a1 Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712, U.S.A.
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.
(Received June 30 1993)
(Revised September 29 1993)