STABILITY OF TEARING MODES IN TOKAMAK PLASMAS

The stability properties of m greater-than-or-equal-to 2 tearing instabilities in tokamak plasmas are analyzed. A boundary layer theory is used to find asymptotic solutions to the ideal external kink equation, which are used to obtain a simple analytic expression for the tearing instability parameter DELTA'. This calculation generalizes previous work on this topic by considering more general toroidal equilibria (however, toroidal coupling effects are ignored.) Constructions of DELTA' are obtained for plasmas with finite beta and for islands that have nonzero width. A simple heuristic estimate is given for the value of the saturated island width when the instability criterion is violated. A connection is made between the calculation of the asymptotic matching parameter in the finite beta and island width case to the nonlinear analog of the Glasser effect [Phys. Fluids 18, 875 (1975)].