Nonlinear Asymmetric Tearing Mode Evolution in Cylindrical Geometry

Authors: Q. Teng, N. Ferraro, D.A. Gates, S.C. Jardin, R.B. White

Abstract: The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation i.e. the nonlinear
0(w). For low beta plasma without external heating,
0(w) can be approximately described by two terms,
0 ql(w),
0 A(w).1,2 In this work, we present a simple method to calculate the quasilinear stability index
0 ql rigoriously, for poloidal mode number m  2.  0 ql is derived by solving the outer equation through the Frobenious method.
0 ql is composed of four terms proportional to: constant
0 0, w, w lnw and w2.
0 A is proportional to the asymmetry of island which is roughly proportional to w. The sum of
0 ql and
0 A is consistent with the more accurate expression calculated perturbatively.3. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1.4 The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. It's also confirmed by the simulation that the
0 A has to be considered in calculating island saturation.

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