Influence of toroidality on a magnetic configuration with a helical magnetic axis

The authors investigate analytically the changes which occur in a configuration with a helical magnetic axis upon bending to form a torus. Such a magnetic configuration can be created by various combinations of magnetic fields produced by helical conductors. In the calculations it is assumed that the pitch of the helical winding and the radius of the circular axis of the torus are significantly greater than the minor radius of the torus. This means that δ = b/R ≪ 1 and ε = ℓb/R ≪ 1, where b and R are, respectively, the minor and major radii of the torus and ℓ is the number of turns of the helical conductor around the torus. Toroidality is regarded as a perturbation superposed on the configuration with a helical magnetic axis. The authors consider the conditions under which the helical magnetic axis breaks down. The distance to which the resulting magnetic axes move away from the magnetic axis of the unperturbed configuration is indicated approximately.