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.
Submitted to: Physics of Plasmas
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