A study of nonlinear properties of tearing modes

The tool used for this study is a numerical code which treats the plasma as an incompressible fluid of low resistivity and which utilizes simplifying assumptions on geometry. For a given set of "almost ideal magnetohydrodynam ic (MHD) constraints" [T. H. Jensen, A. W. Leonard, R. J. La Haye, and M. S . Chu, Phys. Fluids B 3, 1650 (1991)], the code can find equilibria which s atisfy these constraints when boundary conditions and external currents are specified. Thus, given an initial MHD equilibrium (without an island), and thereby its constraints, the code can be used to find external currents ne eded for establishing an equilibrium with the same constraints and an islan d of specified width. The sign of these external currents determines whethe r the island would grow or shrink if the external currents were removed. Th us the code can provide information on nonlinear growth or decay, but not o n the time scales involved. The two main points of the paper are (i) that t he stability limit and saturated island width depend not only on the quanti ty Delta' [H. P. Furth, J. Killeen, and M. N. Rosenbluth, Phys. Fluids 6, 4 59 (1963)] but also on the constraints imposed, and (ii) that a current den sity gradient at the singular surface can drive a tearing mode nonlinearly to a certain island width followed by a decrease until the island vanishes. (C) 2001 American Institute of Physics.