The coil shape is determined by requiring that the curvature of the flexible conductor be proportional to the distance from the toroidal axis. The resulting second order differential equation for the coil coordinates can be integrated once but for the second and final integration no closed form has been found and the integration has been done numerically. This solution of this differential equation is analytical in terms of an absolutely and uniformly convergent infinite series. The series converges quite rapidly and in practice ignoring all but the first five terms of the series introduces an error of less than 2 ...
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The coil shape is determined by requiring that the curvature of the flexible conductor be proportional to the distance from the toroidal axis. The resulting second order differential equation for the coil coordinates can be integrated once but for the second and final integration no closed form has been found and the integration has been done numerically. This solution of this differential equation is analytical in terms of an absolutely and uniformly convergent infinite series. The series converges quite rapidly and in practice ignoring all but the first five terms of the series introduces an error of less than 2 percent. (MOW)
Gralnick, S.L. & Tenney, F.H.Analytical solution of the toroidal constant tension solenoid,
article,
January 1, 1975;
New Jersey.
(digital.library.unt.edu/ark:/67531/metadc872120/:
accessed August 19, 2017),
University of North Texas Libraries, Digital Library, digital.library.unt.edu;
crediting UNT Libraries Government Documents Department.