1. The force on a coil from the coil on the opposite side is reduced because the conductive ball of B-field-excluding plasma in the center shields them from each other. (pushes their lines away from each other)
Likewise the far sides of the 4 adjacent coils. (depending on the plasma ball diameter)
My first cut would be to approximate the field seen by a coil as the current in the near halves (or so) of the 4 adjacent coils. Modeling them as one coil at maybe twice the spacing of the actual nearest approach.
No I have not gotten around to it yet.
![Embarassed :oops:](./images/smilies/icon_redface.gif)
2. Any force on a coil from induced plasma currents would reduce the force from the other coils.
3. Any force on a coil from induced plasma currents would (I think) be equal to the physical pressure of the plasma itself. So, how much force would we see from a pressure that really is still a pretty hard vacuum. Not much I think.
4. Consider the bottom coil of the 6 coil structure before the plasma is formed:
The fields on it from the top coil and the top parts of the 4 side coils cancel each other.
Also the fields from the sides of the 4 side coils (where they come together) cancel each other.
All horizontal forces cancel by symmetry. (That works for the whole coil, but this assumption needs to be revisited later when calculating hoop stresses within the coil. My first look tells me that they mitigate hoop stresses because the nearer currents predominate and are opposite to the current in the coil in question.)
What is left is the field from the horizontal components of the bottom portions of the 4 side coils. And, as a second order term some portion of the horizontal current component of the 4 triangular virtual coils at the top corners must be considered (but might also cancel).
Conclusion: I think a conservative worst case model would be to calculate the force on the bottom coil from an identical (parallel) coil located at the height of the bottoms of the 4 side coils.
A closer approximation would be to place it at the height of the rms average of the height of the bottom semicircles of the 4 side coils.
(I could have done the integral in college but...)