The destruction of magnetic surfaces in tokamaks by current perturbations

Investigations of the feasibility of the hypothesis that the disruptive instability in tokamaks is caused by the break-up of magnetic surfaces are presented. The envisioned break-up is caused by the interaction of m = 2, n = 1 and m = 3, n = 1 helical perturbations or by the interaction of the m = 2, n = 1 perturbation and the m = 1, n = 0 toroidal field (with R/a = 5). Both numerical and analytic work has been done for two MHD-equilibrium current profiles: parabolic [q ∼ (1 – r2/2a2)−1] and the peaked model (q ∼ 1 + λr2/a2). For the parabolic profile, perturbation strengths of 1.5% are required to break up surfaces when m = 2 and m = 3 perturbations are present. When the m = 2 perturbation alone interacts with the toroidal field, perturbation strengths greater than 4% are required. For the peaked model with q(0) = 1.1, q(a) = 3.7, perturbation strengths of 0.5% were found to be sufficient to break the surfaces when both m = 2 and m = 3 perturbations are present, whereas strengths of 1.5% are required when only the m = 2 perturbation interacts with the toroidal field. These perturbation amplitudes are in reasonable agreement with experimental measurements. The peaked model allows break-up of surfaces for smaller perturbation strengths, primarily because of its greater shear. This dependence on shear permits speculation on a possible mechanism for the disruptive instability.