On Island Formation in a Locally Perturbed Tokamak Equilibrium

To control the plasma transport at the edge of a tokamak the outer flux surfaces can be artificially destroyed by applying a resonant helical magnetic field, as it is demonstrated at Pulsator [1],[2], [3], Tore Supra [4],[5] and proposed for TEXTOR‐94 [6] in the concept of “ergodic divertors”. As a measure of the efficiency of the perturbation field e.g. the level of the field line diffusion coefficient DFL the width Δ i of the magnetic islands and the related Chirikov parameter are of importance [7],[8],[9],[10]. For the planned Dynamic Ergodic Divertor (DED) at TEXTOR‐94 where the perturbation coils are located at the high field side the standard expression for Δ i using the Fourier components of the magnetic field perturbation [7] leads to results significantly different from field line tracing calculations [11]. The standard expression is commonly used in terms of the perturbation magnetic field δ B [5],[7],[8],[9],[12],[13]. But when replacing the Fourier components of the perturbation vector potential by those of the magnetic field finite aspect ratio effects have been neglected so far. For present tokamaks with ϵ = r / R ≃ 0.3 this can lead to an error in the field line diffusion of one to two orders of magnitude. In this paper it is shown that taking into account the finite aspect ratio at this point leads to correct results compared to the highly precise field line tracing calculations by the Gourdon code. The island width then is recognized to depend significantly on the poloidal position of the perturbation field. This is in contrast to the standard expression. Also the role of the choice of the magnetic coordinate system is considered.