To my knowledge the properties of the postulated flux loop are not
determined precisely, so I will design an approximation which appears
reasonable. For simplicity, I will construct the - and
-components separately, and then at time form the product
The flux loop appears to be very compact in both the - and -directions. Unfortunately compact functions are often the most difficult to approximate with Fourier-type series, but it is possible. In the direction I found that a Gaussian profile is most straightforward to construct, which is achieved by generating coefficients with a broad Gaussian distribution: , and with lt-sec.
In the radial dimension I found that the prescription, constructed a suitable radial profile for the toroidal field, where lt-sec. This profile is very compact, being nearly constant and non-zero in the interval lt-sec, but nearly zero everywhere else. Here I used 300 terms for both the and terms.
The following figure shows the geometry of the toroid with respect to the X-Y plane (the iso-surface is about 5% of peak value).