Topology of toroidal helical fields in non-circular cross-sectional tokamaks

The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade (HT-7U) when the equilibrium field with a monotonic $q$-profile is perturbed by a helical magnetic field. We find that a single mode ($m,n$) helical perturbation can cause the formation of islands on rational surfaces with $q=m/n$ and $q=(m\pm 1, \pm 2, \pm 3,\ldots) /n$ due to the toroidicity and plasma shape (i.e. elongation and triangularity), while there are many undestroyed magnetic surfaces called Kolmogorov--Arnold--Moser (KAM) barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field $\tilde {B}_r (r)$ and the toroidal magnetic field amplitude $B_{\phi 0} $ is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.