ABSTRACT Rutherford's theory of the tearing instability is extended to cases where current nonlinearities are important, such as long-wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded.

A rigorous technique for selecting an optimal basic set of Gaussian-Laguerre eigenmodes is presented. This technique allows control of expansion truncation errors and preserves higher resolution in the electromagnetic field. Detailed algorithms are presented.

By modulating the small gas feed required to maintain a steady-state Tokamak discharge a small density perturbation may be induced from whose propagation particle transport parameters may be adduced. Experiments in TEXT show that the phenomena may be adequately described by a simple model with constant diffusion plus inward convection except near the density limit. Diffusion coefficients and convective velocities has been determined for a broad range of hydrogen discharges and found to scale approximately as (nq) -1 . The results are plausibly related to impurity transport parameters, thermal diffusivity, and particle confinement times. Diffusion coefficients for deuterium are systematically lower than for hydrogen.