Nonlinear asymmetric tearing mode evolution in cylindrical geometry
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 Δ'(w). For a low beta plasma without external heating, Δ'(w) can be approximately described by two terms, Δ'ql(w), Δ'A(w). In this work, we present a simple method to calculate the quasilinear stability index Δ'ql rigorously, for poloidal mode number m ≥ 2. Δ'ql is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ'0, w, wlnw, and w2. Δ'A is proportionalmore »