So, you're saying it's identical to the stray inductance of the single turn in free space?
LL (or rather, k) of an infinite solenoidal transformer is only the ratio of areas, right? Loop it around sideways into a toroid and you get much the same thing, but now the diameters are constrained to be less than the torus diameter. For the inner winding being much smaller than the outer, it could still be around A1/A2, but when they're both fairly similar to the torus diameter there's going to be something else at work, like a log of a ratio. And that doesn't say anything about a single turn, only a current sheet (infinite turns, infinnitessimal current per turn; finite total current). Ah, but counting only the stuff going through the toroid (thereby assuming that everything outside sums magically to the same flux, which fortunately, Kirchoff assures us it does), a single turn (particularly at HF where skin effect dominates) will look like a current sheet anyway, so that at least isn't too hard. So what it comes down to is, the space between the primary winding (which is a winding as such) and the secondary (a hunk of copper tubing) is where the leakage flux goes? And so, to minimize LL, one must have that pipe as large as possible, so it's as close to the primary as possible? Or alternately, have the primary wires gathered as close to the pipe as possible?
What are the limiting factors? An infinitely thin secondary seems like it should have infinite LL, but I know that a current transformer works by enclosed current alone. What's missing here?
Tim