Asymptotic theory of the non-linearly saturated m=1 mode in tokamaks with q(0) < 1
The necessary and sufficient conditions required for the existence of a non-linearly saturated m = 1 tearing mode in tokamaks with q(0) < 1 are considered in cylindrical tokamak ordering using the asymptotic techniques developed in an earlier paper. The outer equations for the helical perturbation amplitude are solved exactly, in closed form for an arbitrary mean profile in leading order. This is shown to result in a "no disturbance" theorem: the m = 1 perturbation must be confined to within the radius r(i) such that q(r(i)) = 1. The bifurcation relation for the non-dimensional perturbation amplitude is then constructed by solving the non-linear inner critical layer equations using an ordered iterative technique. The considerations are also extended to non-monotonic profiles. When the conditions are met, a non-linearly saturated m = 1 tearing mode is shown to exist with a novel island structure, quite different from those obtained from the usual Delta' analysis, which is shown to be inappropriate to the present problem. The relevance of the results of the present theory to sawtooth phenomena reported in JET and other tokamaks is briefly discussed. The solution constitutes an analytically solved test case for numerical simulation codes to leading orders in a/R and the shear parameter.
Bibliographic Reference: Report: CLM-P887 EN (1990) 32 pp.
Availability: Available from the Librarian, UKAEA, Culham Laboratory, Abingdon, Oxon. OX14 3DB (GB)
Record Number: 199011117 / Last updated on: 1994-12-01
Original language: en
Available languages: en