores the energy for rapid discharge.
I measured the inductance with the plunger in the coil, because that is the real application.
My expectation, and it may be false, is as the wire becomes bigger and the turns become fewer, the inductance becomes less so the reactance is less so there is less resistance to the capacitor discharge, thus keeping the discharge period about the same.