Suppose the magnet has to be separated from the beam by a distance s.

Suppose the NSFFAG magnet is quad-like and the maximum beam radius from the magnetic centre is a*s for some number a.

Suppose the radius of curvature, beam rigidity and magnet packing factor are fixed, so the maximum B field at that radius is a fixed value B.

The gradient is then G=B/(as).

The stored energy in the magnet bore is proportional to G^2r^4=(Gr^2)^2 where r=as+s is the bore radius.  The stored energy can be minimised by minimising Gr^2.

Gr^2 = B/(as) * ((a+1)s)^2
 = Bs * (a+1)^2/a

Suppose s is fixed technologically (B is fixed by the FFAG design requirements).  Then the minimum of (a+1)^2/a occurs at a=1.

So the max beam radius a*s must be equal to the standoff distance s.
The total beam excursion (diameter) in a QF magnet should be 2s.
The magnet aperture diameter should be 2r = 4s.

Real estimates for s include s=11mm (Stephen) and s=17mm (Georg, fairly pessimistic).
So the total beam excursion diameter should be 22-34mm and the magnet aperture diameter should be 44-68mm.

This is the magnetic stored energy optimum.  Smaller is worse, larger is worse.  The only reason to move from this area is if another design constraint (e.g. time of flight or a hard limit on pole-tip field) is present.  Lowering the pole tip field increases the excursion, whereas lowering the TOF spread decreases it.

This also implies that (absent pole tip field limits), the pole tip field will be twice the on-beam max field.

For combined function magnets, the dependence is a little weaker, favouring slightly smaller magnet apertures, although the quad part still contributes the bulk of the stored energy since it becomes largest around the edge of the aperture where there is the most area.