Sorry, but the name of the CAVITY used in MRI (and NMR) has, unfortunately, been named a "toroid cavity" but it is really just a hollow solenoid.
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The person is placed in the cavity and the elongated donut is wrapped as shown, to create a magnetic field as shown. A Toroidal cavity is much, much, much (did I say much?) different than a toroid inductor.
An NMR and MRI are all about maximizing the applied a magnetic field to the sample. Using a toroidal inductor would be both uncomfortable for the patient to contort themselves into the center of the round cake area of the donut instead of the center of the hollow solenoid. The center of a toroid inductor is all about MINIMIZING the magnetic field (in the center of a circle made by a bunch of coils) .
I am very familiar with MRIs and NMRs and yes, they have large external magnetic fields but a really bad analogy for toroidal inductors.
And, as for your Falstad simulations, those are fine but I've never made a toroid with an air core. The leakage of a real toroid with an iron powder or ferrite core does note lead to any interference with adjacent cores that I have ever scene in real, practical applications.