Toroidal effects on Island formation in a helically perturbed tokamak equilibrium

The characteristics of the ergodic magnetic field at the edge of a tokamak plasma produced by an additional helical field are described usuall in terms of the Fourier components of the perturbing field to lowest order in the aspect ratio $\epsilon$ [1]. Fieldline tracing calculations for the planned Dynamic Ergodic Divertor (DED) at TEXTOR-94 [2], which has an aspect ratio of $\epsilon$ = 0.25 lead to about 30 % smaller values for the island width and the related Chirikov parameter and to quite larger deviations in the neId line diffusion coefficient D$_{FL}$. This effect was found to have a significant dependence on the poloidal location of the perturbation coils.Starting from the expression for the island width in t.erms of the vector potential, given in [1], which is correct to any order in the aspect ratio, we derive an expression, which is in fulagreement with the numerical results. This is achieved by taking into account the full toroidal geometry when replacing the perturbation of the vector potential by the perturbation of the magnetic field